Stefan flow-inclusive mass transfer in a narrow cylindrical channel with a two-layer medium

Abstract

The exploration and extraction of oil, coal, and gas reserves are closely tied to mass transfer phenomena within porous and fractured rock formations. Frequently, these processes involve the adsorption or desorption, dissolution, or evaporation of certain components on the surface of the pore channels. In these cases, Stefan hydrodynamic flows arise, and although they may be individually small, they can have a noticeable impact on mass transfer and flow structure considering particular length of the channel. The authors explore the issue of inert component diffusion from the surface of a capillary into a suspension flow. The analysis involves a two-layer flow, including a central two-phase (liquid and particles) component and a near-wall flow of the fluid carrier. A certain component from the channel's surface permeates deep into the flow without interacting with the solid phase. In this research the authors solve a diffusion problem with boundary conditions that consider the presence of Stefan hydrodynamic flows. The calculations reveal that, depending on the magnitude of the Stefan flows and the length of the affected area, the porosity, and consequently, the viscosity of the two-phase flow zone can undergo significant variations.