Numerical Study On Rheology Of Suspension And Migration Dynamics Of Particles

Particle suspensions are common in nature and industrial design and understanding the properties of suspensions is important in scientific researches and industrial design processes,for example,microfluidics and papermaking.In this dissertation,the rheology of suspensions and the migration dynamics of particles in typical flow are studied using the lattice Boltzmann method.The effects of the channel(shape and confinement)and particle properties(shape and permeability)are investigated in detail.The results and conclusions are briefly given as follows:1.The rheology of porous particle suspensions in a two-dimensional shear flow is studied.The effects of fluid inertia,the permeability of the particle,and confinement of the bounding walls are investigated.Darcy number Da represents the permeability of the particle.For dilute particle suspensions,three regimes are observed for the relation between the intrinsic viscosity and Darcy number:nonlinear regime with small Da,linear regime,and nonlinear regime with large Da.For the nonlinear regime with small Da,the effects of boundary confinement and Reynold number are important and the intrinsic viscosity increases with the increase of confinement and Reynolds number.While for the nonlinear regime with large Da,the effect of the permeability of particle is dominant and the effects of boundary confinement and Reynold number are negligible.Through the analysis of a number of simulation results,an equation for intrinsic viscosity as a function of Darcy number is proposed.Based on this equation,an empirical formula is proposed to predict the relation between intrinsic viscosity and Darcy number for different confinement and Reynolds numbers.For semi-dilute and dense particle suspensions,the relative viscosity decreases with the increase of Darcy number.The effect of Darcy number is higher for higher particle concentrations.And the empirical formula for intrinsic viscosity as a function of Darcy number is applicative for dense particle suspension.2.The rheological properties and microstructure of neutrally buoyant elliptical and ellipsoid particle suspensions are studied.For dilute suspensions containing only one particle,the effects of particle aspect ratio Ar and Reynolds number are studied.with the increase of Ar,the particle ceases to rotate due to the inertia at a critical aspect ratio Arc and the value of Arc decreases with increasing Re.The inertia-induced rotation arrest causes non-monotonic variations of particle alignment along the flow direction and the relative viscosity ηr.An orientational order parameter Txx is used to represent the degree of particle alignment along the flow direction.A larger Txx means that particle align more.Results show that ηr is directly related to Txx.The larger Txx is,the smaller ηr is.With the increase of Ar,minimum ηr is observed corresponding to maximum Txx.What’s more,scaling trends are found between the viscosity and the particle alignment for any Re considered here.For dense suspensions containing multiple particles,with increasing Ar,Txx increases.But Txx becomes almost constant when Ar is greater than a threshold Art.Smaller values of Art are observed for higher Res.Meanwhile,with the increase of Ar,ηr decreases due to particle alignment for Ar<Art and then increases due to high particle-particle interaction for Ar>Art.Further,the contributions of stresslet,particle acceleration stress,and Reynolds stress on ηr and the first normal stress difference N1 are analyzed.Besides the major contribution of stresslet,Reynolds stress contributes more as Ar and Re increases.In addition,three-dimensional simulations of ellipsoid particle suspensions are performed and some 3D results are similar to the 2D simulations.3.The migration dynamics of the sphere and ellipsoid particles in triangular channels with 60° and 120° apex angle are studied.The effects of blockage ratio β(a ratio of particle diameter and the hydraulic diameter of the cross section)and Reynolds number Re are investigated.The particle size is changed to get different βs.For a small β,three face-focusing equilibrium positions are observed for sphere particles in 60° channels.For a large β,three corner-focusing equilibrium positions are observed.In 120° channels,for a small two equilibrium positions are observed containing a face-focusing position located near the bottom wall and a comer-focusing position near the apex angle.With the increase of the particle size,the face-focusing position disappears and new equilibrium positions are observed near the bottom corner.If further increasing the particle size,the equilibrium position near the apex angle disappears.With the increase of Re,non-monotonic behaviors are observed for both the equilibrium positions and focusing length.For oblate particles,the migration dynamics are similar to those of spheres and the particle moves in a log-rolling mode finally.For prolate particles,the motions of particles are similar to those of spheres for a small β.With the increase of the particle size,new equilibrium positions are observed between the center of the bottom wall and the bottom corner.And the particle moves in a log-rolling or tumbling mode in 60° channels.In 120° channels,particles near the bottom wall can move in a log-rolling mode and with the increase of particle size,new equilibrium positions are observed near the bottom corner.The above results show that the particle shape can be used to separate particles with different shapes in the triangular channels.