Group 1 2014 - Revision history

Chiral2014 at 20:25, 12 December 2014

2014-12-12T20:25:15Z

← Older revision		Revision as of 16:25, 12 December 2014
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	* [[Media: Chiral_whitepaper.pdf \| Whitepaper]]		* [[Media: Chiral_whitepaper.pdf \| Whitepaper]]
	* [[Media: Chiral_presentation.pdf \| Project presentation slides]]		* [[Media: Chiral_presentation.pdf \| Project presentation slides]]
	* [[Media: ~~Chiral_whitepaper~~.~~pdf~~ \| Paper ~~(not uploaded yet)~~]]		* [[Media: Separation-chiral-particles.pdf‎ \| Paper]]

	This is the website for the Chiral group. As a project for our Nonlinear Dynamics and Chaos class at Georgia Tech, we are investigating a method for the mechanical separation of chiral particles. The project is finished as far as this course concerns, but it will most likely result in more research and a more comprehensive paper. At the moment you can view our presentation material, whitepaper, actual paper, data, pictures and videos of our setup at this website.		This is the website for the Chiral group. As a project for our Nonlinear Dynamics and Chaos class at Georgia Tech, we are investigating a method for the mechanical separation of chiral particles. The project is finished as far as this course concerns, but it will most likely result in more research and a more comprehensive paper. At the moment you can view our presentation material, whitepaper, actual paper, data, pictures and videos of our setup at this website.

Chiral2014 at 19:24, 12 December 2014

2014-12-12T19:24:26Z

Chiral2014 at 19:12, 12 December 2014

2014-12-12T19:12:38Z

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 == Figures ==
 {|style="margin: 0 auto;"
 | [[File:CW_angle.png | thumb | 300px | Figure 5: The alignment of one right handed and one left handed particle over time, 1.88 rev/s]]
 | [[File:Cw_angle2.png | thumb | 300px | Figure 6: The alignment of one right handed and one left handed particle over time, 0.578 rev/s]]
 |}
 {|style="margin: 0 auto;"
 | [[File: Plot1.png | thumb | 300px | Figure 8: The average positions of ten particles of each hand- edness versus time. Data is shown for one clockwise (CW) and one counter-clockwise (CCW) experiment.]]
 | [[File: Plot2.png | thumb | 300px | Figure 9: lot of velocity versus time generated from the time derivitive of the couter-clockwise position vs. time data ]]
 |}

Chiral2014 at 19:09, 12 December 2014

2014-12-12T19:09:09Z

← Older revision		Revision as of 15:09, 12 December 2014
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	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	\| [[File:CW_angle.png \| thumb \| 300px \| Figure 5: ]]		\| [[File:CW_angle.png \| thumb \| 300px \| Figure 5: The alignment of one right handed and one left handed particle over time, 1.88 rev/s]]
	\| [[File:Cw_angle2.png \| thumb \| 300px \| Figure 6: ]]		\| [[File:Cw_angle2.png \| thumb \| 300px \| Figure 6: The alignment of one right handed and one left handed particle over time, 0.578 rev/s]]
	\| [[File: Linefit.png \| thumb \| 300px \| Figure 7: ]]		\| [[File: Linefit.png \| thumb \| 300px \| Figure 7: Example of a linear function fit to the first data points, rsquare = 0.7929]]
	\|}		\|}
	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	\| [[File: Plot1.png \| thumb \| 300px \| Figure 8: ]]		\| [[File: Plot1.png \| thumb \| 300px \| Figure 8: The average positions of ten particles of each hand- edness versus time. Data is shown for one clockwise (CW) and one counter-clockwise (CCW) experiment.]]
	\| [[File: Plot2.png \| thumb \| 300px \| Figure 9: ]]		\| [[File: Plot2.png \| thumb \| 300px \| Figure 9: lot of velocity versus time generated from the time derivitive of the couter-clockwise position vs. time data ]]
	\|}		\|}

