Numerical Study Of Fluid-Structure Interaction Dynamics Of Elastic Capsules In Typical Simple Flow

In this manuscript,the dynamics of two dimensional elastic capsules in shear flow and Poiseuille flow are investigated numerically.Specifically,the dynamic modes of a capsule under oscillating shear flow with finite inertia,as well as the effect of membrane mechanical properties on the capsule motion in the Poiseuille flow are investigated.First,we carry out a study on the effect of inertia in the transient deformation and steady-state structure of the capsule.At finite Reynolds number,we numerically simulate the dynamical behavior of a two-dimensional elastic capsule in shear flow,focusing on the effects of different Reynolds numbers Re and oscillation frequency f.As f increases,we observed persistent oscillation,asymmetric oscillation,deflected oscillation,and stable modes.The phase diagram in the Re-f plane is presented.At low frequencies,a capsule shows a phase-lag phenomenon between the deformation and the applied shear.At moderate frequencies,the anomaly of decreasing maximum deformation with increasing Re is observed.The anomaly is attributed to the mode shift.In addition,a scaling law of the maximum deformation of the capsule as a function of Re and f is proposed.In addition,the effects of the internal and external viscosity ratios A,membrane mechanical properties Ca and dimensionless bending modulus Eb on the deformation and motion modes of the capsules are further investigated.Second,the nature of the membrane significantly affects the motion and deformation of the capsule in the flow field.The behavior of a two-dimensional elastic capsule passing through a microtubular Poiseuille flow is mainly investigated.The effects of capillary number Ca,Eb and capsule radius to duct radius constraint ratio a/R on capsule deformation are mainly investigated.It is found that as Eb increases,the stable shape of the capsule transitions from a parachute shape to a bullet shape,and the decreasing of Ca and a/R promotes this modal shift,which can be clearly observed from the plotted Ca-Eb and a/R-Eb planes phase diagrams.The evolution of the capsule outlines with these dimensionless parameters is further observed.The decreasing of Eb and increasing of Ca tend to elongate the capsule in the flow direction,compress it in the longitudinal direction,depress the tail inward and deepen it gradually,and the velocity of the capsule increases among the same inlet flow of Poiseuille flow.And the increase of a/R makes the concave in the middle of the capsule deeper.The variation of these characteristic sizes and equilibrium velocities with dimensionless parameters is quantitatively analyzed.It is observed that the centerline length Lfr of the capsule increases and then decreases with Eb at low Ca numbers,which is analyzed by the contour of pressure coefficients in the flow field.