Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session D15: General Fluid Dynamics: Viscous Flows |
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Chair: Longhua Zhao, Case Western Reserve University Room: 203 |
Sunday, November 22, 2015 2:10PM - 2:23PM |
D15.00001: Volume effect for particles transported in highly viscous fluids Longhua Zhao For various shapes and sizes, particles are treated differently in the fluid system. The level complexity of models needs to be determined to capture the sufficient physical phenomena and such a decisions is based on the assessment of the volume effect. This study is to measure the effect of a non-zero volume spherical particle transported in highly viscous flows. Utilizing the regularized Stokeslet method, particles are studied in three different approaches: a passive fluid tracer at the center of the particle, a sphere with Fax\'{e}n's correction, and a detailed non-zero volume particle. We compare the discrepancies in velocity field, Lagrangian trajectory and force exerted on the particle with three approaches and provide qualitative information for future studies. [Preview Abstract] |
Sunday, November 22, 2015 2:23PM - 2:36PM |
D15.00002: Slow viscous flow of two particles in a cylindrical tube Xin Yao, Teck Neng Wong, - Marcos The slow viscous flow around two particles in a cylindrical tube is obtained theoretically. We employ the Lamb's general solution based on spherical harmonics and cylindrical harmonics to solve the flow field around the particles and the flow within the tube, respectively. We compute the drag and torque coefficients of the particles which are dependent on the distance among the cylinder wall and the two particles. The hydrodynamic forces are also a function of particle velocities and background velocity. Our results are in agreement with the existing theory of a single particle traveling in the tube when the distance between the two particles increases. We found that particle-particle interactions can be neglected when the separation distance is three times larger than the sum of particles radii. Furthermore, such analysis can give us insights to understand the mechanisms of collision and aggregation of particles. [Preview Abstract] |
Sunday, November 22, 2015 2:36PM - 2:49PM |
D15.00003: Deformation of an Elastic beam due to Viscous Flow in an Embedded Channel Network Yoav Matia, Amir Gat Elastic deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotic applications. In this work, we analyze the time dependent interaction between elastic deformation of a slender beam and viscous flow within a long serpentine channel, embedded in the elastic structure. The channel is positioned asymmetrically with regard to the midplane of the elastic beam, and thus pressure within the channel creates a local moment deforming the beam. We focus on creeping flows and small deformations of the elastic beam and obtain, in leading order, a convection--diffusion equation governing the pressure-field within the serpentine channel. The beam time-dependent deformation is then obtained as a function of the pressure-field and the geometry of the embedded network. This relation enables the design of complex time-dependent deformation patterns of beams with embedded channel networks. Our theoretical results were illustrated and verified by numerical computations. [Preview Abstract] |
Sunday, November 22, 2015 2:49PM - 3:02PM |
D15.00004: Transient Dynamics of Elastic Hele-Shaw Cell due to External Forces with Application to Impact Mitigation Arie Tulchinsky, Amir Gat We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid plate and an elastic plate. The elastic plate is under the influence of an externally applied time varying force acting perpendicular to its surface. We model the flow in the narrow gap via the lubrication approximation, and the plate by the Kirchhoff-Love plate theory. The viscous-elastic interaction yields a governing 6$^{\mathrm{th}}$-order linear partial differential equation. We obtain a semi-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation. [Preview Abstract] |
Sunday, November 22, 2015 3:02PM - 3:15PM |
