Numerical Study On Flow Properties Of Capsule Suspensions

The capsule,consisting of a droplet encapsulated by a layer of elastic membrane,is one of the most basic deformable objects.Flow of capsule suspensions is common in both natural and industrial settings,playing an important role in daily life,biomedical and industrial fields.In this paper,a combined lattice Boltzmann(LB)-finite element(FE)-immersed boundary(IB)method is used to numerically simulate the migration characteristics of capsules and the rheological properties of the suspensions under different flow conditions.The main work and research conclusions are as follows:1.The effects of Reynolds number(Re),bending modulus(Eb)and volume fraction(φ)on the apparent viscosity(μa)of the suspension are explored in wallconfined flows.It is found that μa varies with φ and can be divided into four regimes.In each regime,there is a distinct equilibrium spatial configuration:one-file confguration,transition confguration,two-file confguration and random confguration.The spatial configurations are quantitatively described by the lateral position of capsules,the width of capsule-free layer and volume density of the capsules.Next,the suspension is divided into dilute cases and concentrated cases.For the dilute cases,phase diagrams of flow regimes on the(φ,Eb)plane are plotted.The effects of Re and the height of the computational domain on the phase diagrams are studied.For the concentrated cases,"inertial focusing"is observed.μa first increases,then decreases with Re.We also observe that the optimal volume fraction,at which the transport of capsules is at a maximum,increases with Re.For the two-component capsule suspension,we analyze the spatial position through diffusion-drift theory and find that stiffer capsules are more easily able to migrate laterally.By changing Re,we find that there is an optimal Re that maximizes the lateral distance between the two component(different Ca)capsules.For the multi-component suspension,the Ca of capsules conforms to a normal distribution.We find that the larger the standard deviation of Ca,the larger the μa.2.The flow properties of capsule suspensions in curved tubes are studied.It is found that at medium Re,e.g.Re～10,μa decreases with increasing Re,which is different from the trend of viscosity change in straight tubes.Dean’s vortices play an important role.As fluid inertia increases,the vortices are strengthened,greatly promoting the capsules’ circumferential transportation by trapping the capsules into their centers and making the location of maximum azimuthal velocity close to them.The effect of tube curvature(κ)on μa is then studied.When κ is large,the variation trend of μa is completely opposite to that in a straight tube(κ=0).When Re is not large(<20),μa increases with κ.At this stage,a scaling law of μa as a function of κ and Re is proposed and all simulation data conform to this scaling law.On the other hand,when Re is large(>20),μa decreases with increasing Re and is not sensitive to κ.In addition,the distribution of capsules in curved and straight tubes is compared.In a straight tube,the capsules are mainly located inside an annulus between the center and wall.In curved tubes,when Re is low,the capsules concentrate on the symmetry plane and are close to the inner wall.When Re is large,capsules stay close to the center of Dean’s vortices.Finally,for both the dilute and semidilute regimes,a scaling law connecting the effective viscosity and the average location of capsules is proposed.3.The rupture mechanism of encapsulated polymer capsules in shear flow is studied.According to the stress-strain curve,the capsule rupture criterion is set:when the strain between adjacent Lagrangian points exceeds 20%,the force between the Lagrangian points disappears,and the capsule ruptures.Based on the change inμa,the rupture process is divided into three stages:the deformation stage,the rupture stage,and the stable stage.Subsequently,the configurations of the capsules after rupture are classified into three types,and a phase diagram of the configuration after rupture is constructed.The release and diffusion of the polymer are then described by the concentration-convection-diffusion equation.Using this model,the entire process of capsule rupture and release of polymer is numerically simulated.Finally,the effect of viscosity ratio(λ)on μa is investigated when the capsule is not ruptured.A universal law of μa as a function of Ca,λ,and φ is proposed.