When MHD-based microfluidics is equivalent to pressure-driven flow

Abstract

Magnetohydrodynamics (MHD) provides a convenient, programmable means for propelling liquids and controlling fluid flow in microfluidic devices without a need for mechanical pumps and valves. When the magnetic field is uniform and the electric field in the electrolyte solution is confined to a plane that is perpendicular to the direction of the magnetic field, the Lorentz body force is irrotational and one can define a "Lorentz" potential. Since the MHD-induced flow field under these circumstances is identical to that of pressure-driven flow, one can utilize the large available body of knowledge about pressure-driven flows to predict MHD flows and infer MHD flow patterns. In this note, we prove the equivalence between MHD flows and pressure-driven flows under certain conditions other than flow in straight conduits with rectangular crosssections. We determine the velocity profile and the efficiency of MHD pumps, accounting for current transport in the electrolyte solutions. Then, we demonstrate how data available for pressure driven flow can be utilized to study various MHD flows, in particular, in a conduit patterned with pillars such as may be useful for liquid chromatography and chemical reactors. Additionally, we examine the effect of interior obstacles on the electric current flow in the conduit and show the existence of a particular pillar geometry that maximizes the current. solution is confined to a plane that is perpendicular to the direction of the magnetic field, the Lorentz body force is irrotational and one can define a "Lorentz" potential. Since the MHDinduced flow field under these circumstances is identical to that of pressure-driven flow, one can utilize the large available body of knowledge about pressure-driven flows to predict MHD flows and infer MHD flow patterns. In this note, we prove the equivalence between MHD flows and pressure-driven flows under certain conditions other than flow in straight conduits with rectangular cross-sections. We determine the velocity profile and the efficiency of MHD pumps, accounting for current transport in the electrolyte solutions. Then, we demonstrate how data available for pressure driven flow can be utilized to study various MHD flows, in particular, in a conduit patterned with pillars such as may be useful for liquid chromatography and chemical reactors. Additionally, we examine the effect of interior obstacles on the electric current flow in the conduit and show the existence of a particular pillar geometry that maximizes the current.

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates

“…Here, is the electrical conductivity, u = (u, v, w) is the liquid velocity vector with components u, v, w in the x, y, z directions, respectively. We assume that B = Be z is a uniform magnetic field because the half-height H of the microchannel is sufficiently small compared to the size of the source of the magnetic field [55,56]. The continuity, momentum balance equations for a fluid can be expressed in the dimensional form as:…”

Mixing by chaotic advection in a magneto-hydrodynamic driven flow

“…In these cases the magnetohydrodynamic (MHD) induced flows are similar to those obtained usually by pressure driven devices. 2 Propelling liquids by electromagnetic forces does not necessarily lead to thorough mixing of an additive in the liquid. Under Stokes flow conditions, an ideal device would be one in which mixing would be promoted by chaotic advection and where the fluid is propelled by non-intrusive means such as electromagnetic forces.…”

Magneto‐convection in a rotating layer of nanofluid

“…This force, in turn, affects the buoyant flow field and the heat transfer rate. The mathematical model for MHD flows of electrolyte solutions in microfluidic systems was described by Qin and Bau when MHD‐based microfluidics is equivalent to pressure‐driven flow.…”