Motion of Single Drops in Linear Shear Flows

2007 ◽  
Author(s):  
Win Myint ◽  
Shigeo Hosokawa ◽  
Akio Tomiyama
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Drag Coefficient ◽  
Shear Flows ◽  
Viscosity Ratio ◽  
Continuous Phase ◽  
Glycerol Water ◽  
Silicon Oil ◽  
Drag Forces ◽  
Linear Shear

Motions of single silicon oil drops rising in linear shear flows of glycerol-water solutions are measured to investigate the effects of the viscosity ratio κ and dimensionless shear rate Sr on drag forces under the conditions of −6.3 ≤ logM ≤ −4.8, 0.94 ≤ κ7.04, 1 < Re ≤ 23 and 3.2 ≤ ω ≤ 6.0 s−1, where M is the Morton number and ω the magnitude of the velocity gradient of the continuous phase. As a result, we confirmed that (1) the drag coefficient CD of a drop in a linear shear flow takes a higher value than the drag coefficient CD0 of the same-size drop in a stagnant liquid, (2) CD/CD0 increases with Sr, and (3) the augmentation of CD becomes large as κ increases.

Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

2011 ◽  
Vol 678 ◽  
pp. 221-247 ◽  
Author(s):  
P. M. VLAHOVSKA ◽  
Y.-N. YOUNG ◽  
G. DANKER ◽  
C. MISBAH
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscosity Ratio ◽  
Perturbation Expansion ◽  
Shear Plane ◽  
Creeping Flow ◽  
Regular Perturbation ◽  
Cell Dynamics ◽  
Initial Shape ◽  
Flow Equations

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

Viscous Flows Involving a Liquid-Vapor Compound Droplet

2001 ◽  
Author(s):  
D. Palaniappan
Keyword(s):  
Exact Solutions ◽  
Viscosity Ratio ◽  
Numerical Algorithms ◽  
Flow Fields ◽  
Continuous Phase ◽  
Boundary Integral ◽  
Liquid Volume ◽  
Drag Forces ◽  
Compound Droplet ◽  
Fluid Interactions

Abstract Exact analytical solutions for steady-state axisymmetric creeping flows in and around a compound multiphase droplet are presented. The solutions given here explain the droplet fluid interactions in uniform and nonuniform flow fields. The compound droplet has a two-sphere geometry with the two spherical surfaces (of unequal radii) intersecting orthogonally. The surface tension forces are assumed to be sufficiently large so that the interfaces have uniform curvature. The singularity solutions for the uniform and paraboloidal flows in the presence of a compound droplet are derived using the method of reflections. The exact solutions for the velocity and pressure fields in the continuous and dispersed phases are given in terms of the fundamental singularities (Green’s functions) and their derivatives. It is found that flow fields and the drag forces depend on two parameters namely, the viscosity ratio and the radii ratio. In the case of paraboloidal flows, a single or a pair of eddies is noticed in the continuous phase for various values of these parameters. The eddies changes their size and shape if the size of the droplet is altered. These observations may be useful in the study of hydrodynamic interactions of compound droplets in complex situations. It is found that the Stokes resistance is greater when the liquid volume is large compared to the vapor volume in uniform flow. It is also noticed that the maximum value of the drag in paraboloidal flow depends on the viscosity ratio and significantly on the liquid volume in the dispersed phase. The exact solutions presented here may be useful for boundary integral formulations that are based on special kernels and also in validating numerical algorithms and codes on multiphase flow and droplet-fluid interactions.

scholarly journals Numerical simulations of vorticity banding of emulsions in shear flows

Soft Matter ◽  
2020 ◽  
Vol 16 (11) ◽  
pp. 2854-2863 ◽  
Author(s):  
Francesco De Vita ◽  
Marco Edoardo Rosti ◽  
Sergio Caserta ◽  
Luca Brandt
Keyword(s):  
Shear Flow ◽  
Numerical Simulations ◽  
Effective Viscosity ◽  
Shear Flows ◽  
Viscosity Ratio ◽  
Low Viscosity

Emulsion under shear flow can exhibit banded structures at low viscosity ratio. When coalescence is favoured, it can stabilize bands generated by migration of droplets. The reduction of the total surface results in a lower effective viscosity state.

