Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session A2: Suspensions: Theory and Modeling |
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Chair: Lorenzo Botto, Queen Mary University of London Room: 3002 |
Sunday, November 23, 2014 8:00AM - 8:13AM |
A2.00001: Does Suspension Crowding Screen Hydrodynamic Interactions? Roseanna Zia, James Swan, Yu Su Resistance and mobility functions describe linear couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, these functions are well known and have been applied directly in the solution of many important problems for dilute colloidal dispersions. We have devised a new stochastic technique to calculate an analogous set of functions for two spheres immersed in a suspension that are then used to model the near-equilibrium dynamics of concentrated dispersions, including viscoelasticity and long-time diffusion. Of interest is the degree of screening of hydrodynamic interactions by the intervening medium. We find that the mobility is unscreened at the pair level, even in suspensions of high concentration, confirming that hydrodynamic interactions are an essential part of the dynamics of crowded systems and cannot be neglected in favor of simple renormalization schemes. We compare our results for the hydrodynamic interactions between suspended particles to predictions from two-point microrheology. This technique can be used to infer the complex viscosity from long-ranged decay of the pair mobility in viscoelastic materials. Its validity when not in the continuum limit is addressed. [Preview Abstract] |
Sunday, November 23, 2014 8:13AM - 8:26AM |
A2.00002: Fluctuation, dissipation, and a non-equilibrium ``equation of state'' via nonlinear microrheology of hydrodynamically interacting colloids Henry Chu, Roseanna Zia In our recently developed non-equilibrium Stokes-Einstein relation for microrheology, we showed that, in the absence of hydrodynamic interactions, the stress in a suspension is given by a balance between fluctuation and dissipation. Here we generalize our theory to develop a simple analytical relation connecting diffusive fluctuation, viscous dissipation and suspension stress in systems of hydrodynamically interacting colloids. In active microrheology, a Brownian probe is driven through a complex medium. The strength of probe forcing compared to the entropic restoring force defines a Peclet number, \textit{Pe}. In the absence of hydrodynamics, normal stress differences scale as \textit{Pe}$^{4}$ and \textit{Pe} for weak and strong probe forcing, respectively. But as hydrodynamics become important, interparticle forces give way to lubrication interactions and the normal stresses scale as \textit{Pe}$^{2}$ and \textit{Pe}$^{\delta }$\textit{ln}(\textit{Pe}), where 0.773$\le \delta \le $1 as hydrodynamics vary from strong to weak. The new phenomenological theory is shown to agree with standard micromechanical definitions of the stress. A connection is made between the stress and an effective temperature of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a ``non-equilibrium equation of state.'' [Preview Abstract] |
Sunday, November 23, 2014 8:26AM - 8:39AM |
A2.00003: Effect of Amphiphiles on the Rheology of Triglyceride Networks Jyoti Seth Networks of aggregated crystallites form the structural backbone of many products from the food, cosmetic and pharmaceutical industries. Such materials are generally formulated by cooling a saturated solution to yield the desired solid fraction. Crystal nucleation and growth followed by aggregation leads to formation of a space percolating fractal-network. It is understood that microstructural hierarchy and particle-particle interactions determine material behavior during processing, storage and use. In this talk, rheology of suspensions of triglycerides (TAG, like tristearin) will be explored. TAGs exhibit a rich assortment of polymorphs and form suspensions that are evidently sensitive to surface modifying additives like surfactants and polymers. Here, a theoretical framework will be presented for suspensions containing TAG crystals interacting via pairwise potentials. The work builds on existing models of fractal aggregates to understand microstructure and its correlation with material rheology. Effect of amphiphilic additives is derived through variation of particle-particle interactions. Theoretical predictions for storage modulus will be compared against experimental observations and data from the literature and micro structural predictions against microscopy. Such a theory may serve as a step towards predicting short and long-term behavior of aggregated suspensions formulated via crystallization. [Preview Abstract] |
Sunday, November 23, 2014 8:39AM - 8:52AM |
A2.00004: Dissipative Particle Dynamics modeling of nanorod-polymer composites Shaghayegh Khani, Joao Maia Recent years have seen a plethora of experimental methods for fabricating nanorod-polymer composites with enhanced physical and mechanical properties. The macroscopic properties of the composites are directly related to the dispersion and organization of the nanoparticles in the matrix. For instance, a significant improvement in the properties of the nanorod-polymer composites is observed upon formation of a percolating network. Thus, controlling the structure of the nanoparticles in the matrix will advance the technology in the field. One way of doing this is by adjusting the chemical interactions which is done through grafting polymer chains on the surface of the rods. Although the enthalpic interactions play the major role in such systems other entropic variables such as the dimension of the rods, density of grafting and etc. may influence the final morphology of the system. The recent developments in the computational techniques have paved the road for further understanding of the controlled assembly of nanorods in polymer matrices. In this study, Dissipative Particle Dynamics (DPD) is employed in order to investigate the effect of enthalpic and entopic variables on the phase behavior of the nanorod-polymer composites. DPD is a coarse-grained mesoscale method which has been found very promising in simulating multi component systems. The interaction parameter between the components of the systems can be mapped onto the Flory-Huggins $\chi $-parameter via well-known Groot-Warren expression. The main goal of this work is to provide a phase diagram that can be used to guide the experiments in designing new materials. [Preview Abstract] |
