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The Magnitude of the Soret Force on Colloidal Particles Measured in Microgravity

Matthew L. Lynch
Matthew L. Lynch
, 
Thomas E. Kodger
Thomas E. Kodger
, 
Paolo Palacio-Mancheno
Paolo Palacio-Mancheno
, 
Mark W. Pestak
Mark W. Pestak
 e 
William V. Meyer
William V. Meyer
   | 12 feb 2024
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Article Category: Research Note
Pubblicato online: 12 feb 2024
Pagine: 1 - 17
DOI: https://doi.org/10.2478/gsr-2023-0002
Parole chiave
© 2024 Matthew L. Lynch et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1.

The rheological behavior of the XK gum polymer gel system described in Lynch et al. (2018) and Lynch et al. (2020). (A) The creep flow behavior with different applied stresses. With low applied stress (1.000 Pa, red), the gel strains but exhibits no fluid-like flow at long times; however, at high applied stress (2.500 Pa, green), the gel strains and eventually breaks resulting in viscous flow at long times. (B) The gel breakage follows a power-law behavior with applied stress and time. This is the same rheological behavior in colloidal gels described in Landrum et al. (2016) and more broadly described in Coussot et al. (2002).
The rheological behavior of the XK gum polymer gel system described in Lynch et al. (2018) and Lynch et al. (2020). (A) The creep flow behavior with different applied stresses. With low applied stress (1.000 Pa, red), the gel strains but exhibits no fluid-like flow at long times; however, at high applied stress (2.500 Pa, green), the gel strains and eventually breaks resulting in viscous flow at long times. (B) The gel breakage follows a power-law behavior with applied stress and time. This is the same rheological behavior in colloidal gels described in Landrum et al. (2016) and more broadly described in Coussot et al. (2002).

Figure 2.

Electron micrographs of the colloidal particles used in these experiments. (A) The larger particles were measured 1.92 ± 0.31 um in diameter. (B) The smaller particles were measured 1.59 ± 0.19 um in diameter.
Electron micrographs of the colloidal particles used in these experiments. (A) The larger particles were measured 1.92 ± 0.31 um in diameter. (B) The smaller particles were measured 1.59 ± 0.19 um in diameter.

Figure 3.

The experimental hardware used in these experiments. (A) An edge-on drawing of the showing the glass capillary cell (center) with sample chamber (orange), the thermal bridge (bottom), several of the electromagnets (left, right), and the confocal objective (top). (B) Sketch of the borosilicate VitroCom glass capillary cell. (C) Image of the glass capillary cell mounted on the thermal bridge, with the two thermoelectric heaters mounted at each end. (D) Top-view showing the glass capillary cell and thermal bridge mounted in a bank of electromagnets.
The experimental hardware used in these experiments. (A) An edge-on drawing of the showing the glass capillary cell (center) with sample chamber (orange), the thermal bridge (bottom), several of the electromagnets (left, right), and the confocal objective (top). (B) Sketch of the borosilicate VitroCom glass capillary cell. (C) Image of the glass capillary cell mounted on the thermal bridge, with the two thermoelectric heaters mounted at each end. (D) Top-view showing the glass capillary cell and thermal bridge mounted in a bank of electromagnets.

Figure 4.

A representation of the fluorescence emitted from a particle in the experiments. The layers represent the image slices in the z-direction measured with the confocal microscope. There is 1.4-um separation between image slices, which is on the order of the diameter of the particles. The optics in the confocal microscope attenuate the fluorescence from the particle, showing the smaller diameter and smaller intensity in the image slices above and below the centroid of the physical particle.
A representation of the fluorescence emitted from a particle in the experiments. The layers represent the image slices in the z-direction measured with the confocal microscope. There is 1.4-um separation between image slices, which is on the order of the diameter of the particles. The optics in the confocal microscope attenuate the fluorescence from the particle, showing the smaller diameter and smaller intensity in the image slices above and below the centroid of the physical particle.

Figure 5.

Three image slices pulled from an image stack adjacent to the centroid of a representative particle, where the particle is at the very center of each image. (A) the image slice next (no. 25) above the physical centroid. (B) The image slice (no. 26) closest to the centroid of the physical particle. (C) The image slice (no. 27) next below the centroid of the physical particle.
Three image slices pulled from an image stack adjacent to the centroid of a representative particle, where the particle is at the very center of each image. (A) the image slice next (no. 25) above the physical centroid. (B) The image slice (no. 26) closest to the centroid of the physical particle. (C) The image slice (no. 27) next below the centroid of the physical particle.