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

1998 ◽  
Vol 361 ◽  
pp. 117-143 ◽  
Author(s):  
S. RAMANUJAN ◽  
C. POZRIKIDIS
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Large Deformations ◽  
Viscosity Ratio ◽  
Curvilinear Coordinates ◽  
Triangular Element ◽  
Elastic Membrane ◽  
Simple Shear Flow ◽  
Liquid Drops

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Reynolds numbers using a boundary-element method. The surface of the capsule is discretized into quadratic triangular elements that form an evolving unstructured grid. The elastic membrane tensions are expressed in terms of the surface deformation gradient, which is evaluated from the position of the grid points. Compared to an earlier formulation that uses global curvilinear coordinates, the triangular-element formulation suppresses numerical instabilities due to uneven discretization and thus enables the study of large deformations and the investigation of the effect of fluid viscosities. Computations are performed for capsules with spherical, spheroidal, and discoidal unstressed shapes over an extended range of the dimensionless shear rate and for a broad range of the ratio of the internal to surrounding fluid viscosities. Results for small deformations of spherical capsules are in quantitative agreement with the predictions of perturbation theories. Results for large deformations of spherical capsules and deformations of non-spherical capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially spherical capsules deform into steady elongated shapes whose aspect ratios increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed for any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymmetric capsules subject to a stagnation-point flow. When the shear rate is sufficiently high and the viscosity ratio is sufficiently low, liquid drops exhibit continuous elongation leading to breakup. Axisymmetric capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of capsules in shear flow, large elastic tensions develop at large deformations and prevent continued elongation, stressing the importance of the vorticity of the incident flow. The long-time behaviour of deformed capsules depends strongly on the unstressed shape. Oblate capsules exhibit unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sphericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinning behaviour.

The Deformation of a Vesicle in a Linear Shear Flow

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Shu Takagi ◽  
Takeshi Yamada ◽  
Xiaobo Gong ◽  
Yoichiro Matsumoto
Keyword(s):  
Shear Flow ◽  
Inclination Angle ◽  
Viscosity Ratio ◽  
Point Of View ◽  
Swelling Ratio ◽  
Fluid Membrane ◽  
Membrane Modeling ◽  
Linear Shear ◽  
Membrane Models ◽  
Good Agreement

In this paper, we discuss the motion of a vesicle in a linear shear flow. It is known that deformable vesicles such as liposomes show the so-called tank-treading and tumbling motions depending on the viscosity ratio between the inside and outside of the vesicle, the swelling ratio, and so on. First, we have conducted numerical simulations on the tank-treading motion of a liposome in a linear shear flow and compared the results with other numerical and experimental results. It is confirmed that the inclination angle of the vesicle becomes smaller when the viscosity ratio becomes larger or the swelling ratio becomes smaller and that the present results show quantitatively good agreement with other results. Then, the effects of membrane modeling are discussed from the mechanics point of view. There are two types of modeling for the lipid bilayer biomembrane. One is a two-dimensional fluid membrane, which reflects the fluidity of the lipid molecules. The other is a hyperelastic membrane, which reflects the stiffness of cytoskeleton structure. Liposome is usually modeled as a fluid membrane and red blood cell (RBC) is modeled as a hyperelastic one. We discuss how these differences of membrane models affect the behaviors of vesicles under the presence of shear flow. It is shown that the hyperelastic membrane model for RBC shows a less inclination angle of tank-treading motion and early transition from tank-treading to tumbling.