Sunday, November 23, 2014 8:52AM - 9:05AM |
A2.00005: Simulation of particle sedimentation in the interface of a stretched capillary bridge Lorenzo Botto This talk examines the classical problem of particle sedimentation. In contrast to traditional studies focusing on bulk suspensions, we consider particles entrapped in nearly vertical fluid interfaces and sedimenting owing to gravity or a magnetic field. The interface shape corresponds to that of an axi-symmetric capillary bridge held captive between two parallel circular disks. A transport equation for the particle concentration field has been developed and coupled to the Navier-Stokes equation for the fluid; the resulting system solved numerically in the thin-thread approximation for small capillary and Reynolds numbers. The lower disk is stationary and the upper disk moves with an assigned velocity. The ratio of the settling to stretching velocities is varied. The competition between the sedimentation-induced particle flux and the extensional flow in the neck leads, for intermediate settling velocities, to the formation of a ``ring'' of high particle concentration; for sufficiently large settling velocities, the particles settle at the bottom of the bridge, potentially modifying the interface shape. These results may help understand the effect of body forces on interfacial tranport, with application to froth flotation processes and the stability of Pickering emulsions. [Preview Abstract] |
Sunday, November 23, 2014 9:05AM - 9:18AM |
A2.00006: The dynamics of orientable particles in simple shear flow Navaneeth Kizhakke Marath, Ganesh Subramanian In simple shear flow, in the Stokes limit, a spheroid rotates indefinitely in any of an infinite single parameter family of periodic orbits, called Jeffery orbits. We have recently used an analytical framework based on spheroidal harmonics to show that weak particle inertia at O(St) and weak fluid inertia at O(Re), St and Re being, respectively, the Stokes number and Reynolds number, lead to an irreversible drift across Jeffery orbits. The spheroid eventually adopts a tumbling or spinning mode, and for an oblate spheroid, the choice of mode depends on its initial orientation. The leading-order inertial corrections leave the time period of rotation (Tp) unchanged. We consider the effects of particle inertia at O(St$^{\mathrm{2}})$ and fluid inertia at O(Re$^{\mathrm{3/2}})$ on Tp using a reciprocal theorem formulation. It is shown that particle inertia at O(St$^{\mathrm{2}})$ results in a decrease in Tp. The fluid inertial contribution is singular in character, arising from the outer region at length scales of O(Re$^{\mathrm{-1/2}})$.This allows for a Fourier-space formulation, and the results for moderate- aspect-ratio spheroids show an increase in the Tp. The theoretical predictions are consistent with the results of recent simulations. [Preview Abstract] |
Sunday, November 23, 2014 9:18AM - 9:31AM |
A2.00007: The concentration instability of a sedimenting suspension of flexible fibers Harishankar Manikantan, Lei Li, Saverio Spagnolie, David Saintillan The stability of a dilute suspension of sedimenting flexible fibers is studied theoretically. Fiber compliance causes individual particles to reorient while sedimenting in a quiescent fluid. We incorporate the rate of reorientation for weakly flexible fibers into a mean-field model to study the stability of a suspension of such fibers to perturbations in concentration. Fiber flexibility is shown to have two opposing effects on suspension stability. First, it establishes a base state that is anisotropic in orientation distribution. We show that such a base state is more prone to a concentration instability than an isotropic distribution, and we illustrate the underlying mechanism. Second, the proclivity of particles to reorient due to flexibility hinders horizontal migration - a key ingredient of the instability mechanism - and suppresses the growth of concentration fluctuations. We analyze this effect by extending our theory to the next order in fiber flexibility, and indeed the growth rate of perturbations is shown to decrease for more compliant fibers. In a Brownian suspension, the dominant effect depends on the relative scales of rotational diffusion and flexibility-induced reorientation. [Preview Abstract] |
Sunday, November 23, 2014 9:31AM - 9:44AM |
A2.00008: Sedimentation of a flexible fiber in a weak vertical fluid flow Dewei Qi, Guowei He Lattice Boltzmann and lattice spring model is used to simulate the later al migration of a flexible fiber in a weak vertical fluid flow. Fiber aspect ratio, rigidity, sediment Reynolds number, and shear Reynolds number are varied. At a low Reynolds number, the fiber migrates to a lower fiber density area. In contrary, at a higher Reynolds number, the fiber migrates to a higher fiber density area. Effect of rigidity on lateral migration is studied. [Preview Abstract] |
Sunday, November 23, 2014 9:44AM - 9:57AM |
A2.00009: Structure and dynamics of a layer of sedimented microspheres near a horizontal planar wall Jerzy Blawzdziewicz, Adar Sonn, Haim Diamant, Eligiusz Wajnryb, Maria Ekiel-Jezewska, Yael Roichman Structure and dynamics of a sedimented layer of silica microspheres is investigated using computer simulations and confocal-microscopy measurements. The system is characterized by the particle area fraction $\phi_s$ and the dimensionless sedimentation parameter $l_0=k_BT/(mgd)$, where $k_BT$ is the thermal energy, $m$ is the buoyancy-corrected particle mass, $g$ is the gravitational acceleration, and $d$ is the particle diameter. The range $0<\phi_s<0.62$ and $l_0\approx 1.6$ is explored in our experiments. The near-wall particle distribution exhibits a layered structure, with the second layer developing at $\phi_s\approx0.4$. Particle distribution is well described by a phenomenological model that involves equilibration of a quasi-two dimensional chemical potential. The effective self-diffusivity of the first and second particle layer has been determined. We find that the suspension microstructure is significantly affected by particle polydispersity, whereas the self-diffusivity is only moderately affected. [Preview Abstract] |
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