ISSN:0899-8213    

DOI:10.1063/1.3480468

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A theory is presented to describe the time‐dependent and steady transport properties of composite media containing randomly placed, aligned slender fibers. The formalism is based on a diagrammatic representation of the multiple scattering expansion for the configurational‐averaged Green’s function. Several topological reductions are performed on the series to remove long‐wavelength singularities and to render the theory self‐consistent. Approximations based on partial summation of the renormalized series have structures that are similar to, but distinct from, effective medium theories. The present approach is systematic and retains a unique subset of the multiple scattering series at each level of approximation. The formalism is appliedto the specific cases of steady diffusion‐controlled reaction and heat conduction in composites that contain slender, aligned rods. Both the dilute and semidilute regimes are investigated. Theseresults for the diffusion‐controlled reaction problem are new, and known results are recovered for heat conduction in the case of highly conductive rods. However, the method has uncovered a new semidilute expansion for the latter problem. The screening of disturbances in fibrous composites is also discussed.

ISSN:0899-8213    

DOI:10.1063/1.857546

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The planar singular solutions of Stokes and Laplace equations are derived and applied to a number of transport problems associated with porous surfaces. The velocity, pressure, concentration, and temperature slip coefficients are determined exactly for the semi‐infinite periodic arrays of spheres and these are compared with the predictions of two approximate continuum theories formulated by Brinkman [Appl. Sci. Res.A1, 27 (1947)] and Chang and Acrivos [J. Appl. Phys.59, 375 (1986)] to assess the utility of such theories in accurately predicting various overall properties related to the porous surfaces. It is found that in general these theories provide fairly accurate estimates of these propertiesevenwhen the length scales based on the relevant macroscopic properties such as the permeability are much smaller than the length scales characterizing the microstructure of the porous media.

ISSN:0899-8213    

DOI:10.1063/1.857544

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Calculations are presented for a periodic grain consolidation model of porous media. The model is an extension of previous work on lattices of spheres, in which the radius of the spheres is allowed to increase past the point of close touching to form a consolidated medium. A collocation method is used for the solution of Stokes flow in terms of Lamb’s general solution in spherical coordinates. Excellent accuracy is achieved with only moderate computational effort. At low concentrations up to the close touching limit excellent agreement is found with the earlier calculations of Zick and Homsy [J. Fluid Mech.115, 13 (1982)]. For high concentrations above the close touching limit, an asymptotic theory is presented that agrees within a few percent with the numerical computations over the entire consolidated range.

ISSN:0899-8213    

DOI:10.1063/1.857545

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The dispersion of a tracer in a heterogeneous medium in which the tracer’s velocity has zero mean and a covariance that decays asx−&ggr;with distancexis studied using nonlocal advection–diffusion theory. If the velocity covariance decays slowly, &ggr;≤2, the tracer’s dispersive motion is non‐Fickian even at long times after its release. Under these circumstances, it is not possible to predict the dispersion by assuming that the tracer samples the velocity fluctuations primarily by molecular diffusion, even if the fluctuations are weak. Instead, we develop a self‐consistent theory in which the tracer samples each velocity fluctuation by the motion resulting from the other fluctuations. It is shown that in cases of anomalous diffusion, the tracer’s mean‐square displacement grows faster than linearly with time—ast4/(2+&ggr;)for 0<&ggr;<2 and ast(ln t)1/2for &ggr;≡2 ast→∞.

ISSN:0899-8213    

DOI:10.1063/1.857522

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A new technique for measuring the surface roughness of noncolloidal spheres is presented. The time for a sphere initially in contact with a smooth surface to fall away under the influence of gravity through a viscous fluid is shown to be related to the largest scale of surface roughness of sufficient surface coverage to support the particle. The ratio of the time taken for a sphere to fall one particle diameter from a smooth mica plane to that for the sphere to fall between one radius and one diameter from the plane thus provides a means of measuring the effective hydrodynamic surface roughness of spheres. This technique was employed to measure the roughness of eight types of particles ranging from 43–6350 &mgr;m in diameter. The roughnesses were found to be on the order of 10−2to 10−3particle radii, and were in agreement with independent observations using a scanning electron microscope and an optical profilometer.

