We present a model for the steady dynamic friction of a block of an elastomer, sliding steadily on a hard surface. The model uses population balance of the bonds between the hard surface and the polymer chains of the elastomer to estimate the force of friction. Although the basic premises of the present model are the same as those of the Schallamach model for dynamic friction (1963), the present formulation is a clearer representation of the phenomena involved. Moreover, the model is not based on the ergodic hypothesis and is therefore more versatile. It also allows us to correct the error in the expression for the force of friction in the Schallamach model. The present model exhibits the same qualitative trends as the Schallamach model. However, there are significant quantitative differences between the two models. We also show that our expression for the force of friction is equivalent to that obtained by the Chernyak and Leonov (1986) model, which is based on the ergodic hypothesis. The model is further modified to account for both the non-Hookean extension of the bonded chains and the viscous retardation effect. The model is validated using the experimental data of Vorvolakos and Chaudhury (2003) on sliding of crosslinked PDMS solid on silane coated silicon wafer. From this analysis, scaling laws, which relate the model parameters to the molecular weight of the polymer chains and the temperature, are derived and justified.

This paper presents laminar fully developed free convection flow between two coaxial vertical cylinders partially filled with a porous matrix when the cylinders are kept at different temperatures. The Brinkman-extended Darcy model is used to simulate momentum transfer in the porous region. The two regions are coupled by equating the velocity and by considering shear stress jump condition at the interface. The effect of Darcy number on the velocity throughout porous domain and adjustable coefficient in the stress jump condition at the interface is shown graphically. It is observed that velocity is influenced by the shear stress jump condition at the interface.

We show that highly enhanced and selective adhesion can be achieved between surfaces patterned with complementary microchannel structures. An elastic material, poly(dimethylsiloxane) (PDMS), was used to fabricate such surfaces by molding into a silicon master with microchannel profiles patterned by photolithography. We carried out adhesion tests on both complementary and mismatched microchannel/micropillar surfaces. Adhesion, as measured by the energy release rate required to propagate an interfacial crack, can be enhanced by up to 40 times by complementary interfaces, compared to a flat control, and slightly enhanced for some special noncomplementary samples, despite the nearly negligible adhesion for other mismatched surfaces. For each complementary surface, we observe defects in the form of visible striations, where pillars fail to insert fully into the channels. The adhesion between complementary microchannel surfaces is enhanced by a combination of a crack-trapping mechanism and friction between a pillar and channel and is attenuated by the presence of defects.

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