Vertical flow of a multiphase mixture in a channel

Constitutive relations for the interaction force in multicomponent particulate flows

Abstract: In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.

A Mixture Theory formulation for hydraulic or pneumatic transport of solid particles

Abstract: In this paper, we discuss the importance of constitutive modeling of the stress tensors in certain engineering issues, related to the pressure drop and skin friction, encountered in solids transport. To study this problem, we first give a brief account of the formulation of a two-component mixture based on the theory proposed by Massoudi, Rajagopal and co-workers. The mixture consists of a linearly viscous fluid infused with solid particles. The solids particles are modeled as a granular media and it is assumed that the mixture is dense enough so that we can use the theory of interacting continua. The subsequent boundary value problem, flow between two flat plates, is then solved numerically and results for various dimensionless numbers are presented for velocities and volume fraction profiles. The engineering quantities of interests discussed are related to the pressure drop and skin friction at the walls.

On the importance of material frame-indifference and lift forces in multiphase flows

Abstract: In this paper, we discuss the importance of the Principle of Material Frame-Indifference, sometimes referred to as Objectivity, in multiphase flows. We first give a brief account of the formulation of a two-phase mixture and then indicate where and how this principle should be utilized. We will then give a brief review of the meaning of this principle in continuum mechanics and how it has been used in various fields of physics. We also give examples of frame-indifferent and frame-dependent constitutive relations which have been used in multiphase flow studies. The importance of lift forces is also discussed. Finally, we derive a general constitutive relation which is frame-invariant and general enough to be used in many applications.

Removal of malaria-infected red blood cells using magnetic cell separators: A computational study

Abstract: High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. In this paper, we model the malaria-infected RBCs (pRBCs) as paramagnetic particles suspended in a Newtonian fluid. Trajectories of the infected cells are numerically calculated inside a micro-channel exposed to a periodic magnetic field gradient. First-order stiff ordinary differential equations (ODEs) governing the trajectory of particles under periodic magnetic fields due to an array of wires are solved numerically using the 1st to 5th order adaptive step Runge–Kutta solver. The numerical experiments show that in order to achieve a capture efficiency of 99% for the pRBCs it is required to have a longer length than 80 mm; this implies that in principle, using optimization techniques the length could be adjusted, i.e., shortened to achieve 99% capture efficiency of the pRBCs.

Modeling and numerical simulation of blood flow using the Theory of Interacting Continua.

Abstract: In this paper we use a modified form of the mixture theory developed by Massoudi and Rajagopal to study the blood flow in a simple geometry, namely flow between two plates. The blood is assumed to behave as a two-component mixture comprised of plasma and red blood cells (RBCs). The plasma is assumed to behave as a viscous fluid whereas the RBCs are given a granular-like structure where the viscosity also depends on the shear-rate.