^{1}, Ezinwa Elele

^{2}, Mike Yeksel

^{2}, Boris Khusid

^{2}, Zhiyong Qiu

^{3}and Andreas Acrivos

^{3,a)}

### Abstract

We present a method for measuring both the fluid and particle velocities in strong electric fields and carefully analyze the repeatability and reproducibility of the measurements. The experiments were conducted in capillaries containing dilute aqueous suspensions of polystyrene spheres subjected to dc as well as ac fields of strengths up to and , respectively. These measurements indicate that the predictions of classical linear theories for electrokinetic phenomena apply well beyond the range of relatively weak electric fields for which these theories were developed. The results of our studies are critical for the quantification of microanalytical systems which make use of electrokinetic phenomena for the transport, control, and manipulation of fluids and particles.

We are grateful to German Drazer (Johns Hopkins University) and Fabio Baldessari (Stanford University) for their critical reading and comments on an earlier version of this manuscript, Ilona Kretzschmar (City College of New York) for her help in translating Quincke’s (1861) article from German to English, and Anubhav Tripathi (Brown University) for his valuable suggestions during the development phase of our experimental protocol. This work was supported in part by grants from NASA (Grant No. NAG3-2698), NSF (Grant No. CTS-0307099), and NSF/Sandia (Grant No. NIRT/NER-0330703) (B.K).

I. INTRODUCTION

II. METHODS

III. EXPERIMENTAL PROCEDURES

A. Experimental setup

B. Channel pretreatment

C. Suspension preparation

D. Filling the setup and measuring procedures

IV. EXPERIMENTAL RESULTS AND DISCUSSION

A. DC fields

B. AC fields

C. Comparison with theoretical predictions

V. CONCLUSIONS

### Key Topics

- Electroosmosis
- 49.0
- Electrophoresis
- 19.0
- Suspensions
- 16.0
- Velocimetry
- 14.0
- Carrier mobility
- 13.0

## Figures

(Color online) Schematic of the experimental setup. Syringe 1 is connected to the high-voltage output of the power supply while Syringe 2 is connected to the ground. The volume of the fluid flowing through the capillary is measured by observing the displacement of the meniscus position as the fluid enters into the microsyringe. The particle motion in the capillary is recorded by a camera connected to a microscope. The whole assembly is fixed onto a stage and is kept *horizontal*. The inset shows the airtight connection between the capillary and the syringe reservoirs.

(Color online) Schematic of the experimental setup. Syringe 1 is connected to the high-voltage output of the power supply while Syringe 2 is connected to the ground. The volume of the fluid flowing through the capillary is measured by observing the displacement of the meniscus position as the fluid enters into the microsyringe. The particle motion in the capillary is recorded by a camera connected to a microscope. The whole assembly is fixed onto a stage and is kept *horizontal*. The inset shows the airtight connection between the capillary and the syringe reservoirs.

(Color online) The diagram for choosing the dimensions of the needle and the initial position of the meniscus. (a) Flow diagram. (b) The isoclines of the ratios and are plotted in the plane. The ratio is decreasing with time as the fluid flows into the needle. The points show the values of these parameters for our experimental conditions.

(Color online) The diagram for choosing the dimensions of the needle and the initial position of the meniscus. (a) Flow diagram. (b) The isoclines of the ratios and are plotted in the plane. The ratio is decreasing with time as the fluid flows into the needle. The points show the values of these parameters for our experimental conditions.

(Color online) dc-field data on the apparent particle velocity, , recorded in two, presumably identical, capillaries for several successive cycles of increasing and then decreasing the field strength (both in steps every ). Each data point is the average value of the observed motion of 10 randomly chosen particles.

(Color online) dc-field data on the apparent particle velocity, , recorded in two, presumably identical, capillaries for several successive cycles of increasing and then decreasing the field strength (both in steps every ). Each data point is the average value of the observed motion of 10 randomly chosen particles.

