Stability of the tank treading modes of erythrocytes and its dependence on cytoskeleton reference states

2015 ◽  
Vol 771 ◽  
pp. 449-467 ◽  
Author(s):  
Zhangli Peng ◽  
Sara Salehyar ◽  
Qiang Zhu
Keyword(s):  
Capillary Number ◽  
Shear Flows ◽  
Structural Model ◽  
Viscosity Ratio ◽  
Reference State ◽  
Central Plane ◽  
Cell Dynamics ◽  
Mode 2 ◽  
Linear Shear ◽  
A Cell

We studied the tank treading motion of an erythrocyte (red blood cell, or RBC) in linear shear flows by using a boundary-element fluid-dynamics model coupled with a multiscale structural model of the cell. The purpose was to investigate the correlation between the reference (stress-free) state of the cytoskeleton and the cell dynamics in shear flows with relatively high capillary numbers. We discovered that there exist two distinctive modes of tank treading, mode 1 and mode 2. In mode 1 the membrane elements originating from the dimple areas keep close to the central plane, whereas in mode 2 these elements remain near the farthermost locations from the central plane. Mode 1 is also characterized by significantly higher breathing and swinging oscillations. During tank treading one mode may become unstable and switch to the other. Their stability depends on the viscosity ratio and the capillary number. At a fixed viscosity ratio, when the capillary number is increased the cell experiences sequentially a region dominated by mode 2, a mode 1/mode 2 bistable region and a region dominated by mode 1. More profoundly, these regions are highly sensitive to the reference state of the cytoskeleton. For example, compared with a cell with a biconcave reference state, a cell with a spheroidal reference state features a much smaller region dominated by mode 2. This finding may guide experiments to identify the actual reference state of these cells.

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.

Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

2021 ◽  
Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr
Keyword(s):  
Porous Medium ◽  
Dynamic Viscosity ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Immiscible Fluids ◽  
Pore Scale ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.

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.

Stability of linear shear flows in shallow water

1995 ◽  
Vol 303 ◽  
pp. 203-214 ◽  
Author(s):  
Charles Knessl ◽  
Joseph B. Keller
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Special Functions ◽  
Rigid Wall ◽  
Eigenvalue Equation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Shear ◽  
The Stability ◽  
Rigid Walls

The stability or instability of various linear shear flows in shallow water is considered. The linearized equations for waves on the surface of each flow are solved exactly in terms of known special functions. For unbounded shear flows, the exact reflection and transmission coefficients R and T for waves incident on the flow, are found. They are shown to satisfy the relation |R|2= 1+ |T|2, which proves that over reflection occurs at all wavenumbers. For flow bounded by a rigid wall, R is found. The poles of R yield the eigenvalue equation from which the unstable mides can be found. For flow in a channel, with two rigid walls, the eigenvalue equation for the modes is obtained. The results are compared with previous numerical results.

scholarly journals Study on Lift Force acting on Single Drops in Linear Shear Flows

2007 ◽  
Vol 2 ◽  
pp. 55-62 ◽  
Author(s):  
Kohei OGAWA ◽  
Win MYINT ◽  
Shigeo HOSOKAWA ◽  
Akio TOMIYAMA
Keyword(s):  
Lift Force ◽  
Shear Flows ◽  
Linear Shear

scholarly journals Nature and dynamics of overreflection of Alfvén waves in MHD shear flows

2014 ◽  
Vol 80 (5) ◽  
pp. 667-685
Author(s):  
D. Gogichaishvili ◽  
G. Chagelishvili ◽  
R. Chanishvili ◽  
J. Lominadze
Keyword(s):  
Shear Flows ◽  
Alfven Waves ◽  
Wave Number ◽  
Alfvén Waves ◽  
Transient Growth ◽  
Mean Velocity ◽  
Linear Dynamics ◽  
Linear Shear ◽  
Basic Physics ◽  
Cascade Processes

Our goal is to gain new insights into the physics of wave overreflection phenomenon in magnetohydrodynamic (MHD) nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, U0=(Sy,0,0), that contain two different types of Alfvén waves. These waves are reduced to pseudo- and shear-Alfvén waves when wavenumber along Z-axis equals zero (i.e. when kz=0). Therefore, for simplicity, we labeled these waves as: P-Alfvén and S-Alfvén waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetrically coupled with P-AWs; S-AWs do not participate in the linear dynamics of P-AWs, (3) the transient growth of S-AWs is somewhat smaller compared with that of P-AWs, (4) the linear transient processes are highly anisotropic in wave number space, (5) the waves with small streamwise wavenumbers exhibit stronger transient growth and become more balanced, (6) maximal transient growth (and overreflection) of the wave energy occurs in the two-dimensional case – at zero spanwise wavenumber.To the end, we analyze nonlinear consequences of the described anisotropic linear dynamics – they should lead to an anisotropy of nonlinear cascade processes significantly changing their essence, pointing to a need of revisiting the existing concepts of cascade processes in MHD shear flows.

111 Drag and Lift Forces Acting on Single Drops in Linear Shear Flows

2009 ◽  
Vol 2009.84 (0) ◽  
pp. _1-11_
Author(s):  
Hiroyuki HIGASHINO ◽  
Daiki ISHII ◽  
Shigeo HOSOKAWA ◽  
Akio TOMIYAMA
Keyword(s):  
Shear Flows ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift
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