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 H2: Suspensions: Theory and Modeling |
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Chair: Joao Maia, Case Western Reserve University Room: 101 |
Monday, November 23, 2015 10:35AM - 10:48AM |
H2.00001: Non-equilibrium tuning of attractive colloidal gels Arman Boromand, Joao Maia In colloidal gel systems, the presence of multiple interactions in multiple length scales such as Van der Waals, depletion attractions, and electrostatic repulsions makes these systems challenging from both experimental and simulation aspects. Recently, there has been growing interest to tune and manipulate the structural and dynamics properties of those systems without adjusting interparticle interactions, just by taking them out of equilibrium. In this work, we used Core-Modified Dissipative Particle Dynamics (CM-DPD) with a modified depletion potential, as a coarse-grain model to address the gel formation process in short ranged-attractive colloidal suspensions for a range of volume fractions and attraction strengths. It is suggested that at high volume fractions and near the glass transition, there is a transformation from non-bonded glass to bonded-glass for which that the effect of topological frustration (caging) will be alleviated by the presence of attractive potentials (bonding) i.e. melting during cooling. In the first part of the presentation, we discuss our similar findings for semi-dilute volume fraction of attractive bimodal colloidal gels at equilibrium, which can be explained through local densification of attractive colloidal gels. In the second part, structural and dynamics properties of arrested gels will be studied under shear and after cessation of shear to study how the different flow profiles and history will alter final morphology of the gel systems. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H2.00002: Constitutive upscaling of MR fluids Grigor Nika, Bogdan Vernescu We consider a suspension of solid magnetizable particles in a viscous fluid with an applied external magnetic field. We assume the fluid to be electrically non-conducting. Thus, we use the quasi-static Maxwell equations coupled with the Stokes equations to capture the magnetorheological effect. We upscale using two scale asymptotic expansions to obtain the effective equations consisting of a coupled nonlinear system in a connected phase domain as well as the new constitutive laws. Qualitative properties of the solution of this nonlinear system are studied. [Preview Abstract] |
Monday, November 23, 2015 11:01AM - 11:14AM |
H2.00003: Hydrodynamically interacting particles confined by a spherical cavity via dynamic simulation: a model for intracellular transport Christian Aponte-Rivera, Yu Su, Roseanna Zia We study the short- and long-time self-diffusion of hydrodynamically interacting colloids enclosed within a spherical cavity as a model for intracellular transport. Prior models of such behavior began with a single enclosed particle; attempts to enlarge such models to many particles have seen limited success owing to the challenges of accurately modeling many-body far-field and singular near-field hydrodynamic interactions. To overcome these difficulties we have developed a new set of hydrodynamic mobility functions to couple particle motion with hydrodynamic force moments which, when inverted and combined with near-field resistance functions form a complete coupling tensor that accurately captures both far-field and near-field physics, for an arbitrary number of particles enclosed by a spherical cavity of arbitrary relative size. The mobility functions are implemented into a Stokesian dynamics framework, and particle motion obtained via dynamic simulation. We present results for a range of volume fractions from dilute to concentrated, and a range of particle-to-cavity size ratios, where an interplay between entropic restriction and hydrodynamic entrainment give rise to novel diffusive behavior. Results are compared to experiments with excellent agreement. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H2.00004: Mean and Fluctuating Force Distribution in a Random Array of Spheres Georges Akiki, Thomas Jackson, Sivaramakrishnan Balachandar This study presents a numerical study of the force distribution within a cluster of mono-disperse spherical particles. A direct forcing immersed boundary method is used to calculate the forces on individual particles for a volume fraction range of [0.1, 0.4] and a Reynolds number range of [10, 625]. The overall drag is compared to several drag laws found in the literature. As for the fluctuation of the hydrodynamic streamwise force among individual particles, it is shown to have a normal distribution with a standard deviation that varies with the volume fraction only. The standard deviation remains approximately 25{\%} of the mean streamwise force on a single sphere. The force distribution shows a good correlation between the location of two to three nearest upstream and downstream neighbors and the magnitude of the forces. A detailed analysis of the pressure and shear forces contributions calculated on a ghost sphere in the vicinity of a single particle in a uniform flow reveals a mapping of those contributions. The combination of the mapping and number of nearest neighbors leads to a first order correction of the force distribution within a cluster which can be used in Lagrangian-Eulerian techniques. We also explore the possibility of a binary force model that systematically accounts for the effect of the nearest neighbors. