Forces on a porous particle in an oscillating flow.

We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter beta = a/square root(k) and the frequency parameter Y = square root(a(2)omega/2nu) = a/delta, respectively. Here a is particle radius, k is its permeability, omega is the angular frequency, delta is the thickness of Stokes layer (penetration depth) and nu is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.

Malignant phyllodes tumor with heterologous liposarcomatous differentiation and tubular adenoma-like epithelial component.

Phyllodes tumor of the breast is a biphasic fibroepithelial neoplasm. A 30-year-old woman presented with a 1-year history of a palpable, asymptomatic right breast mass without axillary lymphadenopathy and family history of breast carcinoma. Malignant phyllodes tumor was diagnosed. The authors present not previously described histological appearance of this tumor where an epithelial component was identical to that of a tubular adenoma of the breast, with the review of the literature. This is in addition to very rare liposarcomatous stromal differentiation in the malignant phyllodes tumor.

Turbulent inertial gelation and acoustic quasi-gelation of submicron aerosol particles.

Inertial turbulent and acoustic orthokinetic particle coagulation mechanisms have physical similarity. We consider analytically and numerically coagulation of discrete compact and fractal submicron agglomerated particles, governed by these mechanisms via Smoluchowski equation. Existence of the inertial turbulent coagulation is mathematically proven. A new gelation scenario is revealed for both of the above coagulation mechanisms. Turbulent inertial gelation is manifested by means of a multi-modal relay-type run-away particle size growth, including formation of infinite set of secondary maxima in volume fraction distribution. When acoustic coagulation mechanism is much stronger than the Brownian coagulation, acoustic coagulation occurs as a quasi-gelation process, with a run-away particle size growth, characterized, however, by a finite set of secondary maxima. The effect of acoustic field on coagulation is shown to be more pronounced for fractal agglomerates than that for compact agglomerated particles.

Porous agglomerates in the general linear flow field.

We calculate the flow within and around a porous spherical agglomerate suspended in the general linear flow field, and also the flow induced by its rotation. We use the Stokes equations exterior to the particle and the Brinkman equations inside it. The effect of particle permeability on the flow is expressed via the Brinkman parameter beta = r(0)/square root of k, where r0 is particle radius and k is its permeability. With translational creeping motion of porous spheres in a quiet fluid investigated by Debye and Bueche [P. Debye, A.M. Bueche, J. Chem. Phys. 16 (6) (1943) 573-579], this study provides information necessary for investigating dynamics of porous particles moving in creeping shear flows under the action of external forces and torques. The agglomerate flow field solutions are used to calculate the effective viscosity of a dilute suspension of porous solid aggregates, which generalizes the well-known Einstein's equation for solid suspensions. The agglomerate effective viscosity diameter is proposed which allows using the Einstein's formula evaluation of the agglomerates suspension viscosity.

Mobility of permeable fractal agglomerates in slip regime.

Hydrodynamic drag and mobility of fractal aggregates in the slip creeping flow regime are calculated. A theoretical continuum model of the gas slip flow past and within agglomerates is developed. It accounts for effects of flow rarefaction and porous fractal structure upon the molecular mean free path, apparent viscosity, and effective permeability of agglomerates. It is shown that flow rarefaction significantly diminishes the aggregates' drag to an extent that cannot be predicted by the Cunningham's drag correction factor. The developed model allows calculation the agglomerates' transport properties in a wide range of fractal dimensions. For low D(f) agglomerates the drag force agrees with the Friedlander's expression based on the Epstein's single sphere drag in the free molecular regime.