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A mathematical model is presented for the problem of apparent slip arising from Stokes shear flow over a composite surface featuring mixed boundary conditions on the microscale. The surface can be composed of a bidimensional array of solid areas placed on an otherwise no-shear surface corresponding to an envelope over the tops of posts, or no-shear areas placed on an otherwise solid surface corresponding to an envelope over

A semianalytical model based on the method of eigenfunction expansions and domain decomposition is developed for Stokes shear flow over a grating composed of a periodic array of parallel slats, with finite slippage on solid surfaces and infinite slippage on the bottom of troughs mimicking a no-shear liquid-gas interface penetrating into the space between slats. The model gives the macroscopic slip lengths for flow parallel or normal to the slats in terms of the microscopic slip length of the liquid-solid interface, area fraction of the no-shear liquid-gas interface, and depth of the liquid-gas interface in the grooves. When the no-shear interface lies flat on the top of the slats, the macroscopic slip lengths are the maximum and can be estimated with reasonably good accuracy by simple formulas. However, the slip lengths, particularly the transverse one, are very sensitive to penetration of the no-shear interface into the grooves. They can be reduced by a large factor when the interface just slightly gets into the grooves. On comparing with some molecular-dynamics simulation measures, it is pointed out that the applied pressure, which has to be less than the capillary pressure in the superhydrophobic state, can be correlated with the penetration depth of the no-shear interface.

Contemporary models of intrafibrillar mineralization mechanisms are established using collagen fibrils as templates without considering the contribution from collagen-bound apatite nucleation inhibitors. However, collagen matrices destined for mineralization in vertebrates contain bound matrix proteins for intrafibrillar mineralization. Negatively charged, high–molecular weight polycarboxylic acid is cross-linked to reconstituted collagen to create a model for examining the contribution of collagen-ligand interaction to intrafibrillar mineralization. Cryogenic electron microscopy and molecular dynamics simulation show that, after cross-linking to collagen, the bound polyelectrolyte caches prenucleation cluster singlets into chain-like aggregates along the fibrillar surface to increase the pool of mineralization precursors available for intrafibrillar mineralization. Higher-quality mineralized scaffolds with better biomechanical properties are achieved compared with mineralization of unmodified scaffolds in polyelectrolyte-stabilized mineralization solution. Collagen-ligand interaction provides insights on the genesis of heterogeneously mineralized tissues and the potential causes of ectopic calcification in nonmineralized body tissues.

Comparisons between slip lengths predicted by a liquid-gas coupled model and that by an idealized zero-gas-shear model are presented in this paper. The problem under consideration is pressure-driven flow of a liquid through a plane channel bounded by two superhydrophobic walls which are patterned with longitudinal or transverse gas-filled grooves. Effective slip arises from lubrication on the liquid-gas interface and intrinsic slippage on the solid phase of the wall. In the mathematical models, the velocities are analytically expressed in terms of eigenfunction series expansions, where the unknown coefficients are determined by the matching of velocities and shear stresses on the liquid-gas interface. Results are generated to show the effects due to small but finite gas viscosity on the effective slip lengths as functions of the channel height, the depth of grooves, the gas area fraction of the wall, and intrinsic slippage of the solid phase. Conditions under which even a gas/liquid viscosity ratio as small as 0.01 may have appreciable effects on the slip lengths are discussed.

In this paper, we report on the thermal properties of a low-dielectric-constant organic spin-on glass, methyl silsesquioxane (MSQ), an important material for semiconductor device fabrication. The compositional and structural changes of this MSQ material, when heated in air and N 2, were investigated in detail with Fourier transform infrared (FT-IR) spectroscopy and thermogravimetric analysis (TGA). MSQ transforms to thermal oxide SiO 2 above 500 °C when heated in air, and it forms oxygen-deficient SiO 2 above 700 °C in N 2. Our results suggest that a cure temperature higher than the current 425 °C is preferred to form films with better cross-linked network structure.

Mathematical models are developed for heat conduction in creeping flow of a liquid over a microstructured superhydrophobic surface, where because of hydrophobicity, a gas is trapped in the cavities of the microstructure. As gas is much lower in thermal conductivity than liquid, an interfacial temperature slip between the liquid and the surface will develop on the macroscale. In this note, the temperature jump coefficient is numerically determined for several types of superhydrophobic surfaces: a surface with parallel grooves, and surfaces with two-dimensionally distributed patches corresponding to the top of circular or square posts, and circular or square holes. These temperature jump coefficients are found to have a nearly constant ratio with the corresponding velocity slip lengths.

A perturbation analysis is carried out to the second order to give effective equations for Darcy-Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy-Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes' flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180 • out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.