Chiral2014 at 19:05, 12 December 2014

2014-12-12T19:05:07Z

← Older revision		Revision as of 15:05, 12 December 2014
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	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	\| [[File:CW_angle.png \| thumb \| 300px \| ~~Caption~~]]		\| [[File:CW_angle.png \| thumb \| 300px \| Figure 5: ]]
	\| [[File:Cw_angle2.png \| thumb \| 300px \| ~~Caption~~]]		\| [[File:Cw_angle2.png \| thumb \| 300px \| Figure 6: ]]
	\| [[File: Linefit.png \| thumb \| 300px \| ~~Caption~~]]		\| [[File: Linefit.png \| thumb \| 300px \| Figure 7: ]]
	\|}		\|}
	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	\| [[File: Plot1.png \| thumb \| 300px \| ~~Caption~~]]		\| [[File: Plot1.png \| thumb \| 300px \| Figure 8: ]]
	\| [[File: Plot2.png \| thumb \| 300px \| ~~Caption~~]]		\| [[File: Plot2.png \| thumb \| 300px \| Figure 9: ]]
	\|}		\|}

Chiral2014 at 18:46, 12 December 2014

2014-12-12T18:46:39Z

← Older revision		Revision as of 14:46, 12 December 2014
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	== Figures ==		== Figures ==
	~~{\|style="margin: 0 auto;"~~
	<videoflash>20H0hCYn1e0</videoflash>		<videoflash>20H0hCYn1e0</videoflash>
	<videoflash>ucM8Mz2ncuE</videoflash>		<videoflash>ucM8Mz2ncuE</videoflash>
	<videoflash>jmCkyvK_RlQ</videoflash>		<videoflash>jmCkyvK_RlQ</videoflash>

			{\|style="margin: 0 auto;"
	\| [[File:CW_angle.png \| thumb \| 300px \| Caption]]		\| [[File:CW_angle.png \| thumb \| 300px \| Caption]]
			\| [[File:Cw_angle2.png \| thumb \| 300px \| Caption]]
			\| [[File: Linefit.png \| thumb \| 300px \| Caption]]
	\|}		\|}
	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	~~\| [[File:Cw_angle2.png \| thumb \| 300px \| Caption]]~~
	~~\| [[File: Linefit.png \| thumb \| 300px \| Caption]]~~
	\| [[File: Plot1.png \| thumb \| 300px \| Caption]]		\| [[File: Plot1.png \| thumb \| 300px \| Caption]]
	\| [[File: Plot2.png \| thumb \| 300px \| Caption]]		\| [[File: Plot2.png \| thumb \| 300px \| Caption]]
	\|}		\|}

Chiral2014 at 18:43, 12 December 2014

2014-12-12T18:43:06Z

← Older revision		Revision as of 14:43, 12 December 2014
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	== Figures ==		== Figures ==
			{\|style="margin: 0 auto;"
	<videoflash>20H0hCYn1e0</videoflash>		<videoflash>20H0hCYn1e0</videoflash>
	<videoflash>ucM8Mz2ncuE</videoflash>		<videoflash>ucM8Mz2ncuE</videoflash>
	<videoflash>jmCkyvK_RlQ</videoflash>		<videoflash>jmCkyvK_RlQ</videoflash>
			\| [[File:CW_angle.png \| thumb \| 300px \| Caption]]
			\|}
	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	~~\| [[File:CW_angle.png \| thumb \| 300px \| Caption]]~~
	\| [[File:Cw_angle2.png \| thumb \| 300px \| Caption]]		\| [[File:Cw_angle2.png \| thumb \| 300px \| Caption]]
	\| [[File: Linefit.png \| thumb \| 300px \| Caption]]		\| [[File: Linefit.png \| thumb \| 300px \| Caption]]