D15.00005: Non-linear dynamics of annular creeping flow enclosed by an elastic membrane Shai Elbaz, Amir Gat This study deals with the fluid-structure-interaction problem of longitudinal annular flow about a varying cross-section centre-body enclosed by an elastic membrane. The gap between the centre-body and membrane wall may be initially filled with a thin fluid layer or devoid of it. We employ elastic shell theory and the lubrication approximation and obtain a forced nonlinear diffusion equation governing the problem. In the case of an advancing liquid front in an initially unpenetrated interface (viscous peeling) the governing equation degenerates into a forced porous medium equation, for which several closed-form solutions can be obtained. Based on self-similarity we define propagation laws for the fluid-elastic interaction which in turn provide the basis for numerical investigation of compound solutions such as pulse trains and other waveforms. The presented interaction between viscosity and elasticity may be applied to fields such as soft-robotics and micro-scale or larger swimmers by allowing for the time-dependent control of a compliant boundary. [Preview Abstract] |
Sunday, November 22, 2015 3:15PM - 3:28PM |
D15.00006: A note on the breathing mode of an elastic sphere in Newtonian and complex fluids Vahe Galstyan, On Shun Pak, Howard Stone Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [Pelton et al., ``Viscoelastic flows in simple liquids generated by vibrating nanostructures,'' Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere in a compressible viscous fluid and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. [Preview Abstract] |
Sunday, November 22, 2015 3:28PM - 3:41PM |
D15.00007: Dragging cylinders in slow viscous flows Elena Luca, Darren Crowdy The so-called ``dragging problem'' in slow viscous fluids is an important basic flow with many applications. In two dimensions, the Stokes paradox means there is no solution to the dragging problem for a cylinder in free space. The presence of walls changes this; the solutions exist, but are not easy to find without purely numerical methods. This talk describes new ``transform methods'' that produce convenient, semi-analytical solutions to dragging problems for cylinders in various geometries. We apply the techniques to low-Reynolds-number swimming where dragging problem solutions can be combined with the reciprocal theorem to compute swimmer dynamics in confined domains. [Preview Abstract] |
Sunday, November 22, 2015 3:41PM - 3:54PM |
D15.00008: Slender Ribbon Theory Lyndon Koens, Eric Lauga Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. Here we determine asymptotically the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical surface located inside the ribbon. Our derivation agrees very well with the known hydrodynamics of long flat ellipsoids, and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems. [Preview Abstract] |
Sunday, November 22, 2015 3:54PM - 4:07PM |
D15.00009: Temperature Variations in Lubricating Films Induced by Viscous Dissipation Farshad Mozaffari, Ralph Metcalfe We have studied temperature distributions of lubricating films. The study has applications in tribology where temperature-reduced viscosity decreases load carrying capacity of bearings, or degrades elastomeric seals. The viscosity- temperature dependency is modeled according to ASTM D341-09. We have modeled the film temperature distribution by our finite element program. The program is made up of three modules: the first one solves the general form of Reynolds equation for the film pressure and velocity gradients. The other two solve the energy equation for the film and its solid boundary temperature distributions. The modules are numerically coupled and iteratively converged to the solutions. We have shown that the temperature distribution in the film is strongly coupled with the thermal response at the boundary. In addition, only thermal diffusion across film thickness is dominant. Moreover, thermal diffusion in the lateral directions, as well as all the convection terms, are negligible. The approximation reduces the energy equation to an ordinary differential equation, which significantly simplifies the modeling of temperature --viscosity effects in thin films. [Preview Abstract] |
Sunday, November 22, 2015 4:07PM - 4:20PM |
D15.00010: Reflections on Lorentz: revisiting image systems for Stokes flows in a half-space William Mitchell, Saverio Spagnolie Green's functions, whether singular or regularized, have found wide use in the analysis and simulation of viscous flows. In problems where there is a significant hydrodynamic effect from a flat no-slip boundary, an image system is added to the free-space Green's function to obtain a bounded version which vanishes on the wall. We show how the Lorentz reflection theorem may be used to obtain these image systems. This approach is simple and leads to convenient formulas, and moreover generalizes two recent methods for developing wall-bounded flows, one using regularized singularities, and the other using a Papkovich-Neuber potential. A numerical ``method of stresslet images'' is also discussed and applied to problems in wall-bounded sedimentation and biolocomotion. [Preview Abstract] |
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