Application Of The Non-Local Theory On Multi-Scale Porous Media Flow

The porous media are widely found in industrial materials,animals and plants,and in nature.Studying the multi-scale porous media flow is conducive to the development of many fields such as industry,life sciences and infrastructure.According to scale,the pore scale,representative elementary volume(REV)scale and macro scale are usually considered.The study of macro scale porous media flow is directly helpful for engineering technology and is based on the understanding of the porous media flow on REV scale.The research of porous media flow on pore scale is the basis for studying the porous media flow on REV scale.Therefore,the transport of mass,energy and momentum in porous media is a typical multi-scale problem.In this thesis,the non-local theory is employed to study the non-local effect in porous media flow.Non-local theory originated in the field of solid mechanics and is concerned with the physical problems that the behavior of an object at a certain point is affected by the state of all points of the body,especially the neighborhood near the point,the distance is longer,the influence is weaker.After decades of development,nonlocal theory has been widely used in disciplines.In recent years,non-local theory has been extended to the field of porous media flow,and a relatively complete theory has been formed to describe the transmission mechanism of energy,momentum,and mass in porous media.Inspired by the theory of non-local elasticity,we propose a multi-scale porous media flow model under the influence of non-local effect.For flows in porous media on the REV scale,the non-local unsteady compressible porous media flow model and non-local steady incompressible porous media flow model are proposed.The non-local unsteady compressible porous media flow model reflects both the spatially and temporally non-local effect.The non-local steady incompressible porous media flow model reflects the spatially non-local effect.The governing equation established by the constitutive relationship of the non-local effects is a fourth-order partial differential equation.In order to make a solvable problem,the additional boundary conditions are prescribed.We examine the proposed non-local porous media flow model and compared the effective permeability of porous media flow under different characteristic non-local length.In addition,our proposed model can be used to describe the propagation of elastic waves in fluid-saturated porous media.In the molecular flow on nano/micro pore scale,we propose the non-local molecular flow model by considering the ballistic transport of molecules and the slip boundary condition near the Knudsen layer.From the non-local transport equation on the pore scale,we find that the ballistic transport of molecules at the micro/nano pore scale is similar to the viscous Poiseuille flow.After analysis,we believe that the effects of ballistic transport and slip boundary condition play an important role in molecular flow problems on the micro/nano pore scale.We finally give the relationship between the characteristic non-local length and the effective permeability.