Chiral2014 at 18:42, 12 December 2014

2014-12-12T18:42:35Z

← Older revision		Revision as of 14:42, 12 December 2014
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	<videoflash>ucM8Mz2ncuE</videoflash>		<videoflash>ucM8Mz2ncuE</videoflash>
	<videoflash>jmCkyvK_RlQ</videoflash>		<videoflash>jmCkyvK_RlQ</videoflash>
	[[File:CW_angle.png \| thumb \| 300px \| Caption]]		{\|style="margin: 0 auto;"
	[[File:Cw_angle2.png \| thumb \| 300px \| Caption]]		\| [[File:CW_angle.png \| thumb \| 300px \| Caption]]
	[[File: Linefit.png \| thumb \| 300px \| Caption]]		\| [[File:Cw_angle2.png \| thumb \| 300px \| Caption]]
	[[File: Plot1.png \| thumb \| 300px \| Caption]]		\| [[File: Linefit.png \| thumb \| 300px \| Caption]]
	[[File: Plot2.png \| thumb \| 300px \| Caption]]		\| [[File: Plot1.png \| thumb \| 300px \| Caption]]
			\| [[File: Plot2.png \| thumb \| 300px \| Caption]]
			\|}

Chiral2014 at 18:39, 12 December 2014

2014-12-12T18:39:23Z

← Older revision		Revision as of 14:39, 12 December 2014
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	<videoflash>ucM8Mz2ncuE</videoflash>		<videoflash>ucM8Mz2ncuE</videoflash>
	<videoflash>jmCkyvK_RlQ</videoflash>		<videoflash>jmCkyvK_RlQ</videoflash>
	~~[[File:TC-device.jpg \| thumb \| 300px \| Figure 1: Sketch of a Taylor-Couette Device (courtesy of IOP Science)]]~~
	[[File:CW_angle.png \| thumb \| 300px \| Caption]]		[[File:CW_angle.png \| thumb \| 300px \| Caption]]
	[[File:Cw_angle2.png \| thumb \| 300px \| Caption]]		[[File:Cw_angle2.png \| thumb \| 300px \| Caption]]
			[[File: Linefit.png \| thumb \| 300px \| Caption]]
			[[File: Plot1.png \| thumb \| 300px \| Caption]]
			[[File: Plot2.png \| thumb \| 300px \| Caption]]

Chiral2014 at 18:29, 12 December 2014

2014-12-12T18:29:19Z

← Older revision		Revision as of 14:29, 12 December 2014
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	== Theory ==		== Theory ==
			[[File:Shear.png \| thumb \| 300px \| Figure 1: Force gradient viewed from above.]]
	We consider a sheer flow, <math>\mathbf{v}(x,y,z) = \dot{\gamma}y\hat{x}</math>. Here, <math>\mathbf{v}</math> is the fluid velocity, <math>\dot{\gamma}</math> is the shear rate, and <math>\hat{x}</math> is the direction of shear flow, in this case a unit vector in the <math>x</math> direction. <math>y</math> represents a linear gradient of force in the <math>\hat{y}</math> direction (see Figure tk). We then consider a particle inserted into this flow:		We consider a sheer flow, <math>\mathbf{v}(x,y,z) = \dot{\gamma}y\hat{x}</math>. Here, <math>\mathbf{v}</math> is the fluid velocity, <math>\dot{\gamma}</math> is the shear rate, and <math>\hat{x}</math> is the direction of shear flow, in this case a unit vector in the <math>x</math> direction. <math>y</math> represents a linear gradient of force in the <math>\hat{y}</math> direction (see Figure tk). We then consider a particle inserted into this flow:

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	<math>\left<V(z)\right> = \chi ga\dot{\gamma}</math>		<math>\left<V(z)\right> = \chi ga\dot{\gamma}</math>

	Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's chiraltiy, <math>g</math> is a constant based on particle geometry, and ~~<math>~~a~~</math>~~ is the particle size. We see that this is simply a reduction of the second equation to one dimension.		Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's chiraltiy, <math>g</math> is a constant based on particle geometry, and a is the particle size. We see that this is simply a reduction of the second equation to one dimension.