(Color online) The datasets (about 200) of the simultaneously measured fluid mobility, (black squares), and of the particle mobilities (each averaged over 25–30 particles), (green triangles) and (blue stars), obtained from all the dc experiments. The means and standard deviations are , , and . The data are plotted versus (a) time, (b) field strength, and (c) capillary length. The horizontal lines show the mean values of the corresponding quantities averaged over all the dc experiments.

(Color online) The datasets (about 200) of the simultaneously measured fluid mobility, (black squares), and of the particle mobilities (each averaged over 25–30 particles), (green triangles) and (blue stars), obtained from all the dc experiments. The means and standard deviations are , , and . The data are plotted versus (a) time, (b) field strength, and (c) capillary length. The horizontal lines show the mean values of the corresponding quantities averaged over all the dc experiments.

The datasets (about 200) of the simultaneously measured particle and fluid mobilities obtained from all the dc experiments: (a) vs and (b) vs . The error bars show the standard deviations of and taken over 25–30 particles. The correlation coefficients are 0.87 between and and between and .

The datasets (about 200) of the simultaneously measured particle and fluid mobilities obtained from all the dc experiments: (a) vs and (b) vs . The error bars show the standard deviations of and taken over 25–30 particles. The correlation coefficients are 0.87 between and and between and .

(Color online) The zero-mean distribution of the relative mobilities for about 5000 individual particles: (a) the apparent particle mobility and (b) the particle electrophoretic mobility. The procedure used to obtain the data in this histogram is described in Sec. IV A. The lines show the best-fitting zero-mean Gaussian distribution yielding a standard deviation of 7% for the apparent particle mobility and 14% for the particle electrophoretic mobility.

(Color online) The zero-mean distribution of the relative mobilities for about 5000 individual particles: (a) the apparent particle mobility and (b) the particle electrophoretic mobility. The procedure used to obtain the data in this histogram is described in Sec. IV A. The lines show the best-fitting zero-mean Gaussian distribution yielding a standard deviation of 7% for the apparent particle mobility and 14% for the particle electrophoretic mobility.

The datasets (about 60) for the electro-osmotic fluid mobility, , measured in the dc experiments without the particles. The means and standard deviations are . The data are plotted vs (a) time, (b) field strength, and (c) capillary length. The horizontal lines show the mean values of the corresponding quantities averaged over these dc experiments.

The datasets (about 60) for the electro-osmotic fluid mobility, , measured in the dc experiments without the particles. The means and standard deviations are . The data are plotted vs (a) time, (b) field strength, and (c) capillary length. The horizontal lines show the mean values of the corresponding quantities averaged over these dc experiments.

(Color online) The datasets (about 200) of the effective particle mobility in ac fields (each averaged over three particles) obtained from all the ac experiments. The mean and the standard deviation are . The data are plotted against (a) field strength, (b) field frequency, and (c) capillary length. The horizontal line shows the mean value.

(Color online) The datasets (about 200) of the effective particle mobility in ac fields (each averaged over three particles) obtained from all the ac experiments. The mean and the standard deviation are . The data are plotted against (a) field strength, (b) field frequency, and (c) capillary length. The horizontal line shows the mean value.

(Color online) The zero-mean distribution of relative mobilities for about 600 individual particles. The procedure used to obtain the data in this histogram is described in Sec. IV B. The lines show the best-fitting zero-mean Gaussian distribution which yields a standard deviation of 4% for .

(Color online) The zero-mean distribution of relative mobilities for about 600 individual particles. The procedure used to obtain the data in this histogram is described in Sec. IV B. The lines show the best-fitting zero-mean Gaussian distribution which yields a standard deviation of 4% for .

## Tables

Correlation coefficients for the pure fluid and particle mobilities in suspensions.

Correlation coefficients for the pure fluid and particle mobilities in suspensions.

Correlation coefficients for fluid mobility without the particles.

Correlation coefficients for fluid mobility without the particles.

Correlation coefficients between the data on the particle and fluid mobilities.

Correlation coefficients between the data on the particle and fluid mobilities.

Correlation coefficients for the effective particle mobility in ac fields.

Correlation coefficients for the effective particle mobility in ac fields.

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