Figure 6.

The average flurorescence intensity (circles) from the same representative particle (Figure 5) measure from the image slices above and below centroid of the physical particle. The data are fit to a Gaussian distribution (dashed line), where the maximum is taken as the actual centroid of the physical particle.
The average flurorescence intensity (circles) from the same representative particle (Figure 5) measure from the image slices above and below centroid of the physical particle. The data are fit to a Gaussian distribution (dashed line), where the maximum is taken as the actual centroid of the physical particle.

Figure 7.

To ensure the fidelity of the centroids of the particles determined through the Avizo software, the z-positions of a number of particles in the image stack at different positions in the z-directly were manual determined and compared the z-positions of the same particles determined through Avizo. The correlation demonstrates good agreement.
To ensure the fidelity of the centroids of the particles determined through the Avizo software, the z-positions of a number of particles in the image stack at different positions in the z-directly were manual determined and compared the z-positions of the same particles determined through Avizo. The correlation demonstrates good agreement.

Figure 8.

A representation of the two calculated volumes: vertical volume and radial volume, used in the analysis in these experiments. (A) The vertical volume is bound by the volume between the n and (n+1) image slices, and the x- and y-dimensions of the image. (B) The radial volume is bound by the volume of the cylindrical annulus of radii of (r· (n-1))/10 and (r·n)/10 through the entire dimension in the z-direction, where n is an integer between 1 and 10.
A representation of the two calculated volumes: vertical volume and radial volume, used in the analysis in these experiments. (A) The vertical volume is bound by the volume between the n and (n+1) image slices, and the x- and y-dimensions of the image. (B) The radial volume is bound by the volume of the cylindrical annulus of radii of (r· (n-1))/10 and (r·n)/10 through the entire dimension in the z-direction, where n is an integer between 1 and 10.

Figure 9.

Data from a representative image stack. (A) Initial image slice with the TEM set at 20°C and at 14 um in the z-direction into the volume. (B) The volume fraction of particles in each vertical volume in the image stack. (C) The volume fraction of particles in each radial volume in the image stack, where the apparent decrease in volume fraction with increasing radius reflects the uneven lighting from the confocal microscope. (D) The pairwise binding between particles in the entire measured volume.
Data from a representative image stack. (A) Initial image slice with the TEM set at 20°C and at 14 um in the z-direction into the volume. (B) The volume fraction of particles in each vertical volume in the image stack. (C) The volume fraction of particles in each radial volume in the image stack, where the apparent decrease in volume fraction with increasing radius reflects the uneven lighting from the confocal microscope. (D) The pairwise binding between particles in the entire measured volume.

Figure 10.

The probability of finding two particles at a distance – r, normalized to unity at large r, for the initial measurement when the TEM was set to different temperatures. These data show a peak at about 1.7 um reflects the separation between bound particles, and where the difference in the magnitude of the peak reflects the difference in particle volume fraction in each experiment.
The probability of finding two particles at a distance – r, normalized to unity at large r, for the initial measurement when the TEM was set to different temperatures. These data show a peak at about 1.7 um reflects the separation between bound particles, and where the difference in the magnitude of the peak reflects the difference in particle volume fraction in each experiment.

Figure 11.

Modeling the temperature gradients in these experiments in COMSOL. (A) Temperature in the glass capillary cell looking down the x-axis. In this computation, the blue along the bottom reflects the 20°C set point of the TEM, the red along the top of the cell reflects the temperature of the objective set to 28°C, and the yellow/green along the balance of the cell reflects the temperature of the cabin at 25°C. (B) The computed temperature gradient across the 200-um width of the solvent in the cell from the center of the objective through the sample to the thermal bridge. The temperature drop is essentially linear through the solvent. (C) The temperature gradient across the solvent gap with different applied TEM temperatures, with large temperature gradient resulting from the small width of the gap.
Modeling the temperature gradients in these experiments in COMSOL. (A) Temperature in the glass capillary cell looking down the x-axis. In this computation, the blue along the bottom reflects the 20°C set point of the TEM, the red along the top of the cell reflects the temperature of the objective set to 28°C, and the yellow/green along the balance of the cell reflects the temperature of the cabin at 25°C. (B) The computed temperature gradient across the 200-um width of the solvent in the cell from the center of the objective through the sample to the thermal bridge. The temperature drop is essentially linear through the solvent. (C) The temperature gradient across the solvent gap with different applied TEM temperatures, with large temperature gradient resulting from the small width of the gap.

