Stability of plane-parallel flow of magnetic fluids under external magnetic fields

In this work,we present a theoretical study on the stability of a two-dimensional plane Poiseuille flow of magnetic fluids in the presence of externally applied magnetic fields.The fluids are assumed to be incompressible,and their magnetization is coupled to the flow through a simple phenomenological equation.Dimensionless parameters are defined,and the equations are perturbed around the base state.The eigenvalues of the linearized system are computed using a finite difference scheme and studied with respect to the dimensionless parameters of the problem.We examine the cases of both the horizontal and vertical magnetic fields.The obtained results indicate that the flow is destabilized in the horizontally applied magnetic field,but stabilized in the vertically applied field.We characterize the stability of the flow by computing the stability diagrams in terms of the dimensionless parameters and determine the variation in the critical Reynolds number in terms of the magnetic parameters.Furthermore,we show that the superparamagnetic limit,in which the magnetization of the fluids decouples from hydrodynamics,recovers the same purely hydrodynamic critical Reynolds number,regardless of the applied field direction and of the values of the other dimensionless magnetic parameters.

Modeling of unidirectional blood flow in microvessels with effects of shear-induced dispersion and particle migration

A cell-free layer,adjacent to microvessel walls,is present in the blood flow in the microcirculation regime.This layer is of vital importance for the transport of oxygen-saturated red cells to unsaturated tissues.In this work,we first discuss the physics of formation of this cell-free layer in terms of a balance between the shear-induced dispersion and particle migration.To this end,we use high-viscosity drops as prototypes for cells,and discuss our results in terms of physical parameters such as the viscosity ratio and the capillary number.We also provide a short-time analysis of the transient drift-dispersion equation,which helps us better explain the formation process of the cell-free layer.Moreover,we present models for investigating the blood flow in two different scales of microcirculation.For investigating the blood flow in venules and arterioles,we consider a continuous core-flow model,where the core-flow solution is considered to be a Casson fluid,surrounded by a small annular gap of Newtonian plasma,corresponding to the cell-free layer.We also propose a simple model for smaller vessels,such as capillaries,whose diameters are of a few micrometers.In this lower-bound limit,we consider a periodic configuration of aligned,rigid,and axi-symmetric cells,moving in a Newtonian fluid.In this regime,we approximate the fluid flow using the lubrication theory.The intrinsic viscosity of the blood is theoretically predicted,for both the lower and upper-bound regimes,as a function of the non-dimensional vessel diameter,in good agreement with the previous experimental works.We compare our theoretical predictions with the experimental data,and obtain qualitatively good agreement with the well-known Fåhræus-Lindqvist effect.A possible application of this work could be in illness diagnosis by evaluating changes in the intrinsic viscosity due to blood abnormalities.