	== Method ==		== Method ==
	To reach our goals for this experiment, we needed a highly viscous fluid in shear flow and, contained in the fluid, particles with of opposing chirality.		To reach our goals for this experiment, we needed a highly viscous fluid in shear flow and, contained in the fluid, particles with of opposing chirality.

			[[File:Particle.png \| thumb \| 300px \| Figure 2: Model of the left hand chiral particle used in this experiment.]]

	A Taylor-Couette device was the centerpiece of our experiment. The device coscisted of a bottom part, a top part, a transparent PVC tube and a rotating dowel. All parts except for the tube were printed on an ordinary 3-D printer (Makerbot Replicator). The distance between the outer tube and the inner dowel gives just enough clearance to let the particles align themselves freely. A larger distance (used in our first iteration) doesn't generate enough shear for the separation effect to be visible. The effect we are demonstrating has only been experimentally examined using rotating parallel plates before, this should be the first time the effect is demonstrated in Taylor-Couette flow.		A Taylor-Couette device was the centerpiece of our experiment. The device coscisted of a bottom part, a top part, a transparent PVC tube and a rotating dowel. All parts except for the tube were printed on an ordinary 3-D printer (Makerbot Replicator). The distance between the outer tube and the inner dowel gives just enough clearance to let the particles align themselves freely. A larger distance (used in our first iteration) doesn't generate enough shear for the separation effect to be visible. The effect we are demonstrating has only been experimentally examined using rotating parallel plates before, this should be the first time the effect is demonstrated in Taylor-Couette flow.

			[[File:Chiral-Setup-Birdseye.jpg \| thumb \| 300px \| Figure 3: Birds eye view of the experiment]]

	The chiral particles are small helices described in Figure tk. Ten left handed particles, ten right handed particles and ten neutral particles (consisting of flat rectangles) were printed and used.		The chiral particles are small helices described in Figure tk. Ten left handed particles, ten right handed particles and ten neutral particles (consisting of flat rectangles) were printed and used.
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	The rotation of the inner dowel was provided by an ordinary cordless drill, connected to a power supply unit. The velocity of the rotation was controlled by regulating the voltage of the drill.		The rotation of the inner dowel was provided by an ordinary cordless drill, connected to a power supply unit. The velocity of the rotation was controlled by regulating the voltage of the drill.
	The data acquisition was all done by a single camera. In the first experiment the dowel was placed in between four tilted mirrors, and the camera was placed above the apparatus. This gave a full 360 degree view of the Taylor-Couette device, seen in Figure tk. In the second and third experiments the camera was mounted facing the side of the Taylor-Couette device, and no mirrors were used.		The data acquisition was all done by a single camera. In the first experiment the dowel was placed in between four tilted mirrors, and the camera was placed above the apparatus. This gave a full 360 degree view of the Taylor-Couette device, seen in Figure tk. In the second and third experiments the camera was mounted facing the side of the Taylor-Couette device, and no mirrors were used.

			[[File:Tc.png \| thumb \| 300px \| Figure 4: An illustration of Taylor vorticies in a Taylor-Couette cylinder, courtesy of APS.org]]

