https://nldlab.gatech.edu/w/index.php?title=Group_6&feed=atom&action=historyGroup 6 - Revision history2024-03-29T07:31:04ZRevision history for this page on the wikiMediaWiki 1.39.3https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1128&oldid=prevCjcrowley at 14:00, 12 January 20122012-01-12T14:00:51Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Media: Presentation.pdf | Presentation]]. '''Papers:''' [[Media: Schoenwald_Group6_Final.pdf | Kipp]], [[Media: Potter_Ferrofluids_-_Potter.pdf | Daniel]], [[Media: Hamid,_Amir_Ferrofluid_Group_6.pdf | Amir]]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluids typically exhibit a complex response to an applied external magnetic field. Here we have isolatated a small volume of ferrofluid material and observe the surface response of the fluid under the application of static and time varying magnetic fields. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluids typically exhibit a complex response to an applied external magnetic field. Here we have isolatated a small volume of ferrofluid material and observe the surface response of the fluid under the application of static and time varying magnetic fields. </div></td></tr>
</table>Cjcrowleyhttps://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1069&oldid=prevCjcrowley at 16:18, 11 January 20122012-01-11T16:18:20Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Ferrofluids typically exhibit a complex response to an applied external magnetic field. Here we have isolatated a small volume of ferrofluid material and observe the surface response of the fluid under the application of static and time varying magnetic fields. </ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
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</table>Cjcrowleyhttps://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1060&oldid=prevCjcrowley at 16:03, 11 January 20122012-01-11T16:03:36Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''' Nonlinear Dynamical Response of Ferrofluid to Magnetic Field '''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''' Nonlinear Dynamical Response of Ferrofluid to Magnetic Field '''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">ABSTRACT</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">Abstract</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluids exhibit an interesting and profound nonlinear dynamical behavior in response to both static and oscillating external magnetic fields. In the present paper, we begin by discussing recent works in the field of qualitatively describing the behavior of ferrofluids. We then proceed to examine a classical model used in several, more recent, studies, pointing out the critical kinematic parameters that may need incorporation into the model. An experiment was conducted to examine such a response and observe some of the interesting behaviors. The apparatus was configured such that a single peak was induced and observed with a high-speed camera. These experiments have shown the existence of both Rosensweig instability and viscous damping. Furthermore, experiments employing time dependent magnetic fields make a case for the significance of the gravitational and inertial forces on the ferrofluid.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluids exhibit an interesting and profound nonlinear dynamical behavior in response to both static and oscillating external magnetic fields. In the present paper, we begin by discussing recent works in the field of qualitatively describing the behavior of ferrofluids. We then proceed to examine a classical model used in several, more recent, studies, pointing out the critical kinematic parameters that may need incorporation into the model. An experiment was conducted to examine such a response and observe some of the interesting behaviors. The apparatus was configured such that a single peak was induced and observed with a high-speed camera. These experiments have shown the existence of both Rosensweig instability and viscous damping. Furthermore, experiments employing time dependent magnetic fields make a case for the significance of the gravitational and inertial forces on the ferrofluid.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">INTRODUCTION</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">Introduction</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluid is a colloidal fluid mixture of oil and ferromagnetic nanoparticles (~10nm) that react paramagnetically to a uniform magnetic field [1]. The fluid becomes magnetized in the presence of a magnetic field and un-magnetized when removed. The particles are coated with a layer of chemically absorbed surfactants to avoid agglomeration [2]. In deriving peaks, there are two important fluid properties: low viscosity and high magnetic permeability. Because these properties are inversely related, it is thus necessary to find a balance between the two. The fluid is known to exhibit an instability condition in which fluid peaks (bullet head like structures) spontaneously appear at the fluid-air interface. This is known as Rosensweig instability. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ferrofluid is a colloidal fluid mixture of oil and ferromagnetic nanoparticles (~10nm) that react paramagnetically to a uniform magnetic field [1]. The fluid becomes magnetized in the presence of a magnetic field and un-magnetized when removed. The particles are coated with a layer of chemically absorbed surfactants to avoid agglomeration [2]. In deriving peaks, there are two important fluid properties: low viscosity and high magnetic permeability. Because these properties are inversely related, it is thus necessary to find a balance between the two. The fluid is known to exhibit an instability condition in which fluid peaks (bullet head like structures) spontaneously appear at the fluid-air interface. This is known as Rosensweig instability. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Though ferrofluids are commonly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied. Interaction between the fluid and a magnetic fields have elicited many interesting phenomena such as new or modified instabilities [3], field dependent viscosities [4], new dissipation mechanisms [5], and viscoelastic effects [6, 7]. Works have sought to describe the fluid response with models based on bifurcation characteristics [8], minimization of thermodynamic potential [6], and approximation by a half-ellipsoid [2]. In 1998, Rehberg et al. documented the nonlinear dynamics of a Ferrofluid–peak [8]. By temporal modulation of an electromagnetic field, Rosensweig instability was observed and fitted to a proposed model. Three characteristically different periods of the peak formation were identified. Rehberg later showed the restoring forces and damping coefficients of various surface waves are changed in response to a static magnetic field [9]. Engel et al. then analytically described both the static and dynamic surface profile [2, 10]. In 2004, Rannacher et al. discovered a double Rosensweig instability of a Ferrofluid film sandwiched between two immiscible nonmagnetic fluids. More recently, Oliveira et al examined the linear stability and nonlinear dynamics of a ferrofluid droplet within an external radial magnetic field [11]. Motivated by such an interesting array of effects we make a case for maturing the classical model by implementing a series of experiments in an attempt to isolate the effects of inertial and gravitational forces on the fluid.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Though ferrofluids are commonly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied. Interaction between the fluid and a magnetic fields have elicited many interesting phenomena such as new or modified instabilities [3], field dependent viscosities [4], new dissipation mechanisms [5], and viscoelastic effects [6, 7]. Works have sought to describe the fluid response with models based on bifurcation characteristics [8], minimization of thermodynamic potential [6], and approximation by a half-ellipsoid [2]. In 1998, Rehberg et al. documented the nonlinear dynamics of a Ferrofluid–peak [8]. By temporal modulation of an electromagnetic field, Rosensweig instability was observed and fitted to a proposed model. Three characteristically different periods of the peak formation were identified. Rehberg later showed the restoring forces and damping coefficients of various surface waves are changed in response to a static magnetic field [9]. Engel et al. then analytically described both the static and dynamic surface profile [2, 10]. In 2004, Rannacher et al. discovered a double Rosensweig instability of a Ferrofluid film sandwiched between two immiscible nonmagnetic fluids. More recently, Oliveira et al examined the linear stability and nonlinear dynamics of a ferrofluid droplet within an external radial magnetic field [11]. Motivated by such an interesting array of effects we make a case for maturing the classical model by implementing a series of experiments in an attempt to isolate the effects of inertial and gravitational forces on the fluid.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Magnetoviscocity, on the other hand, takes in to account the time dependent process of pulling apart agglomerations and chains of larger particles (>10nm) [13]. Both mechanisms may act concurrently, yet the magnitude to which they affect the damping depends both on the particle size and concentration of that particle. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Magnetoviscocity, on the other hand, takes in to account the time dependent process of pulling apart agglomerations and chains of larger particles (>10nm) [13]. Both mechanisms may act concurrently, yet the magnitude to which they affect the damping depends both on the particle size and concentration of that particle. </div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">EXPERIMENTAL SETUP</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">Experimental Setup</ins>=</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The experimental setup is shown in Figure 2. A 2.33mm diameter and 12 mm deep well was drilled into a Teflon bar. The diameter was chosen to be less than the critical wavelength, in order to assure a single peak would emerge. The critical wavelength being \({ \lambda }_{ C }=2\pi \sqrt { \sigma / \rho g } =8.3mm\) , where \(\rho =1.21\cdot { 10 }^{ 3 }\frac { ㎏ }{ { m }^{ 3 } }\) is the fluid density, \(\sigma =2.05\cdot { 10 }^{ -2 }\frac { ㎏ }{ { s }^{ 2 } }\) is the surface tension, and g is gravity. Stock EFH-1 ferrofluid was dispensed into the well using a syringe. The Bar was then placed into a sand filled bowl to allow for fine positioning relative to the electromagnet (unknown make and model). The electromagnet was centered directly over the ferrolfluid at an offset distance of ~7mm to allow for a ferrofluid peak of several mm to arise without being too close to the magnet such that fluid bridging occurs, or too far from the magnet such that the magnetic field strength is too low. