Session BE: Suspensions I

Diffusivity in Simulated Suspensions of Deformable Particles using the Lattice-Boltzmann Method

Diffusion of particles and molecules in suspension flow plays a vital role in many biological and industrial processes. In the paper industry, adequate mixing of pigments during the coating process is essential. In blood flow, diffusion of molecules plays an important role in cell response. For example, transport of NO and reactive oxygen species affects endothelial cell function. In the present study, simulations couple elastic finite-element particles to a lattice-Boltzmann fluid model. This study compares the diffusivities found in suspensions of rigid and deformable particles in wall bounded shear flow.   

An osmotic method to measure particle normal stress in a sheared suspension

A method for measurement of the normal stress response in a sheared liquid-solid suspension of noncolloidal particles under low-Reynolds-number conditions is described. The approach is based on the osmotic concept in which the normal stress associated with the dispersed solid phase is determined by a measurement of the continuous liquid pressure. To demonstrate the method, results are presented from a case in which solid spherical particles are suspended in an equal density and highly viscous Newtonian liquid and subjected to shearing in a concentric cylinder Couette geometry. The key idea is to allow a connection of the suspending liquid to an external bath of the liquid while the particles are constrained to remain in the sheared zone by a screen. Using this design, two means of accessing the shear-rate dependent ``particle pressure'' (actually the radial normal stress, with independent normal stress difference measurements providing evidence of a mean isotropic particle stress) are presented. The first relies on the hydrostatic balance which occurs when liquid is sucked into the sheared zone and measuring the change in level of the bath; the second is more quantitative and simply uses a pressure transducer in the liquid bath outside the screen. The normal stress is found to be roughly linear in shear rate and strongly dependent on particle volume fraction over the range of 35-52{\%} solids studied.   

Oscillatory shear of suspensions of noncolloidal particles

Noncolloidal suspensions undergoing unsteady shear flow present unique behavior not observed under steady shear conditions. To understand the dynamics of suspensions in unsteady shear flow, the rheological behavior under oscillatory flow conditions was studied using experiments and simulations. Experiments were performed to evaluate the stress as a function of the total strain. The rheology has a strong dependence on the applied strain amplitude. The complex viscosity decreased with total strain for high strain amplitudes and increased for low strain amplitudes. The transition point at which the qualitative behavior changed occurred at an amplitude-to-gap ratio between 0.1 and 0.5. The observed results were independent of the shear cell geometry, suggesting that shear-induced particle migration was unimportant and that the observed behavior was instead due to changes in the suspension microstructure. To investigate the microstructure at various strain amplitudes, Stokesian dynamics simulations of bounded suspensions undergoing oscillatory shear flow were performed. A similar dependence of the shear stress on the applied strain amplitude is observed. To identify the relevant mechanism for the observed behavior, the strain evolution of the pair distribution function was calculated. Although particles remain in close contact for all strain amplitudes, there is a strong dependence of the angular pair distribution function which results in the observed changes in shear stress with applied strain amplitude.   

Experimental investigation of particle interaction in Couette flow

We present an experimental investigation of the interaction of two spherical particles in stratified, effectively two-dimensional shear flow inside a Couette cell. The motion is very slow (Reynolds number $R < 0.1$). The experiment is performed with particles of 3 different types of surface texture, to find if particle surface roughness has any effect on the interaction. Particles are initially inserted into the Couette cell close to each other under reliably repeatable initial conditions, and their subsequent motion is driven by the inner rotating cylinder of the cell. In the experiment, this cylinder is repeatedly rotated by the same angle clockwise and counterclockwise, allowing to assess any irreversibility brought upon by the interaction of particles. The collected particle coordinates are analyzed statistically. The experiments provide a benchmark for the analytical and numerical solutions of the general problem of particle interaction in shear flow.   

Hydrodynamic interactions of two particles in confined linear shear flow

The interactions between two solid bodies in a confined shear flow at finite Reynolds number are studied using lattice-Boltzmann numerical solutions of the Navier-Stokes equations. For generic initial conditions two classes of trajectory are found, in which the bodies either repel or bypass each other, depending on their starting spanwise separation and the shear rate. If the particles are initially well separated, a nearly fixed state on the centerline is observed up to a certain Reynolds number, beyond which the centerline is unstable and the shear flow carries the particles apart. Moreover, we find that the motion of one particle relative to a fixed one is qualitatively similar to that of two mobile particles, and that particles move independently when separated by at least several channel widths.   

Shear Induced Diffusivity of spherical and non-spherical particles

The shear induced diffusivity due to two-particle interactions of spherical and non-spherical particles is studied to better understand the consequences of irreversibility and symmetry- breaking for shear-induced diffusion. The diffusivity of spheres, rods, and branched particles is computed by integrating the mean square displacement upon collisions. An approximate upper bound for the diffusivity is calculated by assuming that the particles leave the collision at their maximum separation. Different sources of irreversibility between the two particles are used. For spheres the irreversibilities considered are: surface roughness, repulsive force and electrostatic interaction; for the non spherical particles the diffusivity is calculated in the purely hydrodynamic case and also with a repulsive force between beads belonging to different particles. It is found that spheres are much more sensitive to the irreversibility when compared to the other particles. At small repulsion, when the range of the repulsive force $r_{c}$ is $10^ {-6}$ the particle radius, the shape of the particle has a large impact on the shear induced diffusivity, and therefore particles with broken symmetry have diffusivities that are up to five orders of magnitude larger than the ones of spheres. At high repulsion, $r_{c} = 10^{-1}$, all particles have diffusivities with the same order of magnitude.   

Is there a threshold for irreversibility in sheared suspensions?

Recent experiments (Pine \emph{et al.}, Nature 2005) have identified a finite-shear amplitude transition to irreversible motion for the particles in a periodically sheared suspension -- apparent evidence for the finite-shear-amplitude onset of chaotic dynamics. We present an alternative explanation in which the irreversibility persists down to arbitrarily weak shear amplitudes, highlighting the roles played by long-lived clusters of particles in near-contact and by the particular conditions under which the experimental system is prepared.