	In the first experiment we put 30 particles in the device, evenly divided amongst left handed, right handed and neutral ones. The dowel was spun at 1.4 revolutions per second clockwise and then counter clockwise for about a minute. The position of all particles were recorded and tracked manually in MATLAB. Their mean <math>z</math> position was calculated and plotted.		In the first experiment we put 30 particles in the device, evenly divided amongst left handed, right handed and neutral ones. The dowel was spun at 1.4 revolutions per second clockwise and then counter clockwise for about a minute. The position of all particles were recorded and tracked manually in MATLAB. Their mean <math>z</math> position was calculated and plotted.
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	<videoflash>ucM8Mz2ncuE</videoflash>		<videoflash>ucM8Mz2ncuE</videoflash>
	<videoflash>jmCkyvK_RlQ</videoflash>		<videoflash>jmCkyvK_RlQ</videoflash>
	~~[[File:Chiral-Setup-Birdseye.jpg \| thumb \| 300px \| Birds eye view of the experiment]]~~
	[[File:TC-device.jpg \| thumb \| 300px \| Figure 1: Sketch of a Taylor-Couette Device (courtesy of IOP Science)]]		[[File:TC-device.jpg \| thumb \| 300px \| Figure 1: Sketch of a Taylor-Couette Device (courtesy of IOP Science)]]
	[[File:CW_angle.png \| thumb \| 300px \| ~~Figure 2:~~ ]]		[[File:CW_angle.png \| thumb \| 300px \| Caption]]
	[[File:Cw_angle2.png \| thumb \| 300px \| ~~Figure 3: ]]~~		[[File:Cw_angle2.png \| thumb \| 300px \| Caption]]
	~~[[File:Particle.png \| thumb \| 300px \| Figure 4:]]~~
	~~[[File:Shear.png \| thumb \| 300px \| Figure 5:]]~~
	~~[[File:Tc.png \| thumb \| 300px \| Figure 6:~~]]

← Older revision		Revision as of 15:24, 12 December 2014
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	== Theory ==		== Theory ==
	[[File:Shear.png \| thumb \| 300px \| Figure 1: Force gradient viewed from above.]]		[[File:Shear.png \| thumb \| 300px \| Figure 1: Force gradient viewed from above.]]
	We consider a sheer flow, <math>\mathbf{v}(x,y,z) = \dot{\gamma}y\hat{x}</math>. Here, <math>\mathbf{v}</math> is the fluid velocity, <math>\dot{\gamma}</math> is the shear rate, and <math>\hat{x}</math> is the direction of shear flow, in this case a unit vector in the <math>x</math> direction. <math>y</math> represents a linear gradient of force in the <math>\hat{y}</math> direction ~~(see Figure tk)~~. We then consider a particle inserted into this flow:		We consider a sheer flow, <math>\mathbf{v}(x,y,z) = \dot{\gamma}y\hat{x}</math>. Here, <math>\mathbf{v}</math> is the fluid velocity, <math>\dot{\gamma}</math> is the shear rate, and <math>\hat{x}</math> is the direction of shear flow, in this case a unit vector in the <math>x</math> direction. <math>y</math> represents a linear gradient of force in the <math>\hat{y}</math> direction. We then consider a particle inserted into this flow:

	<math>\left<{\mathbf{V}(t)}\right> = \mathbf{v} + \dot{\gamma}\left<\tilde{\mathbf{g}}\mathbf{N}\right></math>		<math>\left<{\mathbf{V}(t)}\right> = \mathbf{v} + \dot{\gamma}\left<\tilde{\mathbf{g}}\mathbf{N}\right></math>
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	<math>\left<V(z)\right> = \chi ga\dot{\gamma}</math>		<math>\left<V(z)\right> = \chi ga\dot{\gamma}</math>

	Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's ~~chiraltiy~~, <math>g</math> is a constant based on particle geometry, and a is the particle size. We see that this is simply a reduction of the second equation to one dimension.		Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's chirality, <math>g</math> is a constant based on particle geometry, and a is the particle size. We see that this is simply a reduction of the second equation to one dimension.

	== Method ==		== Method ==
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	[[File:Particle.png \| thumb \| 300px \| Figure 2: Model of the left hand chiral particle used in this experiment.]]		[[File:Particle.png \| thumb \| 300px \| Figure 2: Model of the left hand chiral particle used in this experiment.]]

