Keller Box and Smoothed Particle Hydrodynamic Numerical Simulation of Two-Phase Transport in Blood Purification Auto-Transfusion Dialysis Hybrid Device with Stokes and Darcy Number Effects

Abstract

A computational simulation of laminar natural convection fully-developed multi-phase suspension in a porous medium channel is presented. The Darcy model is employed for the porous material which is valid for low velocity, viscous-dominated flows. The Drew-Marble fluid-particle suspension model is employed to simulate both particulate (red blood cell) and fluid (plasma) phases. The transformed two-point nonlinear boundary value problem is shown to be controlled by a number of key dimensionless thermo-physical parameters, namely the Darcy number (Da), momentum inverse Stokes number (Skm), particle loading parameter (pL), inverse thermal Stokes number (SkT), particle-phase wall slip parameter (W) and buoyancy parameter (B). Detailed numerical solutions are presented with an optimized Keller Box implicit finite difference Method (KBM) for the influence of these parameters on the fluid-phase velocity (U) and particle-phase velocity (Up). Validation is also included using the Smoothed Particle Hydrodynamic (SPH) Lagrangian method and excellent correlation achieved. Increasing Darcy number is observed to significantly accelerate the fluid-phase flow and less dramatically enhance particle-phase velocity field. Magnitudes of fluid phase velocity are also elevated with both increasing viscosity ratio and particle-phase wall slip parameter. Increasing buoyancy effect depresses particle phase velocity. An increase in particle loading parameter is also observed to suppress both fluid and particle phase velocities. No tangible change in fluid or particle phase temperatures is computed with increasing Darcy number. The study is relevant to dialysis devices exploiting thermal and porous media filtration features. Keywords: Biotechnology, blood flow, Prandtl number, two-phase suspension, Stokes number, particle phase velocity, Keller box finite difference algorithm, Smoothed particle hydrodynamics (SPH), Thermo-haemotological processing, autotransfusion medicine, biothermal devices. Read more →