Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session MV: Suspensions I |
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Chair: Andreas Acrivos, City College of CUNY Room: Hyatt Regency Long Beach Regency B |
Tuesday, November 23, 2010 8:00AM - 8:13AM |
MV.00001: Microstructure in Concentrated Sheared Dispersions Jeff Morris, Ehssan Nazockdast This work describes a theory for predicting microstructure of concentrated colloidal hard spheres as a function of P\'eclet number $Pe = 6\pi \eta \dot{\gamma} a^3/kT$ and particle volume fraction, $\phi$; $\dot{\gamma}$ is the shear rate, $a$ is the particle radius, $\eta$ is fluid viscosity and $kT$ is the thermal energy. We study the pair distribution using the pair Smoluchowski equation. Many-body effects in the conservation equation were then formulated self-consistently through probabilistic third-particle integrals, with emphasis on capturing the interaction of flow and excluded volume effects. The resulting integro-differential equation was solved iteratively. Comparison between theory predictions and simulation results show that the theory is able to predict known near-equilibrium ($Pe\ll1$) and dilute-suspension large-$Pe$ results. The approach accurately predicts the major features of microstructure at concentrated $\phi$ under strong shear, which differentiates it from previous theoretical work. Rheological quantities of shear stress, normal stress differences, and particle pressure are computed from the structure. [Preview Abstract] |
Tuesday, November 23, 2010 8:13AM - 8:26AM |
MV.00002: Bulk Rheology of Noncolloidal Deformable Fiber Suspension Mubashar Khan, Minh Do-Quang, Gustav Amberg, Jingshu Wu, Cyrus Aidun The effect of fiber flexibility and shear rate on microstructure and rheology of fibers suspended in Newtonian fluid is investigated with direct numerical simulation based on the external boundary force lattice-Boltzmann method (Wu and Aidun, \textit{Int. J. Multiphase Flow}, 36 (3) March 2009). It is shown that the fiber bending ratio (BR), which is proportional to the fiber elastic modulus divided by dynamic viscosity and shear rate, has significant influence on rheology. For fiber suspension under shear, the relative viscosity decreases significantly as BR increases. The primary normal stress difference undergoes a minimum at a critical BR value and increases rapidly as BR decreases further (Wu and Aidun. \textit{J. Fluid Mech}., to appear 2010). In previous studies, the effect of shear rate on bulk rheology at a constant BR and volume fraction has remained unclear. In this study, we show that the ratio of viscosity for deformable (BR=0.25) to rigid fibers for volume fraction 0.05 may reach a maximum at a critical shear rate. We explain this behavior in terms of fiber orientation distribution and fiber-fiber interaction. [Preview Abstract] |
Tuesday, November 23, 2010 8:26AM - 8:39AM |
MV.00003: Normal stresses in non-Brownian suspensions: bulk rheology and particle migration Francois Boyer, Olivier Pouliquen, Elisabeth Guazzelli Concentrated suspensions are known to exhibit non-Newtonian effects and classical rheology often fails to give a consistent description of actual flows. Particle migration has been shown to be the main reason for both thixotropic effects and inhomogeneous microstructure of sheared suspensions, and is thus of primary interest for applications. The suspension balance model relates the particle migration to the suspension normal stresses and is therefore a consistent set of constitutive equations. Recently, this model has been revisited and other mechanisms have been proposed. In that context, an experimental study that characterize both normal stresses and particle migration independently is of great interest. We report measurements of normal stress differences in concentrated suspensions of non-Brownian spheres thanks to a rotating-rod rheometer. Normal stresses are experimentally shown to vanish below a critical volume fraction of 0.22: this could therefore indicate a non-hydrodynamic origin of macroscopic normal stresses. Furthermore, the time-dependent behaviour of the system is the signature of particle migration: comparisons with theoretical predictions allows to test quantitatively particle migration models. [Preview Abstract] |
Tuesday, November 23, 2010 8:39AM - 8:52AM |
MV.00004: Experimental study of structure and rheology of concentrated colloidal suspensions Xiang Cheng, Jonathan McCoy, Jacob Israelachvili, Itai Cohen We investigate the three-dimensional flow structure and rheology of concentrated colloidal suspensions in a newly designed plane shear cell. Using fast confocal microscopy, we optically probe the dynamics of colloidal suspension under shear with single particle resolutions. The rheological properties of the suspensions are also measured simultaneously. Hence, a direct correlation between the microstructure and the rheology of the suspensions is obtained in our experiments. Three regimes are observed with increasing shear rate. At low shear rates where the Brownian motion of particles dominates, the structure of the suspensions is indistinguishable from that at equilibrium. At intermediate shear rates, colloidal particles form sliding layers normal to the shear gradient direction, but keep a disordered structure within the layers. Along with this transition, the suspensions shear thins dramatically. At even higher shear rates, particles in the layers organize into a novel structure -- strings of particles perpendicular to the shear direction. We speculate that this structure may be a precursor to the hydroclusters observed in shear thickening suspensions. [Preview Abstract] |
Tuesday, November 23, 2010 8:52AM - 9:05AM |
