ALBERT

Description: Plastic and metal spheres were dropped from various heights onto a quartz disk covered with a thin layer of viscous oil and inclined at various angles with the horizontal. Rebound was observed only above a critical approach velocity, similar to that observed for head-on collisions when the disk is horizontal. The tangential component of the sphere's velocity is reduced only a small amount by the collision, owing to sliding lubrication/friction forces that also impart a small rotational velocity to the sphere. In contrast, the normal component of velocity is reduced substantially by viscous losses, and so the rebound angle of the sphere relative to the surface of the disk is smaller than the impact angle. The normal component of restitution and the rebound angle increase with the normal Stokes number based on the normal component of the impact velocity. © 2004 Cambridge University Press.

Description: A new law for the thinning of surfactant-free lamellae (applicable to metallic and ceramic foams with mobile interfaces) in a cross-section of an arid gas-liquid foam is derived using matched asymptotic analysis. Two limiting cases are identified at small capillary number: the well-known semi-arid foam having unit-order liquid fraction and the arid foam in which it is small. The lamellar thinning rates in both cases exhibit t-2 power-law behaviour at long times even though the foam liquid area fractions have different orders of magnitude in capillary number. At early times, arid foam thinning is slowed because the curvature of the capillary quasi-static interfacial region must decrease in order to accommodate the flow from the films. Therefore, the thinning of lamellae feeding into a given Plateau border is coupled and the dynamics is distinct from that of the semi-arid foam. Approximations of rupture times in arid and semi-arid foams are found by calculating the times for lamellae to thin to a pre-specified thickness. For given initial lamellar thicknesses, and for arid and semi-arid foams that have identical initial lamellar liquid areas, the arid foam ruptures more quickly than the semi-arid foam. On the other hand the rupture of lamellae is significantly delayed in arid foam compared to semi-arid foam if the initial lamellar thickness and capillary number are the same. © 2005 Cambridge University Press.

Description: An insoluble particle, a solid sphere or a spherical bubble, submerged in a liquid and approached by an advancing solidification front, may be captured by the front or rejected. The particle behaviour is determined by an interplay among van der Waals interactions, thermal conductivity differences between the particle and the melt, solid-liquid interfacial energy, the density change caused by the liquid-solid phase transition, and in the case of a bubble, the Marangoni effect at the liquid-gas interface. We calculate the particle velocity and the deformation of the front when the particle is close to the front, using the lubrication approximation, and investigate how the particle speed, relative to the front, depends on the parameters that characterize the described effects. © 2006 Cambridge University Press.

Description: A novel boundary-integral algorithm is used to study the general, three-dimensional motion of neutrally buoyant prolate and oblate spheroids in a low-Reynolds-number Poiseuille flow between parallel plates. Adaptive meshing of the spheroid surface assists in obtaining accurate numerical results for particle - wall gaps as small as 1.3% of the spheroid's major axis. The resistance formulation and lubrication asymptotic forms are then used to obtain results for arbitrarily small particle - wall separations. Spheroids with their major axes shorter than the channel spacing experience oscillating motion when the spheroid's centre is initially located in or near the midplane of the channel. For both two-dimensional and three-dimensional oscillations, the period length decreases with an increase in the initial inclination of the spheroid's major axis with respect to the lower wall. These spheroids experience tumbling motions for centre locations further from the midplane of the channel, with a period length that decreases as the spheroid is located closer to a wall. The transition from two-dimensional oscillating motion to two-dimensional tumbling motion occurs for an initial centre location closer to a wall as the initial inclination of the major axis is increased. For these spheroids, the average translational velocity along the channel length for two-dimensional oscillating motion decreases for an increase in the initial inclination of the major axis, and the average translational velocity for two-dimensional tumbling motion decreases for a decrease in the initial centre location. A prolate spheroid with its major axis 50% longer than the channel spacing and confined to the (x2, x3)-plane (where x2 is the primary flow direction and xfis normal to the walls) cannot experience two-dimensional tumbling; instead, the spheroid becomes wedged between the walls for initial centre locations near the midplane of the channel when the initial inclination of the large spheroid's major axis is steep, and experiences two-dimensional oscillations for initial centre locations near a wall. When this spheroid's major axis is not confined to the (x2, x3plane, it experiences three-dimensional oscillations for initial centre locations in or near the midplane of the channel, and three-dimensional tumbling for initial centre locations near a wall. © 2006 Cambridge University Press.

