Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Abstract

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Combined Pressure-Driven and Electroosmotic Slip Flow through Elliptic Cylindrical Microchannels: The Effect of the Eccentricity of the Channel Cross-Section

“…Hence, an increase in the eccentricity yields a lower volumetric flow rate. This result is well consistent with Numpanviwat's work [32]. When the slip flow phenomenon is applied, i.e., l = 0, Q * increases as an increase in the slip length.…”

“…They concluded that considering the circular channel with the same perimeter instead of an elliptic channel is inappropriate. In 2021, Numpanviwat et al [32] proposed the mathematical model of transient combined pressure-driven and electroosmotic flow in an elliptic microchannel under the no-slip condition. The effect of the eccentricity of the channel cross-section was studied in two situations by fixing either the area or the perimeter of the cross-section.…”

Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions

“…In particular, two constants C arise in this equation for each fluid layer. Therefore, the boundary conditions for each liquid-liquid and solid-liquid interface must be applied to determine the values of C 2n−1 and C 2n , which are given in Equations ( 16)-( 18) and (21). Then, first the boundary condition in Equation ( 16) is applied into (24) for the fluid n = 1 at the interface placed at r = a, yielding…”

“…where, D n and E n are integration constants, which will be found by implementing the boundary conditions from Equations ( 16) and ( 19)- (21) to Equation (56). First, by applying Equation (16) to Equation ( 56) corresponding to the fluid layer n = 1 at the interface placed at r = a, the following relationship is obtained:…”

“…More recently, Li et al [20] reported the electro-osmotic flow of Jeffreys fluids in a microannulus, showing that, in particular, the wall gap reduction will restrict the fluid's elastic effect. Also, the scientific community has extended its investigations with more complex geometries, such as elliptical [21], triangular [22], semicircular [23], and trapezoidal [24].…”