	A Taylor-Couette device was the centerpiece of our experiment. The device ~~coscisted~~ of a bottom part, a top part, a transparent PVC tube and a rotating dowel. All parts except for the tube were printed on an ordinary 3-D printer (Makerbot Replicator). The distance between the outer tube and the inner dowel gives just enough clearance to let the particles align themselves freely. A larger distance (used in our first iteration) doesn't generate enough shear for the separation effect to be visible. The effect we are demonstrating has only been experimentally examined using rotating parallel plates before, this should be the first time the effect is demonstrated in Taylor-Couette flow.		A Taylor-Couette device was the centerpiece of our experiment. The device consisted of a bottom part, a top part, a transparent PVC tube and a rotating dowel. All parts except for the tube were printed on an ordinary 3-D printer (Makerbot Replicator). The distance between the outer tube and the inner dowel gives just enough clearance to let the particles align themselves freely. A larger distance (used in our first iteration) doesn't generate enough shear for the separation effect to be visible. The effect we are demonstrating has only been experimentally examined using rotating parallel plates before, this should be the first time the effect is demonstrated in Taylor-Couette flow.

	[[File:Chiral-Setup-Birdseye.jpg \| thumb \| 300px \| Figure 3: Birds eye view of the experiment]]		[[File:Chiral-Setup-Birdseye.jpg \| thumb \| 300px \| Figure 3: Birds eye view of the experiment]]

	The chiral particles are small helices described in Figure tk. Ten left handed particles, ten right handed particles and ten neutral particles (consisting of flat rectangles) were printed and used.		The chiral particles are small helices described in Figure 2. Ten left handed particles, ten right handed particles and ten neutral particles (consisting of flat rectangles) were printed and used.
	The Taylor-Couette device was filled with transparent corn syrup, with a viscosity of 1450 - 2170 cSt was chosen.		The Taylor-Couette device was filled with transparent corn syrup, with a viscosity of 1450 - 2170 cSt was chosen.
	The rotation of the inner dowel was provided by an ordinary cordless drill, connected to a power supply unit. The velocity of the rotation was controlled by regulating the voltage of the drill.		The rotation of the inner dowel was provided by an ordinary cordless drill, connected to a power supply unit. The velocity of the rotation was controlled by regulating the voltage of the drill.
	The data acquisition was all done by a single camera. In the first experiment the dowel was placed in between four tilted mirrors, and the camera was placed above the apparatus. This gave a full 360 degree view of the Taylor-Couette device~~, seen in Figure tk~~. In the second and third experiments the camera was mounted facing the side of the Taylor-Couette device, and no mirrors were used.		The data acquisition was all done by a single camera. In the first experiment the dowel was placed in between four tilted mirrors, and the camera was placed above the apparatus. This gave a full 360 degree view of the Taylor-Couette device. In the second and third experiments the camera was mounted facing the side of the Taylor-Couette device, and no mirrors were used.

	[[File:Tc.png \| thumb \| 300px \| Figure 4: An illustration of Taylor ~~vorticies~~ in a Taylor-Couette cylinder, courtesy of APS.org]]		[[File:Tc.png \| thumb \| 300px \| Figure 4: An illustration of Taylor vortices in a Taylor-Couette cylinder, courtesy of APS.org]]

	In the first experiment we put 30 particles in the device, evenly divided amongst left handed, right handed and neutral ones. The dowel was spun at 1.4 revolutions per second clockwise and then counter clockwise for about a minute. The position of all particles were recorded and tracked manually in MATLAB. Their mean <math>z</math> position was calculated and plotted.		In the first experiment we put 30 particles in the device, evenly divided amongst left handed, right handed and neutral ones. The dowel was spun at 1.4 revolutions per second clockwise and then counter clockwise for about a minute. The position of all particles were recorded and tracked manually in MATLAB. Their mean <math>z</math> position was calculated and plotted.
	In the second experiment the Taylor-Couette device was loaded with one left handed particle and one right handed particle placed on opposite sides of the center dowel. They were aligned differently and spun at different speeds. The alignment angle of the particles were tracked manually in ~~matlab~~ and plotted as a function of time.		In the second experiment the Taylor-Couette device was loaded with one left handed particle and one right handed particle placed on opposite sides of the center dowel. They were aligned differently and spun at different speeds. The alignment angle of the particles were tracked manually in Matlab and plotted as a function of time.
	In the third experiment the device was filled with different mixtures of corn syrup and kallieroscope fluid. The goal was to see weather we were experiencing vortices that could interfere with the alignment of the particles.		In the third experiment the device was filled with different mixtures of corn syrup and kallieroscope fluid. The goal was to see weather we were experiencing vortices that could interfere with the alignment of the particles.

