Three-dimensional shape of a drop under simple shear flow

1998 ◽  
Vol 42 (2) ◽  
pp. 395-415 ◽  
Author(s):  
Stefano Guido ◽  
Marco Villone
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Dimensional Shape ◽  
Three Dimensional Shape

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.

Dynamics of capsules enclosing viscoelastic fluid in simple shear flow

2018 ◽  
Vol 840 ◽  
pp. 656-687 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Deformation Behaviour ◽  
Three Dimensional ◽  
High Viscosity ◽  
Deborah Number ◽  
Simple Shear Flow ◽  
Capsule Deformation ◽  
Internal Fluid

Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.

Three-dimensional calculations of the simple shear flow around a single particle between two moving walls

1995 ◽  
Vol 283 ◽  
pp. 273-285 ◽  
Author(s):  
H. Nirschl ◽  
H. A. Dwyer ◽  
V. Denk
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Simple Shear ◽  
Particle Surface ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Number Range ◽  
Grid Scheme

Three-dimensional solutions have been obtained for the steady simple shear flow over a spherical particle in the intermediate Reynolds number range 0.1 [les ] Re [les ] 100. The shear flow was generated by two walls which move at the same speed but in opposite directions, and the particle was located in the middle of the gap between the walls. The particle-wall interaction is treated by introducing a fully three-dimensional Chimera or overset grid scheme. The Chimera grid scheme allows each component of a flow to be accurately and efficiently treated. For low Reynolds numbers and without any wall influence we have verified the solution of Taylor (1932) for the shear around a rigid sphere. With increasing Reynolds numbers the angular velocity for zero moment for the sphere decreases with increasing Reynolds number. The influence of the wall has been quantified with the global particle surface characteristics such as net torque and Nusselt number. A detailed analysis of the influence of the wall distance and Reynolds number on the surface distributions of pressure, shear stress and heat transfer has also been carried out.

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.

Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation

1998 ◽  
Vol 373 ◽  
pp. 287-311 ◽  
Author(s):  
CYRUS K. AIDUN ◽  
YANNAN LU ◽  
E.-JIANG DING
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Density Ratio ◽  
Three Dimensional ◽  
Computational Method ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Fluid Density

An efficient and robust computational method, based on the lattice-Boltzmann method, is presented for analysis of impermeable solid particle(s) suspended in fluid with inertia. In contrast to previous lattice-Boltzmann approaches, the present method can be used for any solid-to-fluid density ratio. The details of the numerical technique and implementation of the boundary conditions are presented. The accuracy and robustness of the method is demonstrated by simulating the flow over a circular cylinder in a two-dimensional channel, a circular cylinder in simple shear flow, sedimentation of a circular cylinder in a two-dimensional channel, and sedimentation of a sphere in a three-dimensional channel. With a solid-to-fluid density ratio close to one, new results from two-dimensional and three-dimensional computational analysis of dynamics of an ellipse and an ellipsoid in a simple shear flow, as well as two-dimensional and three-dimensional results for sedimenting ellipses and prolate spheroids, are presented.

Sign in / Sign up

Export Citation Format

Share Document