Description: We examine steady longitudinal freezing of a two-dimensional single-component free liquid film. In the liquid, there are thermocapillary and volume-change flows as a result of temperature gradients along the film and density change upon solidification. We examine these flows, heat transfer, and interfacial shapes using an asymptotic analysis which is valid for thin films with small aspect ratios. These solutions depend sensitively on contact conditions at the tri-junctions. In particular, when the sum of the angles formed in the solid and liquid phases falls below a critical value, the existence of steady solutions is lost and the liquid film cannot be continuous, suggesting breakage of the film owing to freezing. The solutions are relevant to the freezing of foams of metals or ceramics, materials unaffected by surface active agents. © 2008 Cambridge University Press 2008.

Description: We study the dynamics of a mushy layer in directional solidification for the case of a thin near-eutectic mush with a deformable and permeable mush - liquid interface. We examine the onset of convection using linear stability analysis, and the weakly nonlinear growth of liquid inclusions that signal the onset of chimneys. This analysis is compared to past analyses in which the mush - liquid interface is replaced by a rigid impermeable lid. We find qualitative agreement between the two models, but the rigid-lid approximation gives substantially different quantitative behaviour. In linear theory, the rigid-lid approximation leads to an over-estimate of the critical Rayleigh number and wavenumber of the instability. The condition for the onset of oscillatory instability is also changed by a factor of about 5 in composition number C. In the weakly nonlinear theory, the location of the onset of liquid inclusions is near the undisturbed front for the free-boundary analysis, whereas it lies at the centre of the mushy layer when the rigid-lid approximation is used. For hexagonal patterns, the boundary between regions of parameter space in which up and down hexagons are stable, shifts as a result of coupling between the liquid and mush regions. © 2008 Cambridge University Press.

Description: A contact line on a heated oscillating plate is investigated. The interface is a non-deformable plane and the contact angle is π/2. The amplitude of the oscillation and the temperature deviation of the plate from the ambient temperature of the fluid are assumed to be much smaller than the viscous velocity scale. This flow is then governed by the unsteady Stokes equations coupled to the heat equation in a frame of reference moving with the contact line. Evaporation is assumed to be neglible, but the effects of heat transfer across the interface and unsteadiness are assumed to be significant. For a stationary heated plate, there are two distinct regions of flow that is induced by Marangoni stresses. An outer stagnation-point-type flow is seen, which separates from the plate for non-zero Biot numbers. For an oscillatory, isothermal plate, vortices are generated at the plate during plate reversal and are propagated along the interface. Dissipation of these vortices occurs on the Stokes layer scale. The order-Péclet-number correction in the thermal field is also found, and the presence of the flow field leads to a heated region in the steady case along the separating streamline. For the unsteady case, a localized cooled region propagates into the bulk with a trajectory determined by the relative scale of the thermal diffusive scale and the rate of heat transfer across the interface.

Description: We consider the flow of a dilute suspension of equisized solid spheres in a viscous fluid. The viscosity of such a suspension is dependent on the volume fraction, c, of solid particles. If the particles are perfectly smooth, then solid spheres will not come into contact, because lubrication forces resist their approach. In this paper, however, we consider particles with microscopic surface asperities such that they are able to make contact. For straining motions we calculate the O(c2) coefficient of the resultant viscosity, due to pairwise interactions. For shearing motions (for which the viscosity is undetermined because of closed orbits on which the probability distribution is unknown) we calculate the c2 contribution to the normal stresses N1 and N2. The viscosity in strain is shown to be slightly lower than that for perfectly smooth spheres, though the increase in the O(c) term caused by the increased effective radius due to surface asperities will counteract this decrease. The viscosity decreases with increasing contact friction coefficient. The normal stresses N1 and N2 are zero if the surface roughness height is less than a critical value of 2.11 x 10-4 times the particle radius, and then become negative as the roughness height is increased above this value. N1 is larger in magnitude than N2.