Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session H26: Suspensions: Theory and Modeling |
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Chair: James Swan, Assistant Professor, Dept. of Chemical Engineering, MIT Room: E146 |
Monday, November 21, 2016 10:40AM - 10:53AM |
H26.00001: Rapid Calculation of Thermal Forces in Coarse Grained Simulation of Colloidal Particles James Swan, Andrew Fiore, Aleksander Donev, Florencio Balboa In the presented work, we will demonstrate a spectrally accurate method for calculation of thermal forces in implicit solvent simulations of soft materials such as colloidal dispersions. For implicit solvent models, the stochastic forces must be drawn from a normal distribution whose covariance is a complicated function of the particle configuration. For a system of interacting $N$ particles, drawing a single sample requires $O(N^3)$ operations, if numerically exact techniques from linear algebra are employed. So-called “fast” methods can approximate the sampling with roughly $O(N^m log N)$ computational complexity, where m is a coefficient greater than one which depends on the configuration of the particles. The computational complexity of the presented approach is $O(N (log N)^{d/(d+3)})$, where $d$ is the fractal dimension of the particulate structures being modeled. Remarkably, this new approach adapts to the structure of the material under study by leveraging the algebraic structure of Ewald summation and balancing the computational effort spent evaluating near-field and far-field contributions to the hydrodynamic interactions among the suspended particles. Applications of this approach to modeling colloidal gelation and particulate suspensions will be discussed. [Preview Abstract] |
Monday, November 21, 2016 10:53AM - 11:06AM |
H26.00002: Effect of weak fluid inertia upon Jeffery orbits Jonas Einarsson We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the “Jeffery orbits.” We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. At small shear Reynolds numbers the preferred Jeffery orbit is tumbling for prolate spheroids, and log-rolling for moderately oblate particles (aspect ratio $\lambda > 1/7.3$). For thinner oblate particles both log-rolling and tumbling are stable, separated by an unstable limit cycle. [Einarsson, J., Candelier, F., Lundell, F., Angilella, J. R. and Mehlig, B., PoF 27 063301 (2015)] We solved this long-standing problem by considering the symmetries that constrain the solution. In this case the symmetries reduced the problem to only four scalar integrals. Here I introduce an alternative method that accounts for the symmetries and tensorial nature of the governing equations, enables perturbative calculation of Stokes' equations, and is suitable for computer algebra. [Einarsson, J., and Mehlig, unpublished (2016)] [Preview Abstract] |
Monday, November 21, 2016 11:06AM - 11:19AM |
H26.00003: A Generalized Frictional and Hydrodynamic Model of the Dynamics and Structure of Dense Colloidal Suspensions Joao Maia, Arman Boromand, Brandy Grove, Safa Jamali We perform mesoscopic DPD simulations incorporating both hydrodynamic and frictional interparticle interactions to study the effect of interaction potential on the rheology and structure of dense frictional colloidal suspensions. In particular, we performed a series of viscosity and normal stress measurements in suspensions with different volume fractions and obtained, for the first time, a complete picture of the dynamic state and of the microstructure. We confirmed that N$_{\mathrm{1}}$ for semi-dense suspensions stays negative and grows with shear rate, which is consistent with hydrocluster-induced shear-thickening. We show that CST in colloidal suspensions can be explained solely via hydrodynamics, frictional bonds being transient and negligible to the rheological response. In dense suspensions and close to the jamming transition however, friction is required to obtain DST and replicate the recently experimental findings of a transition from negative to positive N$_{\mathrm{1}}$. We prove that hydroclusters form first at low stresses; this brings the particles together, thus allowing frictional contacts to develop, eventually leading to DST. In addition, when each particle is subject to an average of one frictional contact, N$_{\mathrm{1}}$ reverses its increase but remains negative; at approximately two frictional contacts, a percolating network forms and N$_{\mathrm{1}}$ becomes positive. [Preview Abstract] |
