The inertial migration of a small sphere in a Poiseuille flow is calculated for the case when the channel Reynolds number is of order unity. The equilibrium position is found to move towards the wall as the Reynolds number increases. The migration velocity is found to increase more slowly than quadratically. These results are compared with the experiments of Segré & Silberberg (1962 a, b).

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.

The microscopic details of fluid flow and heat transfer near the contact line of an evaporating extended meniscus of heptane formed between a horizontal substrate and a “washer” were studied at low heat fluxes. The film profile in the contact line region was measured using ellipsometry and microcomputer-enhanced video microscopy, which demonstrated the details of the transition between a nonevaporating superheated flat thin film and an evaporating curved film. Using the augmented Young-Laplace equation, the interfacial properties of the system were initially evaluated in situ and then used to describe the transport processes. New analytical procedures demonstrated the importance of two dimensionless parameters. Both fluid flow and evaporation depend on the intermolecular force field, which is a function of the film profile. The thickness and curvature profiles agreed with the predictions based on interfacial transport phenomena models. The heat flux distribution and the pressure field were obtained. Since there are significant resistances to heat transfer in this small system due to interfacial forces, viscous stresses, and thermal conduction, the “ideal constant heat flux” cannot be attained. The description of the pressure field gives the details of the coupling between the disjoining and capillary pressures.

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