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The experimental setup is shown in Figure 2. A 2.33mm diameter and 12 mm deep well was drilled into a Teflon bar. The diameter was chosen to be less than the critical wavelength, in order to assure a single peak would emerge. The critical wavelength being \({ \lambda }_{ C }=2\pi \sqrt { \sigma / \rho g } =8.3mm\) , where \(\rho =1.21\cdot { 10 }^{ 3 }\frac { ㎏ }{ { m }^{ 3 } }\) is the fluid density, \(\sigma =2.05\cdot { 10 }^{ -2 }\frac { ㎏ }{ { s }^{ 2 } }\) is the surface tension, and g is gravity. Stock EFH-1 ferrofluid was dispensed into the well using a syringe. The Bar was then placed into a sand filled bowl to allow for fine positioning relative to the electromagnet (unknown make and model). The electromagnet was centered directly over the ferrolfluid at an offset distance of ~7mm to allow for a ferrofluid peak of several mm to arise without being too close to the magnet such that fluid bridging occurs, or too far from the magnet such that the magnetic field strength is too low. </div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">METHODS AND RESULTS</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">Methods and Results</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ferrofluid response was analyzed for both the static field case (DC, unmodulated)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ferrofluid response was analyzed for both the static field case (DC, unmodulated)</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In comparison with the highest driving frequency within this study, fD = 10Hz, the downward portion of the period lasts exactly TD/4 = 1/(4fD) = 25ms. The time for the peak to decay naturally (decay time) is thus approximately 25% of the highest driving frequency implemented, 10Hz. Equivalently, the decay time is 0.2% of the slowest driving frequency implemented, 0.1Hz. It is reasoned that the gravitational effect on the hysteresis should be significant in the high frequency domain and insignificant in the low frequency domain, making it another point of interest in the efforts to elaborate on the constitutive model. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In comparison with the highest driving frequency within this study, fD = 10Hz, the downward portion of the period lasts exactly TD/4 = 1/(4fD) = 25ms. The time for the peak to decay naturally (decay time) is thus approximately 25% of the highest driving frequency implemented, 10Hz. Equivalently, the decay time is 0.2% of the slowest driving frequency implemented, 0.1Hz. It is reasoned that the gravitational effect on the hysteresis should be significant in the high frequency domain and insignificant in the low frequency domain, making it another point of interest in the efforts to elaborate on the constitutive model. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">CONCLUSION</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">Conclusion</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the efforts to qualitatively describe the dynamics of ferrofluids, other works either utilize the classical model (through minimization of potential) or generalize the tip dynamics geometrically rather than kinematically. It is thus useful to develop the model further. These experiments have shown, first, the existence of the Rosensweig instability does occur for the experimental setup in which there is a nonuniform magnetic field. The static field analysis helped to identify a minimal model to describe the phenomena. In the dynamic case, modulation of both the amplitude and frequency to maintain a maximum peak height indicated both the existence of magnetically induced viscous damping as well as the relevance of the viscous damping term within the model. In a separate experiment, modulation of the amplitude only has shown that the viscous damping parameter cannot alone accurately describe the dynamics of the system. Furthermore, experiments showed high sensitivity to offset modulation. At a relatively high frequency of 7Hz, the system produces higher period states implying inertia plays a greater role and a possible point for improvement of the model. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the efforts to qualitatively describe the dynamics of ferrofluids, other works either utilize the classical model (through minimization of potential) or generalize the tip dynamics geometrically rather than kinematically. It is thus useful to develop the model further. These experiments have shown, first, the existence of the Rosensweig instability does occur for the experimental setup in which there is a nonuniform magnetic field. The static field analysis helped to identify a minimal model to describe the phenomena. In the dynamic case, modulation of both the amplitude and frequency to maintain a maximum peak height indicated both the existence of magnetically induced viscous damping as well as the relevance of the viscous damping term within the model. In a separate experiment, modulation of the amplitude only has shown that the viscous damping parameter cannot alone accurately describe the dynamics of the system. Furthermore, experiments showed high sensitivity to offset modulation. At a relatively high frequency of 7Hz, the system produces higher period states implying inertia plays a greater role and a possible point for improvement of the model. </div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">REFERENCES</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">References</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[1] R. E. Rosensweig, Ferrohydrodynamics: Cambridge University Press, 1985.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[1] R. E. Rosensweig, Ferrohydrodynamics: Cambridge University Press, 1985.</div></td></tr>
