scholarly journals Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow

2008 ◽  
Vol 52 (6) ◽  
pp. 1459-1475 ◽  
Author(s):  
Anja Vananroye ◽  
Ruth Cardinaels ◽  
Peter Van Puyvelde ◽  
Paula Moldenaers
Keyword(s):  
Shear Flow ◽  
Viscosity Ratio ◽  
Single Droplets ◽  
Transient Shear Flow

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.

Transient shear flow of fluids with deformable microstructure

1973 ◽  
Vol 18 (1-2) ◽  
pp. 1-20 ◽  
Author(s):  
S. J. Allen ◽  
K. A. Kline ◽  
C. C. Ling
Keyword(s):  
Shear Flow ◽  
Transient Shear Flow

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.

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.

scholarly journals Dynamics of sheared droplets filled with non-Brownian particles

2020 ◽  
Vol 59 (12) ◽  
pp. 935-949
Author(s):  
Helene Van Ammel ◽  
Paula Moldenaers ◽  
Ruth Cardinaels
Keyword(s):  
Bulk Viscosity ◽  
Particle Concentration ◽  
Viscosity Ratio ◽  
Viscous Medium ◽  
Particle Sizes ◽  
Droplet Dynamics ◽  
Brownian Particles ◽  
Homogenous Medium ◽  
Single Droplets ◽  
Good Agreement

AbstractThe dynamics of single droplets containing non-Brownian particles are studied. The particle over droplet size ratio (r/R) is changed by using different particle sizes (r/R = 0.02–0.4). Additionally, the effect of particle concentration (5–20 vol%) is investigated. The dynamics of droplets with r/R = 0.02 show good agreement with the corresponding particle-free reference system which has a comparable viscosity ratio. Hence, this droplet phase can be considered as a homogenous medium characterized by its bulk viscosity which is governed by the particle concentration. However, droplets with r/R ≥ 0.1 show a more suppressed deformation and slower transient dynamics and, therefore, behave as a slightly more viscous medium than expected based on their bulk viscosity. These effects become more pronounced at higher particle concentrations and higher r/R. Moreover, local particle effects like asymmetric droplet shapes, oscillating droplet shapes, and tip streaming start to influence the droplet dynamics at particle concentrations around 15 vol%.

Transient shear flow behavior of polymeric fluids according to the Leonov model

1981 ◽  
Vol 20 (5) ◽  
pp. 443-457 ◽  
Author(s):  
R. K. Upadhyay ◽  
A. I. Isayev ◽  
S. F. Shen
Keyword(s):  
Shear Flow ◽  
Flow Behavior ◽  
Polymeric Fluids ◽  
Leonov Model ◽  
Transient Shear Flow

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.

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