Roberto Mauri

Shear-induced resuspension in a couette device

Abstract The viscous resuspension of an initially settled bed of particles resulting from the application of a laminar shear flow was studied experimentally in a narrow-gap Couette device. The measured height of the resuspended layer was found to be in excellent agreement with that predicted theoretically using a model developed by Leighton & Acrivos, in which the downward gravitational particle flux is balanced by a corresponding upward flux due to shear-induced particle diffusion.

Dispersion, convection, and reaction in porous media

The problem of transport of a reactive solute in a porous medium by convection and diffusion is studied for the case in which the solute particles undergo a first‐order chemical reaction on the surface of the bed. Assuming that the geometry is periodic, the method of homogenization is applied, showing explicitly that the effective equation is given by a Kramers–Moyal expansion, i.e., a partial differential equation of infinite order in which the nth term is the product of the nth gradient of the mean concentration by an nth‐order constant tensor. The effective values of reactivity, solute velocity, diffusivity, and of all the tensorial coefficients in the expansion are independent of the initial solute distribution and are expressed in terms of Peclet’s and Damkohler’s numbers, Pe=aV/D and Da=ak/D, respectively, where a is the cell size, V is the solvent mean velocity, D is the solute molecular diffusivity, and k is the surface reactivity, showing that they are independent of the initial solute distributi...

Dispersion and convection in periodic porous media

The problem of transport of a passive solute in a porous medium by convection and dispersion is analysed by the method of homogenization. Assuming that the geometry is periodic, the expressions for the macroscopic dispersion coefficients are derived. A few possible scalings are compared and we find that the most interesting one provides a local balance between drift and diffusion.

Longitudinal shear-induced diffusion of spheres in a dilute suspension

We present a calculation of the hydrodynamic self-diffusion coefficient of a tagged particle in a dilute mono-dispersed suspension of small neutrally buoyant spheres undergoing a steady simple shearing motion. The displacement of the tagged particle parallel to the longitudinal or streamwise direction resulting from a ‘collision’ with one other particle is calculated on the assumption that inertia and Brownian motion effects are negligible. Summing over different pairs leads to a logarithmically divergent integral for the diffusivity which is rendered finite by allowing for the cutoff due to the occasional presence of another pair of particles. The longitudinal shearinduced self-diffusion coefficient is thus found to be 0.267 a 2 γ{ c ln c −1 + O ( c )], where γ denotes the applied shear rate, a is the radius of the spheres and c their volume concentration.

The Transverse Shear-Induced Liquid and Particle Tracer Diffusivities of a Dilute Suspension of Spheres Undergoing a Simple Shear Flow

We study the shear-induced self-diffusion of both a liquid tracer and a tagged spherical particle along the directions perpendicular to the ambient flow in a dilute suspension of neutrally buoyant spheres undergoing a simple shearing motion in the absence of inertia and Brownian motion effects. The calculation of the liquid diffusivity requires the velocity of a fluid point under the influence of two spheres, which was determined via Lambs series expansion; conversely, the calculation of the particle diffusivity involves the trajectories of three spheres, which were determined using far-field and near-field asymptotic expressions. The displacements of the liquid tracer and of the tagged sphere were then computed analytically when the spheres and the tracer are all far apart, and numerically for close encounters. After summing over all possible encounters, the leading terms of the lateral liquid diffusion coefficients, both within and normal to the plane of shear, were thereby found to be 0.12γ a c and 0.004γ a c , respectively, where γ is the applied shear rate, a the radius of the spheres and c their volume fraction. The analogous coefficients of the lateral particle diffusivity were found to be 0.11γ a c , and 0.005γ a c , respectively. Also, liquid and particle diffusivities in a monolayer, with the liquid tracer and all the particle centres lying on the same plane of shear, were found to be 0.067γy a c , and 0.032γ a c , respectively, with c denoting the areal fraction occupied by the spheres on the plane.

