An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow

The effect of particle-particle contact on the stress of a suspension of small spheres in plane strain flow is investigated. We provide an analytic form for the particle pair distribution function in the case of no Brownian motion, and calculate the viscosity and normal stress difference based on this. We show that the viscosity is reduced by contact, and a normal stress difference induced, both at order c(2) for small particle volume concentration c. In addition, we investigate the effect of a small amount of diffusion on the structure of the distribution function, giving a self-consistent form for the density in the O(aPe(-1)) boundary layer and demonstrating that diffusion reduces the magnitude of the contact effect but does not qualitatively alter it

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

The dilation-free semi-staggered finite volume method presented in Sabin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown Copyright (C) 2007 Published by Elsevier B.V. All rights reserved

Competition and interaction of polydisperse bubbles in polymer foams

The e®ects of interactions between bubbles of di®erent sizes during bubble growth in a polymeric foam are investigated. Two models are used: a two-dimensional sim-ulation in which both the e®ects of gas di®usion through the polymer and bubble interactions through °uid stresses are included, and a three-dimensional model in which bubbles are assumed to interact only through direct competition for gas, and di®usion of gas into the bubbles is instantaneous. In the two-dimensional model, two di®erent bubble sizes are used in a hexagonal array. For slow gas di®usion, the additional polymer stresses have little e®ect on the ¯nal bubble size distribution. For faster gas di®usion the growth occurs in two phases, just as was found in earlier work for isolated bubbles: an initial rapid viscous phase and a later phase controlled by the rate of polymer relaxation. In this later phase, polymers in the windows between neighbouring bubbles become highly stretched and these regions of high stress determine the dynamics of the growth. In the three-dimensional model we consider the e®ects of rheology on a pair of di®erent-sized spherical bubbles, interacting only through competition for available gas. Viscoelastic e®ects result in a wider distribution of bubble volumes than would be found for a Newtonian °uid. Key words: Polymeric °uid; bubble growth; foam; bubble interactions; size distribution ¤ To whom correspondence should be addressed

Macroscopic effects of microscopic roughness in suspensions

We study a model suspension consisting of a monolayer of identical spheres in a viscous medium without Brownian effects. In the absence of inertia, and under the influence of finite forces, perfectly smooth spheres will never come into contact because of the strength of the lubrication interaction. Indeed, an interaction between two spheres is perfectly reversible. However, this ideal is not achieved in practice: careful experiments with just two spheres show that some irreversible interaction occurs. We treat this interaction as a simple contact between the spheres: we assume that they are microscopically rough and have surface asperities which are too sparse to affect the hydrodynamics of the system, but which prevent the particles from approaching beyond some nominal surface separation. For a dilute suspensions in steady shear flow, a calculation to order c squared in the particle area concentration shows that roughness actually lowers the viscosity of the suspension relative to its value for smooth spheres; this is because the excluded parts of configuration space are those with very close particles, where the lubrication layers cause high dissipation. Negative normal stress differences are also introduced by the roughness. At higher concentrations we use Stokesian Dynamics to simulate the suspension dynamics. We find that roughness increases the viscosity above an area concentration of around 40% and the normal stress differences become very sensitive to particle configuration, and fluctuate strongly with time

Stokes flow past three spheres

In this paper we present a numerical method to calculate the dynamics of three spheres in a quiescent viscous fluid. The method is based on Lamb’s solution to Stokes flow and the Method of Reflections, and is arbitrarily accurate given sufficient computer memory and time. It is more accurate than multipole methods, but much less efficient. Although it is too numerically intensive to be suitable for more than three spheres, it can easily handle spheres of different sizes. We find no convergence difficulties provided we study mobility problems, rather than resistance problems. After validating against the existing literature, we make a direct comparison with Stokesian Dynamics (SD), and find that the largest errors in SD occur at a sphere separation around 0.1 radius. Finally, we present results for an example system having different-sized spheres

Macroscopic effects of microscopic roughness in suspensions

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We study a model suspension consisting of a monolayer of identical spheres in a viscous medium without Brownian effects. In the absence of inertia, and under the influence of finite forces, perfectly smooth spheres will never come into contact because of the strength of the lubrication interaction. Indeed, an interaction between two spheres is perfectly reversible. However, this ideal is not achieved in practice: careful experiments with just two spheres show that some irreversible interaction occurs. We treat this interaction as a simple contact between the spheres: we assume that they are microscopically rough and have surface asperities which are too sparse to affect the hydrodynamics of the system, but which prevent the particles from approaching beyond some nominal surface separation. For a dilute suspensions in steady shear flow, a calculation to order c(2) in the particle area concentration shows that roughness actually lowers the viscosity of the suspension relative to its value for smooth spheres; this is because the excluded parts of configuration space are those with very close particles, where the lubrication layers cause high dissipation. Negative normal stress differences are also introduced by the roughness. At higher concentrations we use Stokesian Dynamics to simulate the suspension dynamics. We find that rough- ness increases the viscosity above an area concentration of around 40% and the normal stress differences be- come very sensitive to particle configuration, and fluctuate strongly with time

Rolie-Poly fluid flowing through constrictions: Two distinct instabilities

Elastic instabilities of entangled polymer melts are common in industrial processes but the physics responsible is not well understood. We present a numerical linear stability study of a molecular based constitutive model which grants us physical insight into the underlying mechanics involved. Two constriction flows are considered – one shear dominated, the other extension dominated – and two distinct instabilities are found. The influence of the molecular structure and the behaviour of the polymer dynamics are investigated and in both cases chain relaxation and orientation play a crucial role. This suggests a molecular-based physical interpretation of the underlying mechanisms responsible for flow instabilities

Simulations of a heavy ball falling through a sheared suspension

In recent experiments, Blanc et al. (J Fluid Mech 746:R4, 2014) dropped a heavy sphere through a concentrated suspension of smaller, neutrally buoyant particles. They found that the application of a lateral oscillatory shear flow caused the heavy ball to fall faster on average, and that for highly concentrated suspensions, at certain moments of the cycle of shear oscillation, the heavy ball moved upwards. We use Stokesian Dynamics to model these experiments and other related scenarios. We show how the motion of the heavy particle and the microstructure of the suspension depend on two key dimensionless parameters: the frequency of the oscillations (relative to a typical settling time) and the strength of repulsive interparticle forces, relative to the buoyancy-adjusted weight of the heavy ball. We offer a mechanism which describes some of the observed behaviours: the formation and breakup of vertical repulsion chains