The lift force on a spherical bubble in a viscous linear shear flow

1998 ◽  
Vol 368 ◽  
pp. 81-126 ◽  
Author(s):  
DOMINIQUE LEGENDRE ◽  
JACQUES MAGNAUDET
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Bubble Surface ◽  
Vorticity Field ◽  
Linear Shear ◽  
High Reynolds

The three-dimensional flow around a spherical bubble moving steadily in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubble. The main goal of the present study is to provide a complete description of the lift force experienced by the bubble and of the mechanisms responsible for this force over a wide range of Reynolds number (0.1[les ]Re[les ]500, Re being based on the bubble diameter) and shear rate (0[les ]Sr[les ]1, Sr being the ratio between the velocity difference across the bubble and the relative velocity). For that purpose the structure of the flow field, the influence of the Reynolds number on the streamwise vorticity field and the distribution of the tangential velocities at the surface of the bubble are first studied in detail. It is shown that the latter distribution which plays a central role in the production of the lift force is dramatically dependent on viscous effects. The numerical results concerning the lift coefficient reveal very different behaviours at low and high Reynolds numbers. These two asymptotic regimes shed light on the respective roles played by the vorticity produced at the bubble surface and by that contained in the undisturbed flow. At low Reynolds number it is found that the lift coefficient depends strongly on both the Reynolds number and the shear rate. In contrast, for moderate to high Reynolds numbers these dependences are found to be very weak. The numerical values obtained for the lift coefficient agree very well with available asymptotic results in the low- and high-Reynolds-number limits. The range of validity of these asymptotic solutions is specified by varying the characteristic parameters of the problem and examining the corresponding evolution of the lift coefficient. The numerical results are also used for obtaining empirical correlations useful for practical calculations at finite Reynolds number. The transient behaviour of the lift force is then examined. It is found that, starting from the undisturbed flow, the value of the lift force at short time differs from its steady value, even when the Reynolds number is high, because the vorticity field needs a finite time to reach its steady distribution. This finding is confirmed by an analytical derivation of the initial value of the lift coefficient in an inviscid shear flow. Finally, a specific investigation of the evolution of the lift and drag coefficients with the shear rate at high Reynolds number is carried out. It is found that when the shear rate becomes large, i.e. Sr=O(1), a small but consistent decrease of the lift coefficient occurs while a very significant increase of the drag coefficient, essentially produced by the modifications of the pressure distribution, is observed. Some of the foregoing results are used to show that the well-known equality between the added mass coefficient and the lift coefficient holds only in the limit of weak shears and nearly steady flows.

scholarly journals Lift and drag forces acting on a particle moving with zero slip in a linear shear flow near a wall

2020 ◽  
Vol 904 ◽  
Author(s):  
Nilanka I. K. Ekanayake ◽  
Joseph D. Berry ◽  
Anthony D. Stickland ◽  
David E. Dunstan ◽  
Ineke L. Muir ◽  
...  
Keyword(s):  
Shear Flow ◽  
Drag Forces ◽  
Linear Shear ◽  
Lift And Drag

Abstract

Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow

2007 ◽  
Vol 570 ◽  
pp. 155-175 ◽  
Author(s):  
KEN-ICHI SUGIOKA ◽  
SATORU KOMORI
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Rigid Sphere ◽  
Fluid Shear ◽  
Spherical Droplet ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift ◽  
Homogeneous Linear

Drag and lift forces acting on a spherical water droplet in a homogeneous linear shear air flow were studied by means of a three-dimensional direct numerical simulation based on a marker and cell (MAC) method. The effects of the fluid shear rate and the particle (droplet) Reynolds number on drag and lift forces acting on a spherical droplet were compared with those on a rigid sphere. The results show that the drag coefficient on a spherical droplet in a linear shear flow increases with increasing the fluid shear rate. The difference in the drag coefficient between a spherical droplet and a rigid sphere in a linear shear flow never exceeds 4%. The lift force acting on a spherical droplet changes its sign from a positive to a negative value at a particle Reynolds number of Rep ≃ 50 in a linear shear flow and it acts from the high-speed side to the low-speed side for Rep ≥ 50. The behaviour of the lift coefficient on a spherical droplet is similar to that on a stationary rigid sphere and the change of sign is caused by the decrease of the pressure lift. The viscous lift on a spherical droplet is smaller than that on a rigid sphere at the same Rep, whereas the pressure lift becomes larger. These quantitative differences are caused by the flow inside a spherical droplet.

