Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: Exact solution of the Navier-Stokes equation

Abstract

The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

Analysis of electroosmotic flow of power-law fluids in a slit microchannel

“…(23) suggests that the integration can be analytically carried out only for specific values of the flow behavior index, n such as 1, 1 2 , and 1 3 .…”

“…(23) can be analytically evaluated only under certain circumstances, in the following we will present an approximate approach to obtain the velocity distributions from Eq. (23). Mathematically, the hyperbolic sine function can be approximated as…”

“…They claimed that the fluid experiences a range of shear rate as it turns around the corner, and the flow field is shown to be sensitive to the non-Newtonian characteristics of the Carreau-type. Otevřel and Klepárník [23] derived the exact solutions for electroosmotic flow in a capillary channel filled with polymer electrolytes having a varying viscosity, and the steady-state velocity profile was calculated by assuming that the viscosity decreases exponentially in the radial direction (i.e., from the capillary wall to the centerline). To our best knowledge, the only relevant study that we could locate is by Das and Chakraborty [24] who analyzed the electroosmotic flow of a non-Newtonian fluid in microchannels.…”

The apparent hydrodynamic slip of polymer solutions and its implications in electrokinetics

“…It is worth noting that the existing models of electrokinetic phenomena in polymer‐coated surfaces involve simple electrolyte solutions . An interesting exception is , where the EOF was calculated by considering nonuniform (Newtonian) fluid viscosities near the capillary wall. A questionable aspect, however, is the definition of the plane of shear with the associated ζ ‐potential.…”

An Approximate Analytical Solution for Electro-Osmotic Flow of Power-Law Fluids in a Planar Microchannel

“…Electroviscous effects in steady, fully developed, pressure-driven flow of powerlaw liquids through a cylindrical microchannel have numerically been investigated by Bharti et al [23], using a finite difference method. Otevrel and Kleparnik [24] theoretically calculated the velocity profile of electro-osmotic flow in a cylindrical capillary, assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. With the implementation of an approximate scheme for the hyperbolic sine function initially introduced by Philip and Wooding [6], an approximate analytical solution for velocity distribution in electro-osmotic flow of power-law fluids through slit microchannels has been presented by Zhao et al [25].…”