Formation of an EDL at a liquid-solid interface. A narrow layer of fixed particles known as the stern layer immediately forms adjacent to the wall, while a diffuse layer of mobile particles forms at the shear plane. The net positive charge on the liquid in this region gives rise to electroosmosis when an external electric field is applied perpendicular to the wall.
Cross-slot geometry. Fluid enters from the top and bottom and exits through the left and right channel sections. Pressure is balanced at all four exits, resulting in pure electroosmotic flow driven by the applied potential difference .
Finite element mesh.
Ion concentrations in the EDL 200 EDL widths downstream of the corner and at the corner. The net charge density is positive within the EDL since . The concentration profiles at the corner are slightly different from those observed in the straight channel section. The ion concentrations quickly find their equilibrium values outside the EDL, resulting in zero net charge density.
Electric charge density in the corner region. There is a net positive charge in the EDL to balance the negative charge at the wall that corresponds to a negative wall zeta potential. The charge density adopts a smooth rounded profile at the corner. The thick line indicates the edge of the EDL used in the macroscale model. The boundary position parameter is taken to be zero at the corner of the EDL region, negative downstream of the corner, and positive upstream of the corner.
Buffer velocity in the vicinity of the corner for (a) the full model and (b) the macroscale model using the new velocity slip boundary conditions at the edge of the EDL.
Fluid velocity in the direction at the edge of the EDL in the corner region for the full solution, macroscale solution with the new velocity boundary conditions, and macroscale solution with the HS velocity boundary conditions. The full solution demonstrates a bounded velocity profile with a discontinuous gradient at the EDL boundary corner. The new boundary condition closely matches the full solution, while the HS boundary condition gives a nonphysical asymptotic velocity jump across the corner.
Electric field strength at the edge of the EDL in the corner region for both the full solution and the macroscale solution. In the case of the full solution, the electric field is bounded in the corner region. In the case of the macroscale solution, where the EDL boundary is taken as the insulating boundary for the applied potential , the computed electric field has a singularity at the corner.
Nondimensional pressure at the edge of the EDL in the corner region for the full solution, macroscale solution with matched velocity boundary conditions, and the macroscale solution with the new velocity boundary conditions. In the case of the full solution, the pressure is bounded in the corner region. The matched velocity boundary conditions ensure that the pressure is also bounded in the macroscale case, while the new boundary conditions result in a small pressure jump at the corner.
Physical quantities used in this study.
Boundary conditions for the full model.
Normalized error integrals for velocity and pressure predictions of the macroscale model compared to the full model solution for the HS boundary condition, new boundary condition, and matched velocity boundary condition. The error integrals are evaluated on three progressively smaller square domains, , , and , centered on the corner of the cross slot.
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