Off-plane motion of a prolate capsule in shear flow

2013 ◽  
Vol 721 ◽  
pp. 180-198 ◽  
Author(s):  
C. Dupont ◽  
A.-V. Salsac ◽  
D. Barthès-Biesel
Keyword(s):  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Shear Plane ◽  
Plane Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Simple Shear Flow ◽  
Flow Vorticity ◽  
Wall Deformation

AbstractThe objective of this study is to investigate the motion of an ellipsoidal capsule in a simple shear flow when its revolution axis is initially placed off the shear plane. We consider prolate capsules with an aspect ratio of two or three enclosed by a membrane, which is either strain-hardening or strain-softening. We seek the equilibrium motion of the capsule as we increase the capillary number$\mathit{Ca}$, which measures the ratio between the viscous and elastic forces. The three-dimensional fluid–structure interaction problem is solved numerically by coupling a boundary integral method (for the internal and external flows) with a finite element method (for the wall deformation). For any initial inclination with the flow vorticity axis, a given capsule converges towards a unique equilibrium configuration which depends on$\mathit{Ca}$. At low capillary number, the stable equilibrium motion is the rolling regime: the capsule aligns its long axis with the vorticity axis, while the membrane tank-treads. As$\mathit{Ca}$increases, the capsule takes a complex wobbling motion at equilibrium, precessing around the vorticity axis. As$\mathit{Ca}$is further increased, the capsule long axis oscillates about the shear plane, while the membrane rotates around a capsule cross-section that also oscillates over time (oscillating–swinging regime). The amplitude of the oscillations about the shear plane decreases as$\mathit{Ca}$increases and the capsule finally takes a swinging motion in the shear plane. It is found that the transitions from rolling to wobbling and from wobbling to oscillating–swinging depend on the mean energy stored in the membrane.

Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes

2011 ◽  
Vol 676 ◽  
pp. 318-347 ◽  
Author(s):  
J. WALTER ◽  
A.-V. SALSAC ◽  
D. BARTHÈS-BIESEL
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Capillary Number ◽  
Shear Plane ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Simple Shear Flow ◽  
Initial State ◽  
Initial Shape ◽  
Aspect Ratios

The large deformations of an initially-ellipsoidal capsule in a simple shear flow are studied by coupling a boundary integral method for the internal and external flows and a finite-element method for the capsule wall motion. Oblate and prolate spheroids are considered (initial aspect ratios: 0.5 and 2) in the case where the internal and external fluids have the same viscosity and the revolution axis of the initial spheroid lies in the shear plane. The influence of the membrane mechanical properties (mechanical law and ratio of shear to area dilatation moduli) on the capsule behaviour is investigated. Two regimes are found depending on the value of a capillary number comparing viscous and elastic forces. At low capillary numbers, the capsule tumbles, behaving mostly like a solid particle. At higher capillary numbers, the capsule has a fluid-like behaviour and oscillates in the shear flow while its membrane continuously rotates around its deformed shape. During the tumbling-to-swinging transition, the capsule transits through an almost circular profile in the shear plane for which a long axis can no longer be defined. The critical transition capillary number is found to depend mainly on the initial shape of the capsule and on its shear modulus, and weakly on the area dilatation modulus. Qualitatively, oblate and prolate capsules are found to behave similarly, particularly at large capillary numbers when the influence of the initial state fades out. However, the capillary number at which the transition occurs is significantly lower for oblate spheroids.

