A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz–van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.

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.

Although microscale phenomena are ubiquitous in fluid flow through nano- or microsized channels and pores, the mechanisms remain unclear. To clarify these mechanisms, we investigate herein Bingham-plastic liquids with electroviscous effects (EVEs) in nano- and microsized circular tubes. The constitutive equation and electroviscous forces are introduced into the governing equations, and approximate analytical solutions are obtained. Velocity reduction results from the combined effects of the Bingham characteristics and EVEs. The Bingham behavior reduces the strength of the EVE electric field, and EVEs increase the width of the flow core. The dimensionless average velocity decreases as the tube radius decreases and goes to zero upon approaching the lower limit of the movable fluid radius (Rm). As the pressure gradient decreases, the average velocity first decreases linearly, then decreases nonlinearly in a concave shape, and finally approaches zero as the pressure reaches the threshold pressure gradient (TPG). The Bingham plastic behavior causes both the Rm and the nonlinear flow with TPG, and Rm is still caused by the van der Waals forces under liquid compressibility more obviously. The EVE parameters only affect the degree of nonlinearity when the liquid exhibits Bingham-plastic behavior. These results are consistent with experimentally observed de-ionized water flowing in microscale silica tubes. We infer that the Newtonian fluid displays the Bingham-plastic behavior in nano- or microsized channels in what we call “microscale effects.” These results elucidate the mechanism that leads to nonlinear or low-speed non-Darcy flow in nano- or microsized channels and pores from the liquid characteristic and liquid-solid interaction.

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Although nano- and micro-scale phenomena for fluid flows are ubiquitous in tight oil reservoirs or in nano- or micro-sized channels, the mechanisms behind them remain unclear. In this study, we consider the wall–liquid interaction to investigate the flow mechanisms behind a compressible liquid flow in nano- or micro-sized circular tubes. We assume that the liquid is attracted by the wall surface primarily by the Lifshitz–van der Waals (LW) force, whereas electrostatic forces are negligible. The long-range LW force is thus introduced into the Navier–Stokes equations. The nonlinear equations of motion are decoupled by using the hydrodynamic vorticity-stream functions, from which an approximate analytical perturbation solution is obtained. The proposed model considers the LW force and liquid compressibility to obtain the velocity and pressure fields, which are consistent with experimentally observed micro-size effects. A smaller tube radius implies smaller dimensionless velocity, and when the tube radius decreases to a certain radius Rm, a fluid no longer flows, where Rm is the lower limit of the movable-fluid radius. The radius Rm is calculated, and the results are consistent with previous experimental results. These results reveal that micro-size effects are caused by liquid compressibility and wall–liquid interactions, such as the LW force, for a liquid flowing in nano- or micro-sized channels or pores. The attractive LW force enhances the flow’s radial resistance, and the liquid compressibility transmits the radial resistance to the streaming direction via volume deformation, thereby decreasing the streaming velocity.