Non-Stokes drag coefficient in single-particle electrophoresis: New insights on a classical problem

Abstract

We measured the intrinsic electrophoretic drag coefficient of a single charged particle by optically trapping the particle and applying an AC electric field, and found it to be markedly different from that of the Stokes drag. The drag coefficient, along with the measured electrical force, yield a mobility-zeta potential relation that agrees with the literature. By using the measured mobility as input, numerical calculations based on the Poisson-Nernst-Planck equations, coupled to the Navier-Stokes equation, reveal an intriguing microscopic electroosmotic flow near the particle surface, with a well-defined transition between an inner flow field and an outer flow field in the vicinity of electric double layer's outer boundary. This distinctive interface delineates the surface that gives the correct drag coefficient and the effective electric charge. The consistency between experiments and theoretical predictions provides new insights into the classic electrophoresis problem, and can shed light on new applications of electrophoresis to investigate biological nanoparticles. † To whom correspondence should be addressed. Emails: hdo0@lehigh.edu, sheng@ust.hk PACS: 47.57.J-(colloidal systems); 82.45.-h (Electrochemistry and electrophoresis); 47.61.-k (Micro-and nano-scale flow phenomena) HDO would also like to thank Prof. Joel A. Cohen, Prof. Daan Frenkel and Dr. Alois Würger for their critical comments and helpful suggestions. AUTHOR CONTRIBUTIONS PS and HDO initiated and supervised the research. ML and MTW carried out the experiments. ML and PS contributed to theory and simulations with help from SX. ML. HDO and PS analyzed the data with help from MTW. ML, PS and HDO wrote the draft manuscript. All participated in revising the manuscript to its final form. ML and MTW contributed equally to this work.

A Focus on Two Electrokinetics Issues

“…The value of the drag evaluated at the inner/outer interface indeed agrees reasonably well with the measured value, on the order of two times the Stokes drag [19]. The measured value displayed a variation with the liquid pH value.…”

“…Experimentally, the problem of measuring the drag force was solved by using an optical tweezer to hold a single silica particle and applying an AC electric field [19]. Since the optical tweezer represents a harmonic potential trap for the held particle, the particle displacement from the center of the trap yields the force as that of a spring.…”

Frequency Response of Induced-Charge Electrophoretic Metallic Janus Particles

“…Using traditional DC measurements to determine the crossover frequency is difficult because the Brownian motion often swamps measurements of the null phoretic motion near the crossover frequency [23]. It is impossible to determine the drag coefficient of any phoretic motion by DC measurements, because the phoretic motion, absent of acceleration, is subject to zero net force, as the drag force perfectly opposes the phoretic force [24].…”

“…It is, however, possible to determine the drag coefficient by an AC measurement from the phase delay of the particle's phoretic motion relative to that of the harmonically varying electrophoretic force, as demonstrated in earlier work [24]. We have used such a detection method to measure the crossover frequency and phoretic force of dielectrophoresis with high precision [23,25].…”

Intracellular nonequilibrium fluctuating stresses indicate how nonlinear cellular mechanical properties adapt to microenvironmental rigidity

“…The laser is highly focused by an oil-immersion microscope objective lens (Olympus, PlanFluo, 100X, numerical aperture = 1.3) to trap a 1 μm polystyrene particle (Thermo Fisher Scientific #4009A). A schematic diagram of the experimental setup is shown in our previous published papers [43][44][45] . Movements of the trapped particle, tracked by the other IR laser beam (0.5 mW, wavelength = 980 nm, Thorlabs, Inc.), are detected by a quadrant photodiode (QPD, Hamamatsu #S7479).…”