Boundary conditions for darcy's flow through porous media

Abstract A novel formulation for the boundary conditions to be applied at a porous surface is proposed. Interfaces between porous and clear media and porous and solid media are considered. The well known Beavers & Joseph boundary condition is applicable for interfaces between porous and clear media. An equivalent boundary condition is obtained for interfaces between porous and impermeable media, namely, v · n = √(κ)∇ t · v 1 where v is the velocity field inside the porous medium, n denotes a unit vector normal to the interface pointing towards the porous medium, κ stands for the permeability and the subscript t refers to components tangential to the interface. A sample problem is solved for the flow fields exterior to a porous spherical particle and interior to it, assuming that the particle has a rigid concentric spherical core and that the submerging flow field is Newtonian. Stokesian and uniform at infinity. Both Brinkmans equation and Darcys law are utilized to obtain general forms of the velocity and pressure fields. Comparison of the two solutions yields the desired boundary conditions applicable to the Darcy problem.

Two-dimensional model of phase segregation in liquid binary mixtures with an initial concentration gradient

We simulate the phase segregation of a deeply quenched binary mixture with an initial concentration gradient. Our theoretical model follows the standard model H, where convection and di!usion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. This driving force induces a material #ux much larger than that due to pure molecular di!usion, as in a typical case the Peclet number a, expressing here the ratio of thermal to viscous forces, is of the order of 105. Integrating the equations of motion in 2D, we show that the behavior of the system depends on the values of the Peclet number a and the non-dimensional initial concentration gradient c. In particular, the morphology of the system during the separation process re#ects the competition between the capillarity-induced drop migration along the concentration gradient and the random#uctuations generated by the interactions of the drops with the local environment. For large a, the nucleating drops grow with time, until they reach a maximum size, whose value decreases as the Peclet number and the initial concentration gradient increase. This behavior is due to the fact that the nucleating drops do not have the chance to grow further, as they tend to move towards the homogeneous regions where they are assimilated. ( 2000 Published by Elsevier Science Ltd. All rights reserved.

Transverse shear-induced gradient diffusion in a dilute suspension of spheres

We study the shear-induced gradient diffusion of particles in an inhomogeneous dilute suspension of neutrally buoyant spherical particles undergoing a simple shearing motion, with all inertia and Brownian motion effects assumed negligible. An expansion is derived for the flux of particles due to a concentration gradient along the directions perpendicular to the ambient flow. This expression involves the average velocity of the particles, which in turn is expressed as an integral over contributions from all possible configurations. The integral is divergent when expressed in terms of three-particle interactions and must be renormalized. For the monolayer case, such a renormalization is achieved by imposing the condition of zero total macroscopic flux in the transverse direction whereas, for the three-dimensional case, the additional constraint of zero total macroscopic pressure gradient is required. Following the scheme of Wang, Mauri & Acrivos (1996), the renormalized integral is evaluated numerically for the case of a monolayer of particles, giving for the gradient diffusion coefficient 0.077γ a 2 c¯ 2 , where is the applied shear rate, a the radius of the spheres and c¯ their areal fraction.

Enhanced heat transport during phase separation of liquid binary mixtures

We show that heat transfer in regular binary fluids is enhanced by induced convection during phase separation. The motion of binary mixtures is simulated using the diffuse interface model, where convection and diffusion are coupled via a nonequilibrium, reversible Korteweg body force. Assuming that the mixture is regular, i.e., its components are van der Waals fluids, we show that the two parameters that describe the mixture, namely the Margules constant and the interfacial thickness, depend on temperature as T−1 and T−1∕2, respectively. Two quantities are used to measure heat transfer, namely the heat flux at the walls and the characteristic cooling time. Comparing these quantities with those of very viscous mixtures, where diffusion prevails over convection, we saw that the ratio between heat fluxes, which defines the Nusselt number, NNu, equals that between cooling times and remains almost constant in time. The Nusselt number depends on the following: the Peclet number, NPe, expressing the ratio betwee...

Nucleation and Spinodal Decomposition of Liquid Mixtures

We simulated the phase segregation of a metastable deeply quenched binary mixture. Our theoretical approach follows the diffuse interface model, where convection and diffusion are coupled via a nonequilibrium capillary force, expressing the tendency of the demixing system to minimize its free energy. As this driving force induces a material flux which, for liquid mixtures, is much larger than that due to pure molecular diffusion, the ratio of thermal to viscous forces is assumed to be of order 103, in agreement with experimental data. Using a pseudospectral method, we integrated the equations of motion in two dimensions, showing that the metastability of the system can be characterized through a critical radius, as in Gibbs’ treatment, or through the (finite) intensity of a white noise superposed on the initial uniform concentration field. This critical intensity grows exponentially as the mean composition of the mixture approaches its equilibrium value. In addition we showed that, in general, the value o...