Monday, November 21, 2016 11:19AM - 11:32AM |
H26.00004: A particle-particle collision strategy for arbitrarily shaped particles at low Stokes numbers Mohsen Daghooghi, Iman Borazjani We present a collision strategy for particles~with any general shape at~low Stokes numbers. Conventional collision strategies rely upon a short -range repulsion force along particles centerline, which is a suitable choice for spherical particles~and may not work for complex-shaped particles.~~In the present method, upon the collision of two particles, kinematics of particles are modified so that particles have zero relative velocity toward each other along the direction in which they have the minimum distance. The advantage of this novel technique is that it guaranties to prevent particles from overlapping without unrealistic bounce back at low Stokes numbers, which may occur if repulsive forces are used. This model is used to simulate sedimentation of many particles in a vertical channel and suspensions of non-spherical particles under simple shear flow. [Preview Abstract] |
Monday, November 21, 2016 11:32AM - 11:45AM |
H26.00005: The Bretherton Problem for a Vesicle Joseph Barakat, Andrew Spann, Eric Shaqfeh The motion of a lipid bilayer vesicle through a circular tube is investigated by singular perturbation theory in the limit of vanishing clearance. The vesicle is treated as a sac of fluid enclosed by a thin, elastic sheet that admits a bending stiffness. It is assumed that the vesicle is axisymmetric and swollen to a near-critical volume such that the clearance ``e" between the membrane and the tube wall is very small. In this limit, bending resistance is of negligible importance compared to the isotropic tension, allowing the vesicle to be treated as a ``no-slip bubble." The effective membrane tension is found to scale inversely with ``e" raised to the 3/2 power with a comparatively weak Marangoni gradient. The extra pressure drop is found to have a leading contribution due to the cylindrical midsection, which scales inversely with ``e," as well as a correction due to the end caps, which scales inversely with the square root of ``e." The apparent viscosity is predicted as a unique function of the geometry. The theory exhibits excellent agreement with a simplified, ``quasi-parallel" theory and with direct numerical simulations using the boundary element method. The results of this work are compared to those for bubbles, rigid particles, and red blood cells in confined flows. [Preview Abstract] |
Monday, November 21, 2016 11:45AM - 11:58AM |
H26.00006: Time evolution of shear-induced particle margination and migration in a cellular suspension Qin M. Qi, Eric S.G. Shaqfeh The inhomogeneous center-of-mass distributions of red blood cells and platelets normal to the flow direction in small vessels play a significant role in hemostasis and drug delivery. Under pressure-driven flow in channels, the migration of deformable red blood cells at steady state is characterized by a cell-free or Fahraeus-Lindqvist layer near the vessel wall. Rigid particles such as platelets, however, “marginate” and thus develop a near-wall excess concentration. In order to evaluate the role of branching and design suitable microfluidic devices, it is important to investigate the time evolution of particle margination and migration from a non-equilibrium state and determine the corresponding entrance lengths.\\ From a mechanistic point of view, deformability-induced hydrodynamic lift and shear-induced diffusion are essential mechanisms for the cross-flow migration and margination. In this talk, we determine the concentration distribution of red blood cells and platelets by solving coupled Boltzmann advection-diffusion equations for both species and explore their time evolution. We verify our model by comparing with large-scale, multi-cell simulations and experiments. Our Boltzmann collision theory serves as a fast alternative to large-scale simulations. [Preview Abstract] |
Monday, November 21, 2016 11:58AM - 12:11PM |
H26.00007: Dispersion of solids in fracturing flows of yield stress fluids Sarah Hormozi, Ian Frigaard Solids dispersion is an important part of hydraulic fracturing. Whereas many frac fluids are low-viscous others transport solids through increased viscosity. In this context, one method for influencing both dispersion and solids carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows and make estimates of the streamwise dispersion in various relevant scenarios. [Preview Abstract] |