	== Results and Conclusions ==		== Results and Conclusions ==

	In Figure tk you can see data for the average $z$ position over time for each handedness. This clearly verifies the existence of the separation effect. During the data acquisition some particles reached the bottom of the device, creating a "knee" in the plot. Figure tk shows the average velocity over time. We also took a linear fit to the data preceding the "knee", pictured in Figure tk. The fit has an <math>r^2</math> value of 0.79, indicating that the trend is indeed linear as expected. However, there is significant noise in the data.		In Figure 8 you can see data for the average $z$ position over time for each handedness. This clearly verifies the existence of the separation effect. During the data acquisition some particles reached the bottom of the device, creating a "knee" in the plot. Figure 9 shows the average velocity over time. We also took a linear fit to the data preceding the "knee", pictured in Figure 7. The fit has an <math>r^2</math> value of 0.79, indicating that the trend is indeed linear as expected. However, there is significant noise in the data.

	The alignment plots (Figures tk, tk) need some explanation. Because no mirrors were used the particles come in and out of visual range, leading to gaps in the data. The reason we didn't collect data from all directions was that the Makino paper predicts that the particles should align, and that long-term effect should be seen even if only one side of the cylinder is observed. Also worth pointing out is a collision at t=5 in Figure tk. The collected data doesn't support the alignment effect predicted in Makino's paper. Even for longer durations of time no visible alignment was discovered. Banding wasn't observed at lower voltages, which indicates that Taylor vortices did not affect particle orientation.		The alignment plots (Figures 5, 6) need some explanation. Because no mirrors were used the particles come in and out of visual range, leading to gaps in the data. The reason we didn't collect data from all directions was that the Makino paper predicts that the particles should align, and that long-term effect should be seen even if only one side of the cylinder is observed. Also worth pointing out is a collision at t=5 in Figure 5. The collected data doesn't support the alignment effect predicted in Makino's paper. Even for longer durations of time no visible alignment was discovered. Banding wasn't observed at lower voltages, which indicates that Taylor vortices did not affect particle orientation.

	== Figures ==		== Figures ==
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	{\|style="margin: 0 auto;"		{\|style="margin: 0 auto;"
	\| [[File: Linefit.png \| thumb \| 300px \| Figure 7: Example of a linear function fit to the first data points, rsquare = 0.7929]]		\| [[File: Linefit.png \| thumb \| 300px \| Figure 7: Example of a linear function fit to the first data points, rsquare = 0.7929]]
	\| [[File: Plot1.png \| thumb \| 300px \| Figure 8: The average positions of ten particles of each ~~hand- edness~~ versus time. Data is shown for one clockwise (CW) and one counter-clockwise (CCW) experiment.]]		\| [[File: Plot1.png \| thumb \| 300px \| Figure 8: The average positions of ten particles of each handedness versus time. Data is shown for one clockwise (CW) and one counter-clockwise (CCW) experiment.]]
	\| [[File: Plot2.png \| thumb \| 300px \| Figure 9: lot of velocity versus time generated from the time derivitive of the couter-clockwise position vs. time data ]]		\| [[File: Plot2.png \| thumb \| 300px \| Figure 9: lot of velocity versus time generated from the time derivitive of the couter-clockwise position vs. time data ]]
	\|}		\|}