Author ORCID Identifier:

https://orcid.org/0009-0008-1203-5282

Date of Graduation

5-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Engineering (PhD)

Degree Level

Graduate

Department

Civil Engineering

Advisor/Mentor

Selvam, Rathinam

Committee Member

Matlock, Marty

Second Committee Member

Hale, W.

Third Committee Member

Zhang, Wen

Keywords

Computational Fluid Dynamics; Counter current flow; Darcy’s law; Membrane; Navier-Stokes; Poiseuille flow

Abstract

Counter current flow in channels separated by membrane were studied in several published studies. The present study aims to numerically and analytically simulate and physically describe the distribution of pressure, volume flow rate and velocity in counter current flow module. Numerical simulation Computational fluid dynamics (CFD) was performed by solving Navier-Stokes (N–S) equations in the channels and membrane pores (vertical channels) to determine pressure and velocity fields. An analytical solution one-dimensional (1-D) model was developed to simulate the flow in the channels and membrane pores by solving the continuity and Darcy’s Law to obtain pressure and volume flow rate. Accordingly, the current study employs both CFD and analytical (1-D) solutions to achieve several objectives and significances, including avoiding extensive experimental testing, reducing the effort associated with expensive and time-consuming module design, and facilitating the observation of variations in pressure, volume flow rate, and velocity within a counter-current flow module. Two-dimensional CFD simulations directly model the flow in channels and membrane pores by solving the N–S equations at each point throughout the computational domain where the horizontal and vertical velocity components and pressure are calculated. The results indicate that the pressure decreases nonlinearly from the inlet to the outlet in both the upper and lower channels. The horizontal velocity decreases from the inlet to the midpoint of the channel length and then increases toward the outlet, while the vertical velocity decreases from the inlet to the midpoint of the channel length (L/2) with an upward (positive) direction and from (L/2) to the outlet of the channel with a downward (negative) direction. The analytical (1 D) model predicts comparable trends for pressure and horizontal velocity along the channel length. The analytical (1-D) model is used to compare with numerical CFD simulations, while the experimental results are used to validate the analytical model for counter-current flow in channels separated by membrane in a hemodialysis module. The results clearly illustrate the flow distribution patterns within the channels and describe the ultrafiltration profiles along the membrane surface and within the porous membrane pores, providing a strong analogy to the hemodialysis process.

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