Monday, November 21, 2016 12:11PM - 12:24PM |
H26.00008: Dynamics of magnetic particles suspended in Newtonian fluids under magnetic field Mingyang Tan, Travis Walker Anisotropic structures are commonly found in natural materials. Researchers are committed to developing meta-materials that mimic natural materials by introducing anisotropic filler particles. These materials can exhibit enhanced magnetic, mechanical, optical, and diffusive properties. In this study, a magnetic field is used to align magnetic oblate spheroids. We present an analytic solution based on a single-particle Stokes-flow model that describes the planar alignment of the particle in a rotating magnetic field. The analytic solution covers the full range of the magnetic field frequency agreeing well with our experimental results. Asymptotic solutions are also developed at both the high-frequency and the low-frequency limits of the field. The induced dipole of each particle can create its own magnetic field that can interact with neighboring particles, causing particles to aggregate. Different structures of particles are formed depending on the characteristics of the field, i.e., one-dimensional columns of particles in a constant field and two-dimensional sheets of particles in a rotating field. To simulate the realistic dynamics of the phenomena, we include hydrodynamic interactions between the particles via Stokesian dynamics. [Preview Abstract] |
Monday, November 21, 2016 12:24PM - 12:37PM |
H26.00009: Particle cage dynamics in flowing colloidal dispersions Stephanie Marenne, Jeffrey F. Morris The idea of the particle in a suspension at rest being trapped in a cage formed by its neighbors, widely used to understand glassy suspensions, has been applied to freely flowing suspensions. Stokesian Dynamics, a discrete particle simulation, is used to simulate the flow of monodisperse colloidal hard sphere suspensions. The cage analogy is useful to study the nonlinear stress in the material during start-up of shear flow, where the neighbor cage deforms and breaks, and during oscillatory shear flow where, depending on the amplitude of oscillation, the particle is trapped inside the cage or escapes during the oscillation cycle. A precise statistical definition of the cage in terms of the nearest neighbor ring in the pair distribution function is developed. We examine the dependence of the cage dynamics on the volume fraction of particles and the Peclet number $Pe$, the ratio between shear and Brownian forces. Under flow, the cage is found to break at quite definite positions, and the structural distortion is found to be clearly related to the shear and normal stress response. The shear strain needed to break the neighbor cage depends on $Pe$ as Brownian motion enhances the total deformation. A simple model captures the strain at the stress overshoot for start-up of steady shear. [Preview Abstract] |
Monday, November 21, 2016 12:37PM - 12:50PM |
H26.00010: Diffusion nearby elastic cell membranes Abdallah Daddi-Moussa-Ider, Achim Guckenberger, Stephan Gekle The physical approach of a small particle to the cell membrane represents the crucial step before active internalization and is governed by Brownian diffusion. Using a fully analytical theory, we show that the stretching and bending of cell membranes induces a long-lived subdiffusive behavior on the nearby particle (1,2). Such behavior is qualitatively different from the normal diffusion in a bulk fluid or near a hard-wall. the scaling exponent of the mean-square displacement can go as low as 0.87 in the perpendicular and 0.92 in the parallel direction. Moreover, we investigate the hydrodynamic interaction between two particles finding that the steady motion of two particles towards an elastic membrane possessing only shearing resistance leads to attractive interaction in contrast to the hard-wall case where the interaction is known to be repulsive. Our analytical predictions are compared with boundary-integral simulations where an excellent agreement is obtained (3). \\ \\ References \\ (1) Daddi-Moussa-Ider, A., Guckenberger, A. and Gekle, S., Phys. Rev. E 93, 012612 (2016) \\ (2) Daddi-Moussa-Ider, A., Guckenberger, A. and Gekle, S., Phys. Fluids 28, 071903 (2016) \\ (3) Daddi-Moussa-Ider, A. and Gekle, S., J. Chem. Phys., 145, 014905 (2016) [Preview Abstract] |
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