Abstract
Dynamics of non-Brownian flexible fibers in Poiseuille flow between two parallel planar solid walls is evaluated from the Stokes equations which are solved numerically by the multipole method. Fibers migrate towards a critical distance from the wall zc, which depends significantly on the fiber length N and bending stiffness A. This effect can be used to sort fibers. Three types of accumulation are found, depending on a shear-to-bending parameter Γ. In the first type, stiff fibers deform only a little and accumulate close to the wall, where their tendency to drift away from the channel is balanced by the repulsive hydrodynamic interaction with the wall. In the second type, flexible fibers deform significantly and accumulate far from the wall. In both types, the fiber shapes at the accumulation positions are repeatable, while in the third type, they are very compact and non-repeatable. The difference between the second and third accumulation types is a special case of the difference between the regular and irregular modes for the dynamics of migrating fibers. At the regular mode, far from walls, the fiber tumbling frequency satisfies Jeffery's expression, with the local shear rate and the aspect ratio close to N.
Highlights
Dynamics of flexible fibers in simple shear and Poiseuille flows has been analyzed theoretically, numerically and experimentally in numerous publications [1,2,3,4,5,6,7,8,9,10,11,12]
For non-Brownian systems, the key question is under what conditions there exist off-center distances from microchannel walls where flexible fibers tend to accumulate, what are their values, and how they depend on the fiber size, aspect ratio and flexibility
We have considered dynamics of fibers, which are immersed in a low-Reynolds-number Poiseuille flow between two parallel planar solid walls at z = 0 and z = h, and are initially aligned with the flow
Summary
Dynamics of flexible fibers in simple shear and Poiseuille flows has been analyzed theoretically, numerically and experimentally in numerous publications [1,2,3,4,5,6,7,8,9,10,11,12]. Fluid flows in microchannel devices often take place at low-Reynolds-numbers In such systems, Brownian rigid rods migrate towards the wall [13, 14], and flexible fibers to an off-center position [24,25,26,27]. For non-Brownian systems, the key question is under what conditions there exist off-center distances from microchannel walls where flexible fibers tend to accumulate, what are their values, and how they depend on the fiber size, aspect ratio and flexibility. The importance of this problem is straightforward.
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