The dynamics of a vesicle in simple shear flow

2011 ◽  
Vol 674 ◽  
pp. 578-604 ◽  
Author(s):  
HONG ZHAO ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Lipid Membrane ◽  
Shear Plane ◽  
Plane Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Lipid Vesicle ◽  
Simple Shear Flow ◽  
Motion Patterns

We have performed direct numerical simulation (DNS) of a lipid vesicle under Stokes flow conditions in simple shear flow. The lipid membrane is modelled as a two-dimensional incompressible fluid with Helfrich surface energy in response to bending deformation. A high-fidelity spectral boundary integral method is used to solve the flow and membrane interaction system; the spectral resolution and convergence of the numerical scheme are demonstrated. The critical viscosity ratios for the transition from tank-treading (TT) to ‘trembling’ (TR, also called VB, i.e. vacillating-breathing, or swinging) and eventually ‘tumbling’ (TU) motions are calculated by linear stability analysis based on this spectral method, and are in good agreement with perturbation theories. The effective shear rheology of a dilute suspension of these vesicles is also calculated over a wide parameter regime. Finally, our DNS reveals a family of time-periodic and off-the-shear-plane motion patterns where the vesicle's configuration follows orbits that resemble but are fundamentally different from the classical Jeffery orbits of rigid particles due to the vesicle's deformability.

Stable equilibrium configurations of an oblate capsule in simple shear flow

2016 ◽  
Vol 791 ◽  
pp. 738-757 ◽  
Author(s):  
C. Dupont ◽  
F. Delahaye ◽  
D. Barthès-Biesel ◽  
A.-V. Salsac
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Simple Shear ◽  
Capillary Number ◽  
Stable Equilibrium ◽  
Viscosity Ratio ◽  
Shear Plane ◽  
Initial Orientation ◽  
Simple Shear Flow ◽  
Mechanical Equilibrium

The objective of the paper is to determine the stable mechanical equilibrium states of an oblate capsule subjected to a simple shear flow, by positioning its revolution axis initially off the shear plane. We consider an oblate capsule with a strain-hardening membrane and investigate the influence of the initial orientation, capsule aspect ratio$a/b$, viscosity ratio${\it\lambda}$between the internal and external fluids and the capillary number$Ca$which compares the viscous to the elastic forces. A numerical model coupling the finite element and boundary integral methods is used to solve the three-dimensional fluid–structure interaction problem. For any initial orientation, the capsule converges towards the same mechanical equilibrium state, which is only a function of the capillary number and viscosity ratio. For$a/b=0.5$, only four regimes are stable when${\it\lambda}=1$: tumbling and swinging in the low and medium$Ca$range ($Ca\lesssim 1$), regimes for which the capsule revolution axis is contained within the shear plane; then wobbling during which the capsule experiences precession around the vorticity axis; and finally rolling along the vorticity axis at high capillary numbers. When${\it\lambda}$is increased, the tumbling-to-swinging transition occurs for higher$Ca$; the wobbling regime takes place at lower$Ca$values and within a narrower$Ca$range. For${\it\lambda}\gtrsim 3$, the swinging regime completely disappears, which indicates that the stable equilibrium states are mainly the tumbling and rolling regimes at higher viscosity ratios. We finally show that the$Ca$–${\it\lambda}$phase diagram is qualitatively similar for higher aspect ratio. Only the$Ca$-range over which wobbling is stable increases with$a/b$, restricting the stability ranges of in- and out-of-plane motions, although this phenomenon is mainly visible for viscosity ratios larger than 1.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

Simiple Shear Flow of a Non-Aligning Nematic

1991 ◽  
Vol 248 ◽  
Author(s):  
W. H. Han ◽  
A. D. Rey
Keyword(s):  
Liquid Crystal ◽  
Numerical Analysis ◽  
Shear Flow ◽  
Three Dimensional ◽  
Shear Plane ◽  
Stationary Solutions ◽  
Secondary Flows ◽  
Simple Shear Flow ◽  
Continuous Transition ◽  
Discontinuous Transition

