Avinoam Nir

On the motion of suspended particles in stationary homogeneous turbulence

The closed equations for the velocity correlation tensor and for the mean-squared displacement of a particle suspended in a stationary homogeneous turbulent flow, with an arbitrary linear law of fluid-particle interaction, are obtained using two assumptions suggested previously for the problem of turbulent self-diffusion: the ‘independence approximation’ and the Gaussian property of the functional distribution of particle velocities. The numerical solution of the derived equations is given for an isotropic system with a model turbulence spectrum. The following characteristics of the particle motion are obtained: ( a ) the mean kinetic energy, ( b ) diffusivity, ( c ) rate of energy dissipation, ( d ) velocity correlation function, and ( e ) the correlation function of the relative fluid-particle velocity. The impact of various spectral modes on the characteristics of the particle motion is discussed.

Shear-induced particle migration in a polydisperse concentrated suspension

The shear-induced particle migration in a polydisperse concentrated suspension is described using migration potentials for the various particle size fractions. The model is applied to solve the flow patterns and the particle concentration distributions in bidisperse suspensions in various viscometric flows. For the case of a continuous particle size distribution a formulation of this model in terms of concentration distribution moments is presented. The model predicts the total migration of the particles in the various flow devices and the size segregation of the various fractions. The calculations capture well the few experimental observations reported so far. It is found that in all calculated cases the total energy dissipation rate and, therefore, the power required to drive the flow were diminished considerably at steady state.

A simulation of surface tension driven coalescence

Abstract Coalescence of particles in a continuous fluid occurs quite commonly, e.g., in engineering, physics, and biology. The motion is induced by the tendency of the interface to reduce its area in order to minimize the interfacial energy. In this communication we present a numerical solution for the equation of motion describing the coalescence of two particles using an integral equation representation for the surface velocities. The results show a similar behavior for all particles to fluid viscosity ratios λ. Processes such as polymer sintering (λ→∞), biological particles fusion (λ→1) and bubble coalescence (λ→0) share a similar dynamics when simulated by surface tension driven flows. It is shown that Frenkels constant power law for the evolution of the neck radius and its velocity of growth does not generally hold during the bulk of the coalescence process. The simulation predicts well the available experimental data describing the isothermal sintering of polymer particles.

Sedimentation and sediment flow on inclined surfaces

The steady sedimentation of a suspension over an inclined surface is analysed by considering the combined effects of settling hindrance, bulk motion and particle resuspension. The coupled momentum and mass balances suggest that a thin high-density sediment layer will form over the inclined surface, reminiscent of the thin thermal boundary layers in the classical problem of natural convection. It is shown that for a given value of the particle volume fraction in the unsettled suspension, a steady flow of the sediment can be maintained only if the angle of inclination exceeds a minimum value. The analysis further predicts the existence of a sharp discontinuity in the particle volume fraction across the suspension–sediment interface along which the bulk velocity has a local maximum. High particle volume fractions within the sediment are predicted when the unsettled suspension is either very dilute or very concentrated. This leads to the formation of relatively large sediment-layer thicknesses which reflect the fact that a large body force is required in these two limiting cases to overcome the viscous resistance to flow near the inclined boundary.

Simultaneous intraparticle forced convection, diffusion and reaction in a porous catalyst—II: Selectivity of sequential reactions

Abstract The selectivity of a sequence of isothermal irreversible heterogeneous reactions within a catalytic pellet is investigated under conditions where intraparticle forced convection is a non-negligible transport mechanism. The nature of the effect of the internal filter flow depends mostly on the value of the Thiele modulus, φ 2 , of the desired (middle) species. The asymptotic values of the selectivity, as φ 2 → 0 and φ 2 → ∞, are unaltered, independent of the strength of the internal flow. The intermediate region is divided into two parts. In the subregion with lower values of φ 2 the selectivity is enhanced. In the other subregion, with higher values of φ 2 , the selectivity is significantly retarded to values which can be markedly below the lower asymptote. These trends are common to both poor and good selective catalysts.

Slow viscous flows of highly concentrated suspensions-part II : Particle migration, velocity and concentration profiles in rectangular ducts

The utilization of the laser-Doppler velocimetry technique in concentrated suspensions facilitated a direct measurement of particle migration velocities. Velocity measurements of dispersions at moderate and high particle concentrations, in the range of 0.3 < φs < 0.50, showed a direct connection between particle lateral migration and changes in suspension velocity profiles. The longitudinal profiles lose their Newtonian shape at high concentrations. A qualitative agreement is shown in this work between the measured lateral and longitudinal velocity profiles and model calculations based on a phenomenological model.

Slow viscous flows of highly concentrated suspensions—Part I: Laser-Doppler velocimetry in rectangular ducts

A non-invasive experimental technique which enables optical penetration into the bulk of a flowing liquid-solid concentrated suspension was employed to study such flows. Matching of refractive indices of the continuous and dispersed phases was used to establish optimal conditions for the quality of the optical signals and can be used to measure concentration in the flowing dispersion. Laser-Doppler anemometry was applied to measure velocity profiles in a rectangular duct and to detect velocity fluctuations in the viscous flow of the concentrated suspension induced by the particles presence. The existence of a net drift of particles in a concentrated suspension is demonstrated.

Shear-induced particle resuspension in settling polydisperse concentrated suspension

Abstract A phenomenological model describing the resuspension of polydisperse suspension in shear flow is presented. The model combines mechanisms of hindered sedimentation and shear-induced particle migration. The latter is expressed in terms of migration potentials for mono and polydisperse mixtures. The calculated results agree well with available experimental observations. It predicts the rise and location of the suspension upper surface, the separation of species in the suspension and the location and sharpness of interfaces between species. It can be used to analyze the flow of concentrated polydisperse suspensions under gravity in complex geometries and to predict macroscopic properties associated with these flows.

Diffusion of macromolecules across the arterial wall in the presence of multiple endothelial injuries.

In this paper, the two-phase arterial wall model developed by Weinbaum and Caro [2] has been extended to obtain analytic solutions for the steady-state flux, uptake and concentration of macromolecules in the arterial wall due to the presence of periodically dispersed local sites of enhanced permeability. In the endothelial cell layer these sites are believed to be associated with the dying and regeneration of individual cells in the endothelial monolayer. Nir and Pfeffer [9] obtained similar solutions for a single dying cell in an otherwise undamaged endothelial cell layer. However this model requires that multiple cell turnover sites be spaced sufficiently far apart such that no interaction between neighboring sites takes place and hence cannot be applied to closely spaced endothelial injuries which have been observed experimentally in physiological studies. The theoretical predictions of the present model compare very favorably with experimental results for the enhanced uptake found in blue versus white areas reported in morphological studies of the endothelial surface (Bell, et al. [10, 11]).

Transport of macromolecules across arterial wall in the presence of local endothial injury.

Abstract The theoretical study of the subendothelial spread of macromolecules in the vicinity of a localized endothelial damage is of importance because of the large increased uptake of macromolecules which has been observed experimentally in certain regions of the arterial tree as compared to other regions. It has been hypothesized that the locally observed increased permeability may be due to endothelial injury produced by naturally occurring hemodynamic factors. The two-phase arterial wall model developed by Weinbaum & Caro (1976) has been extended to obtain analytic solutions for the time dependent and steady state concentration distributions, flux and uptake in the arterial wall as a function of damage size, fraction of damaged surface and position from the damage. It has been demonstrated that with as little as 3% of the endothelial., surface damaged with locally spread holes of size 0·1 the thickness of the arterial media, the total uptake can increase by a factor of 2·5 over that of an artery with no endothelial damage.