</table>Cjcrowleyhttps://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1014&oldid=prevCjcrowley: Protected "Group 6" ([edit=sysop] (indefinite) [move=sysop] (indefinite))2012-01-09T16:52:01Z<p>Protected "<a href="/w/index.php?title=Group_6" title="Group 6">Group 6</a>" ([edit=sysop] (indefinite) [move=sysop] (indefinite))</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:52, 9 January 2012</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>Cjcrowleyhttps://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1007&oldid=prevGroup6 at 17:37, 19 December 20112011-12-19T17:37:57Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Kipp Schoenwald, Daniel Potter, Amin Agha, Amir Hamid</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[https://docs.google.com/presentation/d/192q0Nqefl5Y3D0O-L36NNjOpDLaOdKnume6-7dghois/edit Link To Presentation Slides]</ins></div></td></tr>
</table>Group6https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1006&oldid=prevGroup6: /* Necessity for Additional System Parameters in Classical Model Evidenced by Amplitude Modulation */2011-12-17T17:24:13Z<p><span dir="auto"><span class="autocomment">Necessity for Additional System Parameters in Classical Model Evidenced by Amplitude Modulation</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:24, 17 December 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The model of the system has only a single system parameter, \(\beta\). Once a qualitative agreement is found by iterating the parameter \(\beta\), such as in Figure 11 (a), it is reasonable to say that merely increasing the amplitude, \(\Delta H\), within the numerical model should maintain a qualitative resemblance to the experimental data as the drive amplitude is increased. On the contrary, the qualitative resemblance of Figure 11 (b) was obtained by also iterating the other drive parameters such as offset and frequency. This indicates that the damping coefficient, alone, poorly describes the dynamic behavior of the system. While the viscous damping was shown to be significant in the previous section, additional parameters <del style="font-weight: bold; text-decoration: none;">and </del>are clearly needed.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The model of the system has only a single system parameter, \(\beta\). Once a qualitative agreement is found by iterating the parameter \(\beta\), such as in Figure 11 (a), it is reasonable to say that merely increasing the amplitude, \(\Delta H\), within the numerical model should maintain a qualitative resemblance to the experimental data as the drive amplitude is increased. On the contrary, the qualitative resemblance of Figure 11 (b) was obtained by also iterating the other drive parameters such as offset and frequency. This indicates that the damping coefficient, alone, poorly describes the dynamic behavior of the system. While the viscous damping was shown to be significant in the previous section, additional parameters are clearly needed.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Significance of Inertial Forces as Evidenced by Offset Modulation==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Significance of Inertial Forces as Evidenced by Offset Modulation==</div></td></tr>
</table>Group6https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1005&oldid=prevGroup6: /* Expanding on Classical Model by Dynamic Field Analysis */2011-12-17T16:59:58Z<p><span dir="auto"><span class="autocomment">Expanding on Classical Model by Dynamic Field Analysis</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:59, 17 December 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Expanding on Classical Model by Dynamic Field Analysis==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Expanding on Classical Model by Dynamic Field Analysis==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://www.youtube.com/watch?feature=player_embedded&v=7hcd54_6lDs <del style="font-weight: bold; text-decoration: none;">WATCH THE </del>VIDEO]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://www.youtube.com/watch?feature=player_embedded&v=7hcd54_6lDs VIDEO<ins style="font-weight: bold; text-decoration: none;">: PEAK MOTION</ins>]</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Here, the dark region above is the magnet, while the dark region below is the teflon vessel that holds the fluid.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[http://www.youtube.com/watch?v=YIClG7tpOXk&context=C3219f22ADOEgsToPDskIEgyC06j8r0nBWusVu92Ge VIDEO: PEAK HEIGHT ANALYSIS]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Here, the fluid was excited using a triangle wave that linearly ramps up and then down. The peak is played at 30 frames/second after recording at 1000 frames/second. MatLab was used to follow the peak height. Oddly, on the way up the peak slows momentarily, and on the way down, despite a purely descending magnetic field, the fluid rises at one point before going completely to rest.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the dynamic field study, the magnetic field was modulated. The stability, likewise to the static field case, is determined by the Jacobian. The classification, however, depends on the modulated parameters and </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the dynamic field study, the magnetic field was modulated. The stability, likewise to the static field case, is determined by the Jacobian. The classification, however, depends on the modulated parameters and </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\(\beta\). <del style="font-weight: bold; text-decoration: none;"> </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\(\beta\).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Existence of Viscous Damping Evidenced by Amplitude and Frequency Modulation==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Existence of Viscous Damping Evidenced by Amplitude and Frequency Modulation==</div></td></tr>
