Deformation of spherical compound capsules in simple shear flow

2015 ◽  
Vol 775 ◽  
pp. 77-104 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Long He ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Numerical Simulations ◽  
Simple Shear ◽  
Three Dimensional ◽  
Volume Ratio ◽  
Constitutive Law ◽  
Simple Shear Flow ◽  
Outer Membranes ◽  
Front Tracking Method ◽  
Outer Capsule

The deformation of a compound capsule (an elastic capsule with a smaller capsule inside) in simple shear flow is studied by using three-dimensional numerical simulations based on a front tracking method. The inner and outer capsules are concentric and initially spherical. Skalaket al.’s constitutive law is employed for the mechanics of both the inner and outer membranes. Our results concerning the deformation of homogeneous capsules (i.e. capsules without the inner capsules) are quantitatively in agreement with the predictions of previous numerical simulations and perturbation theories. Compared to homogeneous capsules, compound capsules exhibit smaller deformation. The deformations of both the inner and outer capsules are significantly affected by the capillary numbers of the inner and outer membranes and the volume ratio of the inner to the outer capsule. When the inner capsule is small, it presents smaller deformation than the outer capsule. However, when the inner capsule is sufficiently large, it can present larger deformation than the outer capsule, even if the inner membrane has much lower capillary number than the outer membrane. The underlying mechanisms are discussed: (i) the inner capsule is deformed by rotational flow with lower rate of strain rather than by simple shear flow that deforms the outer capsule, and thus the inner capsule exhibits smaller deformation; and (ii) when the inner and outer membranes are sufficiently close (i.e. the inner capsule is sufficiently large), the hydrodynamic interaction between the two membranes becomes significant, which is found to inhibit the deformation of the outer capsule but to promote the deformation of the inner capsule.

Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

2018 ◽  
Vol 858 ◽  
pp. 91-121 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Xing Long Shang ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Surfactant Concentration ◽  
Constitutive Law ◽  
Simple Shear Flow ◽  
Drop Surface ◽  
Shear Surface ◽  
Surface Viscosity ◽  
Principal Axes ◽  
Surfactant Transport

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.

ON BOUNDARY CONDITIONS IN THE FINITE VOLUME LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES

1999 ◽  
Vol 10 (06) ◽  
pp. 1003-1016 ◽  
Author(s):  
GONGWEN PENG ◽  
HAOWEN XI ◽  
SO-HSIANG CHOU
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Unstructured Meshes ◽  
Simple Shear Flow ◽  
Boltzmann Method

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

Direct Numerical Simulation of Drops in Three Dimensional Viscoelastic Simple Shear Flows

2001 ◽  
Author(s):  
Shriram B. Pillapakkam ◽  
Pushpendra Singh
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Polymer Concentration ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Splitting Technique

Abstract A three dimensional finite element scheme for Direct Numerical Simulation (DNS) of viscoelastic two phase flows is implemented. The scheme uses the Level Set Method to track the interface and the Marchuk-Yanenko operator splitting technique to decouple the difficulties associated with the governing equations. Using this numerical scheme, the shape of Newtonian drops in a simple shear flow of viscoelastic fluid and vice versa are analyzed as a function of Capillary number, Deborah number and polymer concentration. The viscoelastic fluid is modeled via the Oldroyd-B model. The role of viscoelastic stresses in deformation of a drop subjected to simple shear flow and its effect on the steady state shape is analyzed. Our results compare favorably with existing experimental data and also help in understanding the role of viscoelastic stresses in drop deformation.

Chaotic rotation of triaxial ellipsoids in simple shear flow

1997 ◽  
Vol 340 ◽  
pp. 83-100 ◽  
Author(s):  
A. L. YARIN ◽  
O. GOTTLIEB ◽  
I. V. ROISMAN
Keyword(s):  
Shear Flow ◽  
Numerical Simulations ◽  
Newtonian Fluid ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Periodic Motions ◽  
Closed Loops ◽  
Brownian Particles ◽  
Stochastic Layer ◽  
Regular Closed

Chaotic behaviour is found for sufficiently long triaxial ellipsoidal non-Brownian particles immersed in steady simple shear flow of a Newtonian fluid in an inertialess approximation. The result is first determined via numerical simulations. An analytic theory explaining the onset of chaotic rotation is then proposed. The chaotic rotation coexists with periodic and quasi-periodic motions. Quasi-periodic motions are depicted by regular closed loops and islands in the system Poincaré map, whereas chaotic rotations form a stochastic layer.

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