scholarly journals Drag and lift forces acting on a spherical gas bubble in homogeneous shear liquid flow

2009 ◽  
Vol 629 ◽  
pp. 173-193 ◽  
Author(s):  
KEN-ICHI SUGIOKA ◽  
SATORU KOMORI
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Gas Bubble ◽  
Fluid Shear ◽  
Air Bubble ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift

Drag and lift forces acting on a spherical gas bubble in a homogeneous linear shear flow were numerically investigated by means of a three-dimensional direct numerical simulation (DNS) based on a marker and cell (MAC) method. The effects of fluid shear rate and particle Reynolds number on drag and lift forces acting on a spherical gas bubble were compared with those on a spherical inviscid bubble. The results show that the drag force acting on a spherical air bubble in a linear shear flow increases with fluid shear rate of ambient flow. The behaviour of the lift force on a spherical air bubble is quite similar to that on a spherical inviscid bubble, but the effects of fluid shear rate on the lift force acting on an air bubble in the linear shear flow become bigger than that acting on an inviscid bubble in the particle Reynolds number region of 1≤Rep≤300. The lift coefficient on a spherical gas bubble approaches the lift coefficient on a spherical water droplet in the linear shear air-flow with increase in the internal gas viscosity.

Saturation of equatorial inertial instability

2015 ◽  
Vol 767 ◽  
pp. 562-594 ◽  
Author(s):  
R. C. Kloosterziel ◽  
P. Orlandi ◽  
G. F. Carnevale
Keyword(s):  
Shear Flow ◽  
Momentum Distribution ◽  
Shear Flows ◽  
Small Distance ◽  
Initial Momentum ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Inertial Instability ◽  
Linear Shear ◽  
Parallel Shear Flows

AbstractInertial instability in parallel shear flows and circular vortices in a uniformly rotating system ( $f$-plane) redistributes absolute linear momentum or absolute angular momentum in such a way as to neutralize the instability. In previous studies we showed that, in the absence of other instabilities, at high Reynolds numbers the final equilibrium can be predicted with a simple construction based on conservation of total momentum. In this paper we continue this line of research with a study of barotropic shear flows on the equatorial ${\it\beta}$-plane. Through numerical simulations the evolution of the instability is studied in select illuminating cases: a westward flowing Gaussian jet with the flow axis exactly on the equator, a uniform shear flow and eastward and westward flowing jets that have their flow axis shifted away from the equator. In the numerical simulations it is assumed that there are no along-stream variations. This suppresses equatorial Rossby waves and barotropic shear instabilities and allows only inertial instability to develop. We investigate whether for these flows on the equatorial ${\it\beta}$-plane the final equilibrated flow can be predicted as was possible for flows on the $f$-plane. For the Gaussian jet centred on the equator the prediction of the equilibrated flow is obvious by mere inspection of the initial momentum distribution and by assuming that momentum is mixed and homogenized to render the equilibrated flow inertially stable. For the uniform shear flow, however, due to the peculiar nature of the initial momentum distribution and the fact that the Coriolis parameter $f$ varies with latitude, it appears that, unlike in our earlier studies of flows on the $f$-plane, additional constraints need to be considered to correctly predict the outcome of the highly nonlinear evolution of the instability. The mixing range of the linear shear flow and the value of the mixed momentum is determined numerically and this is used to predict the equilibrated flow that emerges from an eastward flowing jet that is shifted a small distance away from the equator. For shifts large enough to induce no shear at the equator the equilibrium flow can be well predicted using the simple recipe used in our earlier studies of parallel shear flows on the $f$-plane. For the westward flowing jet shifted a very small distance from the equator, no prediction appears feasible. For modestly small shifts a prediction is possible by combining the empirical prediction for the linear shear flow with a prediction similar to what we used in our previous studies for flows on the $f$-plane.

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