ISSN:0899-8213    

DOI:10.1063/1.857523

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Analytical results are obtained for mobility functions that describe the hydrodynamic interactions for transverse motions of two unequal viscous drops. In conjunction with the results of an earlier paper on axisymmetric motions, the motion induced by external forces in an arbitrary direction, i.e., the solution of the general mobility problem, is thus obtained. In the problem of interest, the drops are small and the surface tension is sufficiently high so that the drops retain a spherical shape. Exact solutions for the velocity images for Stokeslets and higher‐order Stokes singularities near a viscous drop are introduced and then these image solutions are used to generate expressions valid for all two‐sphere geometries except those for which the gap is much smaller than the diameter of thesmallerdrop. For rigid spheres, these results are used to obtain a closed‐form expression for the Stokes–Einstein Brownian diffusion coefficient.

ISSN:0899-8213    

DOI:10.1063/1.857524

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The hydrodynamic force resisting the relative motion of two unequal drops moving along their line of centers is determined for Stokes flow conditions. The drops are assumed to be in near‐contact and to have sufficiently high interfacial tension that they remain spherical. The squeeze flow in the narrow gap between the drops is analyzed using lubrication theory, and the flow within the drops near the axis of symmetry is analyzed using a boundary integral technique. The two flows are coupled through the nonzero tangential stress and velocity at the interface. Depending on the ratio of drop viscosity to that of the continuous phase, and also on the ratio of the distance between the drops to their reduced radius, three possible flow situations arise, corresponding to nearly rigid drops, drops with partially mobile interfaces, and drops with fully mobile interfaces. The results for the resistance functions are in good agreement with an earlier series solution using bispherical coordinates. These results have important implications for droplet collisions and coalescence.

ISSN:0899-8213    

DOI:10.1063/1.857525

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Sedimentation and ultrafiltration are important processes for removing solids from suspensions. The Kynch theory describes the transient settling of noncolloidal particles forming an incompressible sediment by providing a solution to the convective conservation equation. This solution predicts the existence of several different regions as settling progresses. Subsequent treatments have accounted for compressibility within the sediment. These modifications focus largely on stretching the Kynch theory to fit the problem at hand rather than on formulating a new model to include the relevant physics. In this paper a model of sedimentation for colloidal systems is presented by including a diffusion term in the governing equation. In the regions above the sediment, this term acts as a small perturbation to the Kynch theory. Within the sediment, owing to the high solid volume fraction, diffusion is comparable to convection. Slow compression to the maximum sediment volume fraction contrasts the incompressibility of the Kynch theory. Application of the method of matched asymptotic expansions to the conservation equation enables the formulation of a complete description of the settling process, and, in particular, the volume fraction evolution in the sediment. This method is also applied to the related ultrafiltration process. Where the properties of the sediment, or filtercake, are important, such as in ceramics manufacturing, a quantitative understanding of its formation is of obvious value.

ISSN:0899-8213    

DOI:10.1063/1.857526

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The deformation of biological particles in a quiescent fluid medium is considered by simulating the particle as a viscous droplet surrounded by a thin surface layer in which the forces rendering the motion arise. The dynamics is studied using the boundary integral equation developed by Rallison and Acrivos [J. Fluid Mech.89, 191 (1978)] in conjunction with various formulations for the surface tractions depending on the availability of biological information. The cases of vesicle coalescence, cell division, and embryo development are simulated by regarding the interfacial forces as constant surface tension, variable surface tension, and nonhomogeneous anisotropic tension, respectively.

ISSN:0899-8213    

DOI:10.1063/1.857538

出版商:AIP    

年代:1989

数据来源: AIP