F.R. Cunha

Modeling and Direct Simulation of Velocity Fluctuations and Particle-Velocity Correlations in Sedimentation

We present direct numerical simulations of monodisperse and polydisperse suspensions of non-Brownian particles sedimenting at low Reynolds number. We describe a scheme to generate ergodic ensembles of random particulate systems and a numerical procedure for computing interactions among spherical particles based on Ewald summation technique for hydrodynamic mobility tensors. From the generation process truly random both monodisperse and multimodal size distributions of particles were obtained for dilute and moderate densities based on a minimum energy criterion

A study of emulsion expansion by a boundary integral method

Abstract A new implementation of the conventional three-dimensional boundary-integral formulation for deformable drops in a viscous medium at low Reynolds numbers is presented. We describe a scheme to generate concentrated emulsions and a numerical procedure for computing interactions among deformable drops. Direct numerical simulations are used to describe the expansion of an ordered emulsion at dispersed-phase volume fraction up to 0.98. We also study the viscoelastic response of a monodisperse emulsion which have been concentrated up to 0.68. The results have demonstrated the feasibility of simulating high-volume fraction emulsions, and the method can readily be extended to explore three-dimensional foam problems.

A mathematical formulation of the boundary integral equations for a compressible stokes flow

A general boundary integral formulation for compressible Stokes flows is theoretically described within the framework of hydrodynamic potentials. The integral equation is implemented numerically to the study of drop expansion in compressible viscous flows. Marker point positions on the drop interface are involved by using the boundary integral method for calculation of fluid velocity. Surface discretization is adaptive to the instantaneous drops shapes. The interplay between viscous and surface tension and its influence on the evolving emulsion microstructure during its expansion is fundamental to the science and technology of foam processing. In this article the method is applied for 3D simulations of emulsion densification that involves an uniform expansion of a viscous fluid containing spherical drops on a body centered cubic lattice (BCC).

NUMERICAL SIMULATION OF VELOCITY FLUCTUATIONS AND DISPERSION OF SEDIMENTATING PARTICLES

Velocity fluctuations and hydrodynamic dispersion are studied in a monodisperse dilute suspension of rigid spherical particles. In the absence of Brownian motion and inertia, fluctuations in the velocity of individual particles arise from hydrodynamic interactions varying with the ever-changing configurations of the particles. We show some computer simulations of point particles with excluded volume sedimenting in a rectangular container with periodic sides and impenetrable bottom and top. The simulations reproduce the experimental correlation-time and anisotropy of the velocity fluctuations but have a magnitude increasing proportionally to the size of the system.

A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear

This theoretical work shows how the knowledge of the emulsion microscale, including drop stretching and orientation leads to a continuum description of emulsion flows. A first order small deformation theory is explored for describing the rheology of an emulsion of high viscosity drops undergoing unsteady shear flows. The stationary shape and the interfacial velocity of a drop are used in order to obtain the contribution of the drop to the effective stress tensor of the emulsion. A complex rheology including the nonlinear frequency response of the emulsion under oscillatory shear at arbitrary frequency forcing and strain amplitude is identified.

The dynamic behavior of a collapsing bubble in a magnetic fluid

Abstract In this article it is investigated the nonlinear response of an oscillatory bubble suspended in an incompressible magnetic fluid. After an appropriate non-dimensionalization of the governing equation, it is found that the most relevant physical parameters of the system are: the Reynolds number, the Weber number, the magnetic pressure coefficient and the magnetic permeability ratio bubble-fluid governing equation. The integration of the nonlinear differential equation governing the bubble motion is performed analytically by using a regular expansion and numerically by using a fourth-order Runge–Kutta scheme. Unstable configurations of the bubble motion are shown for different values of the magnetic pressure coefficient. An important consequence of magnetic colloidal particles in the flow is that it may drastically attenuate instabilities, avoiding bubble against collapse. The present findings have implications for acoustic cavitation in cryogenic liquids.

Numerical simulations of magnetic suspensions with hydrodynamic and dipole-dipole magnetic interactions

This work describes a numerical model to compute the translational and rotational motion of N spherical magnetic particles settling in a quiescent viscous fluid under creeping flow condition. The motion of the particles may be produced by the action of gravitational forces, Brownian thermal fluctuations, magnetic dipole-dipole interactions, external magnetic field, and hydrodynamic interactions. In order to avoid particle overlap, we consider a repulsive force based on a variation of a screened-Coulomb potential mixed with Hertz contact forces. The inertia of the particles is neglected so that a mobility approach to describe the hydrodynamic interactions is used. The magnetic dipoles are fixed with respect to the particles themselves. Thus they can only interact magnetically between them and with an external applied magnetic field. Therefore the effect of magnetic field moment rotation relative to the particle as a consequence of a finite amount of particle anisotropy is neglected in this work. On the oth...

A new boundary integral formulation to describe three-dimensional motions of interfaces between magnetic fluids

Abstract A new general three-dimensional hydrodynamic–magnetic boundary integral formulation for a magnetic free surfaces in viscous flows at low Reynolds numbers is developed. The formulation is based on an extension of the Lorentz reciprocal theorem for the incompressible flow of a magnetic fluid. Combining the reciprocal theorem and the fundamental solution of a creeping flow we obtain the integral representation of the flow in terms of hydrodynamic and magnetic potentials. According to this formulation, the magnetic and hydrodynamic quantities which are necessary for determination of the dynamics of a magnetic liquid are established by means of appropriate integral equations at the boundary of the region occupied by the magnetic liquid. The motion of a free surface with arbitrary magnetic properties and with the viscosity of the magnetic liquid and the surrounding fluid not identical may be explored with the present formulation. Two relevant physical parameters are revealed in the present hydrodynamic–magnetic boundary integral formulation: the ratio of the magnetic permeability and the magnetic capillary number. The proposed boundary integral equations has been developed in order to simulate the full time-dependent low Reynolds number distortion and orientation of a three-dimensional ferrofluid droplet under the action of shearing motions and magnetic fields.

Direct numerical simulations of emulsion flows

In this paper, three-dimensional boundary integral computer simulations of emulsions in shear flows are described. Results for ordered BCC emulsions with dispersed-phase volume fractions below the critical concentration are presented. Complex rheological features including: shear-thinning viscosities, normal stress differences, and a nonlinear frequency response are also explored. For deformable drops, pairwise collision produces net cross-flow displacements that govern self-diffusion of drops. We compute trajectories of two interacting drops in shearing and present interesting numerical simulations of three dimensional gravity-induced motion of two drops. The results also demonstrate the feasibility of simulating high-volume-fraction emulsions and foam.

A stability analysis of a magnetic fluidized bed

The aim of this work is to investigate the stability of a polarized fluidized bed of magnetic particles against plane wave disturbances of small amplitudes. A continuum model is proposed so that continuity and momentum equations are written in terms of averaged variables. Magnetostatic equations are averaged and an equation governing the disturbances of the magnetic field is obtained. Two new physical dimensionless parameters are defined: a magnetic pressure coefficient and a magnetic shape factor. The eigenvalue problem is solved and the temporal growth rate of the disturbances and the neutral lines are obtained. Results show that the magnetic pressure coefficient and the magnetic shape factor, which takes into account the orientation of the magnetic field disturbances with relation to the applied field, are the important physical parameters governing the dynamics of magnetic fluidized beds.