</table>Group6https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1004&oldid=prevGroup6 at 01:51, 17 December 20112011-12-17T01:51:39Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Expanding on Classical Model by Dynamic Field Analysis==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Expanding on Classical Model by Dynamic Field Analysis==</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[http://www.youtube.com/watch?feature=player_embedded&v=7hcd54_6lDs WATCH THE VIDEO]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the dynamic field study, the magnetic field was modulated. The stability, likewise to the static field case, is determined by the Jacobian. The classification, however, depends on the modulated parameters and </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the dynamic field study, the magnetic field was modulated. The stability, likewise to the static field case, is determined by the Jacobian. The classification, however, depends on the modulated parameters and </div></td></tr>
</table>Group6https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1003&oldid=prevGroup6 at 01:39, 17 December 20112011-12-17T01:39:22Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:39, 16 December 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Magnetoviscocity, on the other hand, takes in to account the time dependent process of pulling apart agglomerations and chains of larger particles (>10nm) [13]. Both mechanisms may act concurrently, yet the magnitude to which they affect the damping depends both on the particle size and concentration of that particle. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Magnetoviscocity, on the other hand, takes in to account the time dependent process of pulling apart agglomerations and chains of larger particles (>10nm) [13]. Both mechanisms may act concurrently, yet the magnitude to which they affect the damping depends both on the particle size and concentration of that particle. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=<del style="font-weight: bold; text-decoration: none;">Experimental Setup</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">EXPERIMENTAL SETUP</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The experimental setup is shown in Figure 2. A 2.33mm diameter and 12 mm deep well was drilled into a Teflon bar. The diameter was chosen to be less than the critical wavelength, in order to assure a single peak would emerge. The critical wavelength being \({ \lambda }_{ C }=2\pi \sqrt { \sigma / \rho g } =8.3mm\) , where \(\rho =1.21\cdot { 10 }^{ 3 }\frac { ㎏ }{ { m }^{ 3 } }\) is the fluid density, \(\sigma =2.05\cdot { 10 }^{ -2 }\frac { ㎏ }{ { s }^{ 2 } }\) is the surface tension, and g is gravity. Stock EFH-1 ferrofluid was dispensed into the well using a syringe. The Bar was then placed into a sand filled bowl to allow for fine positioning relative to the electromagnet (unknown make and model). The electromagnet was centered directly over the ferrolfluid at an offset distance of ~7mm to allow for a ferrofluid peak of several mm to arise without being too close to the magnet such that fluid bridging occurs, or too far from the magnet such that the magnetic field strength is too low. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The experimental setup is shown in Figure 2. A 2.33mm diameter and 12 mm deep well was drilled into a Teflon bar. The diameter was chosen to be less than the critical wavelength, in order to assure a single peak would emerge. The critical wavelength being \({ \lambda }_{ C }=2\pi \sqrt { \sigma / \rho g } =8.3mm\) , where \(\rho =1.21\cdot { 10 }^{ 3 }\frac { ㎏ }{ { m }^{ 3 } }\) is the fluid density, \(\sigma =2.05\cdot { 10 }^{ -2 }\frac { ㎏ }{ { s }^{ 2 } }\) is the surface tension, and g is gravity. Stock EFH-1 ferrofluid was dispensed into the well using a syringe. The Bar was then placed into a sand filled bowl to allow for fine positioning relative to the electromagnet (unknown make and model). The electromagnet was centered directly over the ferrolfluid at an offset distance of ~7mm to allow for a ferrofluid peak of several mm to arise without being too close to the magnet such that fluid bridging occurs, or too far from the magnet such that the magnetic field strength is too low. </div></td></tr>
