An analytical study on hydrodynamics of an unsteady flow and mass transfer through a channel asymmetrically lined with deformable porous layer

• Endothelial-cell glycocalyx layer(EGL) influences the blood plasma flow rate.
• Hydrodynamics of flow through EGL is modeled with biphasic mixture theory.
• Rate of solute transfer from plasma to EGL is calculated at the interface.
• Higher depth of EGL causes reduction of flow rate through free lumen.
• Permeation velocity controls the solute transport in the endothelial cells.

The present study is motivated by its possible relevance to the rheology of blood and the transport of nutrient and drug molecules (macro–microscopic level) through capillaries, venules and digestive tract under the influence of endothelial-cell glycocalyx (EG). As an approximation, we study unsteady fluid flow through a rectangular channel lined with asymmetric porous lining. In order to model a more realistic situation, we adopt biphasic mixture theory for the unsteady hydrodynamics of fluid transport in poroelastic layer(s) (EG). The flow within the lumen region between the deformable porous layers is governed by unsteady Stoke’s equation. The unsteady nature of the flow is being taken care with the Fourier series expansion analysis. Shear stress is calculated at the interface of free lumen and porous layers along with volumetric flow rate through the free lumen region. An expression for Sherwood number is derived at the said interface from the pseudo steady state solution of the mass transfer equation that quantifies the transport of solute nutrient through the lumenal space. The corresponding convection–diffusion equation is solved within the mass transfer boundary layer using similarity transformation method. It is observed that the rate of volumetric flow through the free lumen increases and interfacial shear stress (i.e., shear stress at the interface of at the porous and free lumen) decreases with stress jump coefficient at the mentioned interface. Length averaged Sherwood number deceases with increase in depth of the porous layer and increases with the constant permeation velocity when the other parameters characterizing the mass transfer process remain constant.