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H2.00005: A continuum theory for two-phase flows of particulate solids: application to Poiseuille flows Davide Monsorno, Christos Varsakelis, Miltiadis V. Papalexandris In the first part of this talk, we present a novel two-phase continuum model for incompressible fluid-saturated granular flows. The model accounts for both compaction and shear-induced dilatancy and accommodates correlations for the granular rheology in a thermodynamically consistent way. In the second part of this talk, we exercise this two-phase model in the numerical simulation of a fully-developed Poiseuille flow of a dense suspension. The numerical predictions are shown to compare favorably against experimental measurements and confirm that the model can capture the important characteristics of the flow field, such as segregation and formation of plug zones. Finally, results from parametric studies with respect to the initial concentration, the magnitude of the external forcing and the width of the channel are presented and the role of these physical parameters is quantified. [Preview Abstract] |
Monday, November 23, 2015 11:40AM - 11:53AM |
H2.00006: The hydrodynamic lift on a slender, neutrally buoyant fiber in a wall bounded shear flow at small Reynolds number Johnson Dhanasekaran, Donald Koch The hydrodynamic lift velocity of a neutrally buoyant fiber in a simple shear flow near a wall is determined for small fiber Reynolds number. The generalized reciprocal theorem is used to relate the lift velocity to the Stokes flow generated by the fiber. This Stokes velocity field is determined using slender-body theory with the no slip velocity at the wall enforced using the method of images. This study is among the first analytical treatments of the lift on a non-spherical particle and illustrates how particle shape can contribute to separation methods such as those in microfluidic channels or cross-flow filtration processes. To leading order the lift velocity at distances large compared with the fiber length and small compared with the Oseen length is found to be 0.029*(rho*gamma$^{2}$*L$^{2}$*d)/(nu*ln(2*L/d)) where L and d are the half-fiber length and diameter, gamma is the shear rate and nu is the kinematic viscosity of the fluid. When the fiber separation from the wall is less than the fiber half-length a process of pole vaulting coupled with inertially induced changes of fiber orientation determine the lift velocity. [Preview Abstract] |
Monday, November 23, 2015 11:53AM - 12:06PM |
H2.00007: Flipping and scooping of curved 2D rigid fibers in simple shear: the Jeffery equations Darren Crowdy The dynamical system (or ``Jeffery equations'') governing the orbits of a curved rigid two-dimensional fiber in simple shear is derived in analytical form. The study is motivated by the need to understand the dynamics of isolated non-axisymmetric rod-like particles in simple flows for use in suspension modeling. Solutions of the dynamical system are shown to display the ``flipping'' and ``scooping'' recently observed in computational studies of three-dimensional fibers using linked rigid rod and bead-shell models [Wang {\em et al.}, {\em Phys. Fluids}, {\bf 24}, (2012)]. Indeed the equations we derive are expected to be the same ones governing curved 3D slender fibers executing motions in the plane of shear. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H2.00008: Periodic dynamics of pairs of sedimenting discs Rahul Chajwa, Narayanan Menon, Sriram Ramaswamy We study the sedimentation in the Stokes regime of pairs of discs released with a variety of orientations relative to each other and to gravity. The orientation of a settling disk is coupled with the translational degree of freedom. Hydrodynamic interactions between settling disks produces richer dynamics than is possible with sedimenting spheres [S. Jung et al., PRE 74, 035302 (2006), S. Kim, Int J Multiphase Flow 11, 699 (1985), Goldfriend et al. http://arxiv.org/abs/1502.00221]. We demonstrate the classes of dynamics that follow from a variety of initial conditions, but focus on the periodic oscillations in position and orientation that result when two discs are released parallel to each other with their normals coaxial and in the horizontal plane. We report experiments that study the frequency, wavelength, and amplitude of the periodic flutter as a function of initial separation between the discs. We analyze the motions within a model that combines the hydrodynamics of single discs with a simplified model of their interaction that includes low order terms of appropriate symmetry. This allows us to examine the initial conditions that demarcate periodic from non-periodic dynamics. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H2.00009: Brownian motion of a particle with arbitrary shape Eligiusz Wajnryb, Bogdan Cichocki, Maria L. Ekiel-Jezewska We consider a single Brownian particle of an arbitrary shape, in general non-axisymmetric. Starting from the Smoluchowski equation we develop a new formalism, which allows to determine the particle rotational and translational motion in a much simpler way as this which is based on the Euler angles and Wigner functions. Our approach makes use of the rotational matrix and irreducible tensors. The essential result of our presentation is that using our new formalism, we derive simple explicit analytical expressions for the cross-correlations of the Brownian translational and rotational displacements. The role of the particle mobility center is determined and discussed. No such formulas have been known yet - instead, numerical Brownian simulations have been extensively used. We compare our analytical results with low Reynolds number experiment and numerical simulations performed at the time scales comparable with the characteristic time of the rotational Brownian diffusion. [Preview Abstract] |
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