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Nov 2007

Volume 19, Issue 11, Articles (11xxxx)

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Phys. Fluids 19, 114108 (2007); http://dx.doi.org/10.1063/1.2800371 (11 pages)

J. P. Kubitschek and P. D. Weidman
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back to top Viscous and Non-Newtonian Flows

Kinetic theory of a confined polymer driven by an external force and pressure-driven flow

Jason E. Butler, O. Berk Usta, Rahul Kekre, and Anthony J. C. Ladd

Phys. Fluids 19, 113101 (2007); http://dx.doi.org/10.1063/1.2801409 (14 pages) | Cited 10 times

Online Publication Date: 6 November 2007

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Kinetic theory is used to investigate the mechanisms causing cross-stream migration of confined polymers and polyelectrolytes under the influence of external forces and flow fields. Numerical simulations and experiments have demonstrated that confined polymers migrate towards the center of the channel in response to both external forces and uniaxial flows. Yet, migration towards the walls has been observed with combinations of external force and flow. In this paper, the kinetic theory for an elastic dumbbell developed by Ma and Graham [Phys. Fluids 17, 083103 (2005)] has been extended to account for the effects of an external force. Further modifications account for counterion screening within a Debye-Hückel approximation. This enables qualitative comparison with experimental results [ Zheng and Yeung, Anal. Chem. 75, 3675 (2003) ] on DNA migration under combined electric and pressure-driven flow fields. The comparison supports the contention [ Long et al., Phys. Rev. Lett. 76, 3858 (1996) ] that the hydrodynamic interactions in polyelectrolytes decay algebraically, as 1/r3, rather than exponentially. The theory qualitatively reproduces results of both simulations and experiments for the migration of neutral polymers and polyelectrolytes. Concentration profiles similar to those found in numerical simulations are observed, but the Peclet numbers differ by factors of 2–3.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.57.Ng Polymers and polymer solutions
36.20.-r Macromolecules and polymer molecules
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Two-dimensional Stokes flow driven by elliptical paddles

Stephen M. Cox and Matthew D. Finn

Phys. Fluids 19, 113102 (2007); http://dx.doi.org/10.1063/1.2789970 (12 pages) | Cited 3 times

Online Publication Date: 6 November 2007

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A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.
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47.11.-j Computational methods in fluid dynamics
47.32.Ef Rotating and swirling flows
47.52.+j Chaos in fluid dynamics

Drift in supported membranes

Ashok Prasad, Jané Kondev, and Howard A. Stone

Phys. Fluids 19, 113103 (2007); http://dx.doi.org/10.1063/1.2805843 (5 pages) | Cited 1 time

Online Publication Date: 19 November 2007

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An object moving in a fluid transports the fluid along the direction of its motion. Using the concept of drift, i.e., the net motion of a small volume of fluid or a tracer particle due to a moving body, we quantify this entrainment for an inclusion in a supported lipid bilayer membrane. Our analysis demonstrates that a moving object in a supported membrane transports a small volume of fluid by a significant distance only when the initial position of the fluid volume in question is within a distance ξ from the line of motion, where ξ is the screening length of the membrane. The total area swept out by a line of such fluid volume elements, initially at rest and oriented perpendicular to the direction of motion, is the drift area. We show that the drift area is related quadratically to the screening length. These calculations suggest that dynamic domains of entrained lipids of size ξ form spontaneously around moving objects in supported membranes due to hydrodynamic interactions. This effect is potentially important for transport processes in biological and artificial membranes.
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82.39.Wj Ion exchange, dialysis, osmosis, electro-osmosis, membrane processes
87.14.Cc Lipids
47.55.Kf Particle-laden flows

Hydrodynamic studies on two traveling wavy foils in tandem arrangement

Jian Deng, Xue-Ming Shao, and Zhao-Sheng Yu

Phys. Fluids 19, 113104 (2007); http://dx.doi.org/10.1063/1.2814259 (10 pages) | Cited 5 times

Online Publication Date: 26 November 2007

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In this study, the hydrodynamic interactions between two tandem foils undergoing fishlike swimming motion are investigated numerically by solving the Navier–Stokes equations with the immersed-boundary method. The two foils represent two tandem propellers attached on a concept ship. The thrusts and efficiencies at three typical Strouhal numbers, i.e., St = 0.4, 0.6, and 0.8, are investigated. The results show that a fish situated directly behind another one does not always undergo a lower thrust. Whether it experiences a thrust enhancement or reduction depends on the Strouhal number. At a relatively low Strouhal number (e.g., St = 0.4), the usual wake drag-reduction effect predominates over the drag-enhancement effect caused by the reverse von Kármán vortices, resulting in a thrust enhancement. The opposite happens at a relatively high Strouhal number (e.g., St = 0.8). The downstream fish can benefit from the upstream one by slalom between the vortices rather than through them. For the upstream fish, the thrusts and efficiencies for all Strouhal numbers studied are higher than those for a single fish when the two fish are closely spaced, and approach those for a single fish as the spacing is increased.
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47.85.Dh Hydrodynamics, hydraulics, hydrostatics
47.32.-y Vortex dynamics; rotating fluids
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