AbstractThis paper presents a nonlinear numerical analysis of the orientational instabilites, textures, and flow patterns of a characteristic rod-like nematic liquid crystal in steady simple shear flow. The parameter vector V=(λ,E) is given by the reactive parameter (λ) and the Ericksen number (E). There are two stationary solutions: in-plane(IP) and out-of-shear-plane(OP), according to whether the average orientation lies in or out of the plane of shear. For a given λ the in-plane stationary solutions may undergo a continuous transition (second order) to two dissipatively equivalent OP solutions when E=Eo or a discontinuous transition (first order) to a highly distorted IP solution when E=Ei. The continuous transition at E=Eo is a supercritical (pitchfork) bifurcation and the discontinuous transition at E=Ei is a limit point instability. Nonlinear numerical analysis shows that for the studied liquid crystal Eo < Ei. The orientation phase diagram for stable stationary solutions therefore consist of a region of OP solutions separated from a region of IP solutions by the curve Vo = (λ,Eo), describing a set of continuous supercritical bifurcations. These stable OP solutions are characterzied by the absence of sharp splay and bend deformations and by the presence of complex secondary flows arising from the three dimensional orientation. Presented results also include the dependence of the three dimensional texture, primary and secondary velocity fields on E.

scholarly journals Buckling of elastic fibers in a shear flow

2021 ◽  
Author(s):  
Agnieszka M. Slowicka ◽  
Nan Xue ◽  
Pawel Sznajder ◽  
Janine K Nunes ◽  
Howard A Stone ◽  
...  
Keyword(s):  
Shear Flow ◽  
Flow Direction ◽  
Three Dimensional ◽  
Shear Plane ◽  
Elastic Fibers ◽  
Small Range ◽  
Qualitative Comparison ◽  
Flow Vorticity ◽  
Flexible Fibers ◽  
Long Time

Abstract Three-dimensional dynamics of flexible fibers in shear flow are studied numerically, with a qualitative comparison to experiments. Initially, the fibers are straight, with different orientations with respect to the flow. By changing the rotation speed of a shear rheometer, we change the ratio A of bending to shear forces. We observe fibers in the flow-vorticity plane, which gives insight into the motion out of the shear plane. The numerical simulations of moderately flexible fibers show that they rotate along effective Jeffery orbits, and therefore the fiber orientation rapidly becomes very close to the flow-vorticity plane, on average close to the flow direction, and the fiber remains in an almost straight configuration for a long time. This ``ordering'' of fibers is temporary since they alternately bend and straighten out while tumbling. We observe numerically and experimentally that if the fibers are initially in the compressional region of the shear flow, they can undergo a compressional buckling, with a pronounced deformation of shape along their whole length during a short time, which is in contrast to the typical local bending that originates over a long time from the fiber ends. We identify differences between local and compressional bending and discuss their competition, which depends on the initial orientation of the fiber and the bending stiffness ratio A. There are two main finding. First, the compressional buckling is limited to a certain small range of the initial orientations, excluding those from the flow-vorticity plane. Second, since fibers straighten out in the flow-vorticity plane while tumbling, the compressional buckling is transient - it does not appear for times longer than 1/4 of the Jeffery period. For larger times, bending of fibers is always driven by their ends.

Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow

2011 ◽  
Vol 672 ◽  
pp. 477-486 ◽  
Author(s):  
É. FOESSEL ◽  
J. WALTER ◽  
A.-V. SALSAC ◽  
D. BARTHÈS-BIESEL
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Viscosity Ratio ◽  
Fluid Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Simple Shear Flow ◽  
Flow Strength ◽  
Capsule Deformation ◽  
Internal Viscosity

The motion and deformation of a spherical elastic capsule freely suspended in a simple shear flow is studied numerically, focusing on the effect of the internal-to-external viscosity ratio. The three-dimensional fluid–structure interactions are modelled coupling a boundary integral method (for the internal and external fluid motion) with a finite element method (for the membrane deformation). For low viscosity ratios, the internal viscosity affect the capsule deformation. Conversely, for large viscosity ratios, the slowing effect of the internal motion lowers the overall capsule deformation; the deformation is asymptotically independent of the flow strength and membrane behaviour. An important result is that increasing the internal viscosity leads to membrane compression and possibly buckling. Above a critical value of the viscosity ratio, compression zones are found on the capsule membrane for all flow strengths. This shows that very viscous capsules tend to buckle easily.

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