The geometry used in calculating the disturbance velocity at caused by a point force at . The calculation includes the first image sources at and which cancel the normal velocity of the source at the top and bottom walls. Additional force dipoles and stress doublets are needed to cancel the tangential velocities at the walls.
Distribution of the center-of-mass for pressure-driven flow only. (a) Results from the theory neglecting gradients in the diffusivity. (b) Results of numerical simulations reported by Usta et al. (Ref. 4). Results are plotted between the bounding wall at and centerline of the channel.
Mechanism for migration away from the wall due to shear flow. The flow field aligns and stretches the dumbbell. The spring force, which is in tension, generates a disturbance flow and a net velocity away from the no-slip boundary.
Distribution of the center-of-mass for pressure-driven flow only. Theoretical results including the gradient in the diffusivity.
Distribution of center-of-mass for an external force when there is no imposed flow field . (a) Results from the theory and (b) results from numerical simulations by Usta et al. (Ref. 8) are shown.
Mechanism for migration away from the wall due to an external force . The external force rotates a dumbbell to an orientation which results in a drift away from the wall, as shown in (c). For example, a dumbbell perpendicular to the wall (a) rotates towards alignment with the wall, whereas a dumbbell parallel with the wall (b) rotates away from the wall.
Distribution for the external force and flow field acting in conjunction. (a) Results from the theory are plotted at different for the case of and (b) results of numerical simulations (Ref. 8) with are shown for comparison.
The shear flow results in a preferred orientation of the polymer similar to that shown. When acting in the direction of flow, the external force (solid arrow) lifts the center-of-mass upwards (away from the wall) with velocity . The force, acting counter to the flow (dashed arrow), results in a drift downwards (towards the wall). Note that this mechanism does not depend upon hydrodynamic interaction with the bounding walls.
Distribution for an applied external force and imposed flow field acting in opposition. (a) Results of the theory for four different numbers at and (b) numerical results (Ref. 8) with are shown.
Distribution for the electrophoretic and pressure-driven flow acting in conjunction. Results are shown for (a) and (b) .
Distribution for the electrophoretic and pressure-driven flow acting in opposition. Results are shown for (a) and (b) .
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