</table>Group6https://nldlab.gatech.edu/w/index.php?title=Group_6&diff=1002&oldid=prevGroup6 at 01:38, 17 December 20112011-12-17T01:38:54Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Though ferrofluids are commonly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied. Interaction between the fluid and a magnetic fields have elicited many interesting phenomena such as new or modified instabilities [3], field dependent viscosities [4], new dissipation mechanisms [5], and viscoelastic effects [6, 7]. Works have sought to describe the fluid response with models based on bifurcation characteristics [8], minimization of thermodynamic potential [6], and approximation by a half-ellipsoid [2]. In 1998, Rehberg et al. documented the nonlinear dynamics of a Ferrofluid–peak [8]. By temporal modulation of an electromagnetic field, Rosensweig instability was observed and fitted to a proposed model. Three characteristically different periods of the peak formation were identified. Rehberg later showed the restoring forces and damping coefficients of various surface waves are changed in response to a static magnetic field [9]. Engel et al. then analytically described both the static and dynamic surface profile [2, 10]. In 2004, Rannacher et al. discovered a double Rosensweig instability of a Ferrofluid film sandwiched between two immiscible nonmagnetic fluids. More recently, Oliveira et al examined the linear stability and nonlinear dynamics of a ferrofluid droplet within an external radial magnetic field [11]. Motivated by such an interesting array of effects we make a case for maturing the classical model by implementing a series of experiments in an attempt to isolate the effects of inertial and gravitational forces on the fluid.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Though ferrofluids are commonly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied. Interaction between the fluid and a magnetic fields have elicited many interesting phenomena such as new or modified instabilities [3], field dependent viscosities [4], new dissipation mechanisms [5], and viscoelastic effects [6, 7]. Works have sought to describe the fluid response with models based on bifurcation characteristics [8], minimization of thermodynamic potential [6], and approximation by a half-ellipsoid [2]. In 1998, Rehberg et al. documented the nonlinear dynamics of a Ferrofluid–peak [8]. By temporal modulation of an electromagnetic field, Rosensweig instability was observed and fitted to a proposed model. Three characteristically different periods of the peak formation were identified. Rehberg later showed the restoring forces and damping coefficients of various surface waves are changed in response to a static magnetic field [9]. Engel et al. then analytically described both the static and dynamic surface profile [2, 10]. In 2004, Rannacher et al. discovered a double Rosensweig instability of a Ferrofluid film sandwiched between two immiscible nonmagnetic fluids. More recently, Oliveira et al examined the linear stability and nonlinear dynamics of a ferrofluid droplet within an external radial magnetic field [11]. Motivated by such an interesting array of effects we make a case for maturing the classical model by implementing a series of experiments in an attempt to isolate the effects of inertial and gravitational forces on the fluid.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=Viscous Damping Effects of Ferrofluids=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=</ins>=Viscous Damping Effects of Ferrofluids<ins style="font-weight: bold; text-decoration: none;">=</ins>=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are two known damping mechanisms unique to ferrofluids, rolling viscosity and magnetoviscocity. Rolling viscosity was first identified [12]. This mechanism takes into account the affect of beads rolling within the fluid as the name suggests. A ferrofluid, in the absence of a magnetic field, acts as any other colloid mixture; when there is fluid flow, shear within the fluid develops and beads begin to role as they are spun by the mechanical torque from the fluid shearing (vorticity of the fluid, v) (Figure 1, left). Under the influence of a magnetic field, however, magnetic particles are forced to align with the magnetic field. In other words, the magnetic moment of the bead, m, is parallel to the magnetic field, H (Figure 1, right). The rotation of the particle is now limited to spinning about its magnetic moment axis. Consider now the specific case in which the magnetic field is perpendicular to the vorticity; the particles will resist the rolling. This is analogous to dragging a car sideways; the wheels are locked on an axis that is perpendicular to the direction the wheels are trying to roll.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are two known damping mechanisms unique to ferrofluids, rolling viscosity and magnetoviscocity. Rolling viscosity was first identified [12]. This mechanism takes into account the affect of beads rolling within the fluid as the name suggests. A ferrofluid, in the absence of a magnetic field, acts as any other colloid mixture; when there is fluid flow, shear within the fluid develops and beads begin to role as they are spun by the mechanical torque from the fluid shearing (vorticity of the fluid, v) (Figure 1, left). Under the influence of a magnetic field, however, magnetic particles are forced to align with the magnetic field. In other words, the magnetic moment of the bead, m, is parallel to the magnetic field, H (Figure 1, right). The rotation of the particle is now limited to spinning about its magnetic moment axis. Consider now the specific case in which the magnetic field is perpendicular to the vorticity; the particles will resist the rolling. This is analogous to dragging a car sideways; the wheels are locked on an axis that is perpendicular to the direction the wheels are trying to roll.</div></td></tr>
</table>Group6