Micro Circular Tube Flow Mathematical Model with the Effect of Van der Waals Force

Abstract

Darcy's law is found be not applicable to fluid flow in small pore throat, and the mechanism for the nonlinear flow is still unclear to date. The paper analyzed the influence of various types of micro forces in porous media on fluid flow, based on the existing experimental results and theoretical knowledge of micro-scale flow. Mathematical model for flow in small tube was established with the consideration of Van der Waals force between solid and liquid. By simulating velocity distribution and the average flow under the Poiseuille flow, we get that with the decrease of the micro tube size, the Van der Waals force between solid and liquid increases and the effect on flow pattern of fluid in the tube increases, so that the Van der Waals force between solid and liquid in the tiny pore flow should not be ignored.

Solid-Liquid Interfacial Effects on Residual Oil Distribution Utilizing Three-Dimensional Micro Network Models

“…At the molecular scale, the relative increment of micro force and solid-liquid interfacial effects become notable, which has a tremendous influence on the rule of fluid flow. These microscopic forces are mainly van der Waals forces [39].…”

“…First, the existence condition and range of van der Walls forces were described in Section 2, and van der Waals forces were dominant among these micro forces [39]. In Section 3, the influence of van der Waals forces on the fluid flow in nano-micron tube was studied and the corresponding mathematical model was established.…”

“…Zhang et al [38] established a mathematical model for weakly compressible fluid flow in nano/micro-size circular tubes with solid wall forces. Wang et al [39] alleged that van der Waals force between solid and liquid should not be ignored in the tiny pore flow. On the other hand, the solid-liquid interfacial effect has been considered in the network model.…”