Lateral migration of flexible fibers in Poiseuille flow between two parallel planar solid walls

Abstract

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 z c, 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 .

Symmetry breaking and cross-streamline migration of three-dimensional vesicles in an axial Poiseuille flow

“…It is found in Ref. [48] that flexible enough fibers (corresponding, in some sense, to large C a in our language) have a terminal finite position out of center. Increasing the bending stiffness of the fiber (equivalent to decreasing the C a ) moves the terminal position further away from the center until the effects of the wall start to play an important role (Fig.…”

“…4 of Ref. [48]). Removing the wall allows the very stiff fibers (equivalent to small C a limit) to migrate further away (Fig.…”

“…Let us make some comments on migration of fibers in a Poiseuille flow [47,48]. Similarly to the case of droplets, the simplest model of a fiber depends on two control parameters: the capillary number (based on the bending modulus of the fiber) and the aspect ratio of the fiber relating the length to the thickness of the fiber.…”

“…6, where the terminal position of the slipper moves away from the center of the flow as the capillary number is decreased. Another common point with the work [48] is that increasing the nonsphericity of the object, i.e., increasing the length to thickness ratio of the fiber or decreasing the reduced volume of the vesicle leads to the terminal position moving further from the center of the flow for the same value of capillary number. For a proper comparison, we need to note that the thickness of the fiber was used as a unit of length in [47,48], while here we use the volume-equivalent radius of the vesicle to rescale the distances; this difference affects the scaling of both the capillary number and the terminal position but the main conclusion remains valid.…”

“…6 have λ = 1 and are tank treading. Second, the flow used in [47,48] was actually a planar Poiseuille flow and not the axial one used here. Whether the observed similarities are a consequence of a general rule or are just a coincidence is still an open question.…”