# Computational Fluid Dynamics Modeling of Counter-Current Flow in Channels Separated by a Membrane

## TL;DR

This paper uses computational fluid dynamics to model fluid flow and pressure in channels separated by a membrane, simulating processes like hemodialysis.

## Contribution

The study introduces a novel CFD approach to simulate counter-current flow in membrane-separated channels, avoiding experimental testing.

## Key findings

- Pressure decreases from the inlet to the outlet of the channel.
- Horizontal velocity decreases to the middle of the channel and then increases toward the outlet.
- Vertical velocity changes direction at the midpoint of the channel.

## Abstract

Several studies have investigated counterflow and concurrent flow in channels separated by a membrane to simulate mass transfer through membranes; however, few of them have used computational fluid dynamics (CFD). The current study aimed to numerically simulate and physically describe the distribution of pressure and velocity in counter-current flow by solving Navier-Stokes (N-S) equations in the channel and membrane pores (vertical channels). This is in contrast to most previous studies, in which the channel flow was simulated using N-S equations while ultra-filtration membrane flow was simulated using Darcy’s law. Consequently, the current study was executed using a CFD simulation to achieve several significant features: avoiding the execution of experimental tests, reducing the effort of model design and the expense and time consumption of fabrication, and facilitating the easy observation of variations in the pressure and the horizontal and vertical velocity for each point in the model. Two-dimensional CFD methods directly simulated the flow in channels and membrane pores to solve the N-S equations for each point in the whole domain, for which the velocity (horizontal and vertical) and pressure were calculated. In the current study, it was found that the pressure decreased from the inlet to the outlet of the channel, the horizontal velocity decreased from the inlet to the middle of the channel length and then increased to the outlet of the channel, and the vertical velocity decreased from the inlet to the middle of the channel length (L/2) with an upward direction (positive) and from L/2 to the outlet of the channel with a downward direction (negative). The analytical solution (1D model) was used to validate a numerical simulation (CFD) for the current study, but there were slight differences in the results between them. The results were perfectly explored and displayed the flow distribution patterns inside the channels and the membrane pores (vertical channels). The current study model represents the hemodialysis process.