Modeling of Flexible Fiber Motion and Orientation in Simple Shear Flow: A Comparison Between the Rod-Chain Model and Jeffery’s Equation

2010 ◽  
Author(s):  
Cong Zhang ◽  
David A. Jack
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Chain Model ◽  
Shearing Flow ◽  
Flexible Fiber ◽  
Fiber Motion ◽  
Blind Area ◽  
Jeffery’S Equation

This paper compares results from the the rod-chain model with those from results based on Jeffery’s equation. A concept of critical buckle aspect ratio is employed to define the rigidity or flexibility of a fiber, above which point a fiber is flexible enough to be bent and twisted. When a fiber has an aspect ratio less than the critical buckle aspect ratio, fiber motion predicted by the rod-chain model corresponds perfectly with that of Jeffery’s equation. The trajectories of a single rigid fiber with different initial orientations are shown by the rod-chain model, which are in line with what Jeffery’s equation predicts. Results are also shown for the configuration of a single flexible fiber at various times under a pure shearing flow. The “blind area” of the rod-chain model is discussed.

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.

Investigation of fiber motion near solid boundaries in simple shear flow

2001 ◽  
Vol 40 (3) ◽  
pp. 296-306 ◽  
Author(s):  
Kelli B. Moses ◽  
Suresh G. Advani ◽  
Andreas Reinhardt
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Fiber Motion

Two-dimensional long-flexible fiber simulation in simple shear flow

2015 ◽  
Vol 37 (8) ◽  
pp. 2425-2433 ◽  
Author(s):  
Gleb Meirson ◽  
Andrew N. Hrymak
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Flexible Fiber

Rigid ring-shaped particles that align in simple shear flow

2013 ◽  
Vol 722 ◽  
pp. 121-158 ◽  
Author(s):  
Vikram Singh ◽  
Donald L. Koch ◽  
Abraham D. Stroock
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Shear Flow ◽  
Simple Shear ◽  
Low Reynolds Number ◽  
Simple Shear Flow ◽  
Rigid Ring ◽  
Axis Of Symmetry ◽  
Low Reynolds ◽  
Axes Of Symmetry

AbstractMost rigid, torque-free, low-Reynolds-number, axisymmetric particles undergo a time-periodic tumbling motion in a simple shear flow, with their axes of symmetry following a set of closed Jeffery orbits. We have identified a class of rigid, ring-like particles whose axes of symmetry instead reach a permanent alignment near the velocity gradient direction with the plane of the particle aligning near the flow–vorticity plane. An asymptotic analysis for small particle aspect ratio (ratio of length parallel to the axis of symmetry to diameter perpendicular to the axis) shows that an appropriate asymmetry of the ring cross-section with a thinner outer edge and thicker inner edge leads to a tendency to rotate in a direction opposite to the vorticity; this tendency can balance the usual rotation rate associated with the finite thickness of the particle. Boundary integral computations for finite particle aspect ratios are used to determine the conditions of aspect ratio and degree of asymmetry that lead to the aligning behaviour and the final orientation of the axis of symmetry of the aligned particles. The aligning particle follows an equation of motion similar to the Leslie–Erickson equation for the director of a small-molecule nematic liquid crystal. However, whereas the alignment of the director arises from intermolecular interactions, the ring-like particle aligns solely due to its intrinsic rotational motion in a low-Reynolds-number flow.

The distortion of a flexible inextensible thread in a shearing flow

1976 ◽  
Vol 74 (2) ◽  
pp. 317-333 ◽  
Author(s):  
E. J. Hinch
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Stokes Flow ◽  
Equations Of Motion ◽  
Simple Shear Flow ◽  
Qualitative Behaviour ◽  
Slender Body Theory ◽  
Shearing Flow ◽  
Numerical Studies ◽  
Body Theory

Using the slender-body theory for Stokes flow, the equations of motion are developed for a small flexible inextensible thread. The nearly straight thread is examined analytically, and is shown to straighten rapidly. In a simple shear flow the distortions decay less rapidly, but rapidly enough not to rotate the thread through the plane of flow. Numerical studies of simple shear with more substantially distorted threads show the same qualitative behaviour. Additionally some differences are revealed in the nonlinear regime between the buckling and stretching processes which occur in the compressive and tensile quadrants of the flow.

Emulsification of particle loaded drops in simple shear flow

2015 ◽  
Vol 470 ◽  
pp. 179-187 ◽  
Author(s):  
Tobias Merkel ◽  
Julius Henne ◽  
Lena Hecht ◽  
Volker Gräf ◽  
Elke Walz ◽  
...  
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow

scholarly journals Do Protein Molecules Unfold in a Simple Shear Flow?

2006 ◽  
Vol 91 (9) ◽  
pp. 3415-3424 ◽  
Author(s):  
Juan Jaspe ◽  
Stephen J. Hagen
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Protein Molecules
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