Figure 12.

Typical images from these experiments. (A) Bright field image taken with a 2.5X air objective, showing section of the cell with sample on left and bubble on the right. (B) Bright field image taken with a 10X air objective, which shows graininess from the dispersed particles and shows a section of the magnetic stir bar. (C) Confocal image taken with 63X oil objective showing one image slice in the stack with the particles as the bright objects.
Typical images from these experiments. (A) Bright field image taken with a 2.5X air objective, showing section of the cell with sample on left and bubble on the right. (B) Bright field image taken with a 10X air objective, which shows graininess from the dispersed particles and shows a section of the magnetic stir bar. (C) Confocal image taken with 63X oil objective showing one image slice in the stack with the particles as the bright objects.

Figure 13.

Initial experiments demonstrating the presence of the Soret forces. (A). Each set of markers represents a single experiments at different TEM temperatures: 20.0°C, 21.0°C (red), 23.0°C, 24.0 °C, 25.0 °C (blue), 26.0 °C, 28.0 °C and 30.0°C, respectively, from left to right. The particle count was measured in a volume slice at 20-um into the sample. The dark lines show the change in the particle count in the volume over time. At 20.0°C, there is large decrease in the particle count while at 30.0°C, there is a significant increase in particle count. (B) The change in particle count plotted versus the TEM set temperature. The change is “flattened” and nulled, between about 24°C and about 26°C.
Initial experiments demonstrating the presence of the Soret forces. (A). Each set of markers represents a single experiments at different TEM temperatures: 20.0°C, 21.0°C (red), 23.0°C, 24.0 °C, 25.0 °C (blue), 26.0 °C, 28.0 °C and 30.0°C, respectively, from left to right. The particle count was measured in a volume slice at 20-um into the sample. The dark lines show the change in the particle count in the volume over time. At 20.0°C, there is large decrease in the particle count while at 30.0°C, there is a significant increase in particle count. (B) The change in particle count plotted versus the TEM set temperature. The change is “flattened” and nulled, between about 24°C and about 26°C.

Figure 14.

Sedimentation of the particles in the presence of the temperature gradient (A) The normalized distribution of particles at the initial condition (red); the distribution after long-time convergence when TEM set to 20°C (blue); the fit in accordance with Mason and Weaver (1924) (black dash). (B) (red) The normalized distribution of particles at the initial condition (red); the distribution after long-time convergence when TEM set to 23°C (blue); the fit in accordance with Mason and Weaver (1924) (black dash).
Sedimentation of the particles in the presence of the temperature gradient (A) The normalized distribution of particles at the initial condition (red); the distribution after long-time convergence when TEM set to 20°C (blue); the fit in accordance with Mason and Weaver (1924) (black dash). (B) (red) The normalized distribution of particles at the initial condition (red); the distribution after long-time convergence when TEM set to 23°C (blue); the fit in accordance with Mason and Weaver (1924) (black dash).

Figure 15.

Force-temperature gradient curves, where force curves are determined from long-time distribution of particles and the temperature gradient determined by COMSOL modeling at three TEM set temperatures. The force is proportionally to the temperature gradient, which is internally consistent despite different approaches to generating the data. The box (dashes) represents region in which the Soret force is comparable to (or less than) the Brownian force, which results in imperceptible separation of the dispersion even with a temperature gradient (i.e., between about 24°C and about 26°C).
Force-temperature gradient curves, where force curves are determined from long-time distribution of particles and the temperature gradient determined by COMSOL modeling at three TEM set temperatures. The force is proportionally to the temperature gradient, which is internally consistent despite different approaches to generating the data. The box (dashes) represents region in which the Soret force is comparable to (or less than) the Brownian force, which results in imperceptible separation of the dispersion even with a temperature gradient (i.e., between about 24°C and about 26°C).

Parameters for force calculations.

TEM Setting a A B Force Force
20 oC 0.2326 7.28 × 10−14 m2 1.56 × 10−9 m 8.85 × 10−17 N 3.0 milli-G
21 oC 0.2868 7.28 × 10−14 m2 1.27 × 10−9 m 7.17 × 10−17 N 2.7 milli-G
23 oC 0.3918 7.28 × 10−14 m2 0.93 × 10−10 m 5.25 × 10−17 N 2.0 milli-G
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