MV.00005: Irreversibility and Chaos: Role of Long Range Hydrodynamic Interactions in Sheared Suspensions Bloen Metzger, Jason E. Butler Non-Brownian particles suspended in an oscillatory shear flow are studied numerically. In these systems it is often assumed that chaos(due to the long-range nature of the hydrodynamic interaction between particles) plus noise (contact or roughness) lead to irreversible behavior. However, we demonstrate that the long-range hydrodynamic interactions are not a source, nor even a magnifier, of irreversibility when coupled with non-hydrodynamic interactions. [Preview Abstract] |
Tuesday, November 23, 2010 9:05AM - 9:18AM |
MV.00006: Direct measurement of a normal stress in a sheared suspension Jerome Martin, Georges Gauthier, Stephen Garland, Angelique Deboeuf, Jeffrey Morris A method was recently proposed (Deboeuf \textit{et al.}, Phys. Rev. Lett., 2009), to measure the shear-induced ``particle pressure'' in a sheared non-colloidal suspension. The ``particle pressure'' was obtained in a Couette device through the liquid pressure, measured behind a grid permeable to the fluid but impermeable to the particles, placed at the outer cylindrical wall of the device. The liquid pressure is equal to the (vertical) component of the particle stress, in the direction of the vorticity. It gives a good estimation of the particle pressure, assuming the shear-induced particle stress is nearly isotropic. The apparatus enables also the measurement of the total pressure at the outer wall. Coupled with the grid pressure, the latter measurement gives access to the radial component of the particle stress. Our collected data demonstrate that anisotropy does exist, with a normal stress one order of magnitude lower than the particle pressure. [Preview Abstract] |
Tuesday, November 23, 2010 9:18AM - 9:31AM |
MV.00007: Rolling and resuspension of a particle for explanation of Shields diagram Hyungoo Lee, S. Balachandar Recent research (Zeng et al. 2009, Lee \& Balachandar 2010) has shown that both the shear- and wall-induced lift contributions on a particle sharply increase as the gap between the wall and the particle is decreased. Explicit expressions that are valid over a range of finite Re were obtained for the drag and lift forces in the limiting cases of a stationary particle in wall-bounded linear flow and of a particle translating parallel to a wall in a quiescent ambient. Here we consider the more general case of a translating and rotating particle in a wall-bounded linear shear flow where shear, translational and rotational effects superpose. We have considered a modest Reynolds number range of 1-100. Direct numerical simulations using immersed boundary method were performed to systematically figure out the characteristics of hydrodynamic forces on a finite-sized particle moving while almost in contact with a wall. We present composite correlation for the hydrodynamic forces which are in agreement with all the available low-Reynolds- number theories. Also, obtained lift, drag and torque are used to explain the Shields diagram. [Preview Abstract] |
Tuesday, November 23, 2010 9:31AM - 9:44AM |
MV.00008: Instability of settling non-spherical particle in a vertical shear flow Dewei Qi, Donald Koch, Ganesh Subramanian Two mechanisms are attributed to the cross-stream migration when fiber settles in a vertical shear flow. First, a particle may migrate toward streamlines of the imposed shear flow with smaller downward fluid velocities, due to relative translation of the particle and fluid, called the Saffman effect. Second, a non-spherical particle at finite Reynolds number will attempt to rotate with its long body along the horizontal direction due to inertial torque. On the other hand, the torque due to the imposed weak vertical shear flow rotates the non-spherical in the opposite direction. The dynamic balance between the two torques may lead to a small angle between the particle long body and horizontal plane and may drive the particle migrate toward the streamlines of the shear flow with the large downward fluid velocity. The second mechanism was recently proposed by Shin, Koch and Subramanian.A fiber with aspect ratio $\kappa=2$, 1.6, 1.2 1.1 and 0 is used to study the lateral migration. It is shown that at a given shear and aspect ratio, fiber lateral migration can be divided into three phases depending on the Reynolds number. The simulation results identified the lateral migration phase diagram and confirm the second mechanism. [Preview Abstract] |
Tuesday, November 23, 2010 9:44AM - 9:57AM |
MV.00009: Anomalous diffusion of non-colloidal suspensions in a Couette flow Kyongmin Yeo, Martin R. Maxey The effects of wall-confinement on the dynamics and particle migration within concentrated non-colloidal suspensions in a Couette flow are investigated. We focus mainly on the shear-induced self-diffusion at 40\% volume fraction. The channel is divided into four zones depending on suspension microstructures and variances of the wall-normal and spanwise displacements for the particles in each zones are studied. Due to the strong spatial coherency, the suspended particles exhibit anomalous diffusion in the wall-normal direction. The diffusive behavior changes from superdiffusion for the particles next to the wall to subdiffusion for the particles near the core of the channel. The results indicate that the intermittent jumps and particle entrapment in particle layers are responsible for the anomalous diffusion near thewall, while the subdiffusion in the core is related with the restriction on the available lengthscale by the size of confinement. Diffusive behaviors of the particles in the core of the channel for four different volume fractions (25\%, 30\%, 35\%, and 40\%) are compared. For a channel of height $20D$, where $D$ is the particle diameter, the regular diffusive behavior in the core is observed for the volume fraction 40\%. [Preview Abstract] |
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