ALBERT

Description: Moss et al. (2006) provided comments and criticisms of our recent paper in this journal (Hall et al. 2005). We can appreciate the need for promoting vigorous dialogue among those interested in the research of early sites along the New World Pacific Margin and thus welcome their intervention; however, we are compelled to respond because they raise several points that require clarification and introduce a critical error that must be corrected.

Description: Radiocarbon dates together with geoarchaeological, soil, and lithic analyses are presented to describe archaeological site 35-CS-9 in Bandon Ocean Wayside State Park, Oregon, northwestern USA. One of the few Oregon middle-Holocene coastal sites that includes sediments and artifacts dating to the early Holocene and possibly to the late Pleistocene, it was recorded in 1951 and surface surveyed by archaeologists in 1975, 1986, and 1991, but its depth and antiquity were not tested. In February 2002, we studied the site's stratigraphy and sediments and described 8 strata from the aeolian surface to bedrock at 350 cm depth. Soil samples taken from a cut bank for texture classification, particle size analysis, pH, carbon content, and chemical analysis suggested that the site represented a complete history of Holocene deposits. Excavation of 2 test units in August 2002 uncovered substantial lithic and charcoal remains that confirm a protracted middle-Holocene occupation and suggest that human occupation began in the early Holocene. Charcoal recovered at 235–245 cm dated to 11,000 14C BP, and the deepest lithic artifact was recovered in a level at 215–225 cm. Whether the human occupation was continuous throughout the Holocene, and whether it began in the early Holocene or in the late Pleistocene, can only be determined with further excavations.

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 few decades ago, the significance of Moffatt vortices was demonstrated by establishing their existence in various flows. Wedge and cusp regions and their axisymmetric counterparts were preferred to conical regions because the associated analyses were simpler. The lowest even and odd modes were always dominant and the streamline patterns of higher modes were assumed to be similarly simple, especially as their minute strength caused computational difficulties. Here, armed with far more computer power, we return to the vortices' canonical structure, with our principal focus on the region exterior to two cones with common axis and vertex. Many interesting features are revealed, the most unexpected being the structure of the third (second odd in a symmetric geometry) mode. The two-cone geometry allows consideration of asymmetric regions, for the first time. Comparisons are made with the well-known wedge and single-cone results and numerical corrections made to the latter. In all cases, eigenvalue plots play a valuable role in guiding the discussion. © 2005 Cambridge University Press.

Description: A three-dimensional boundary-integral algorithm is developed to study the squeezing of a deformable drop through a tight constriction formed by several solid particles rigidly held in space. The drop is freely suspended and driven by a flow that is uniform away from the solid obstacles. Particular emphasis is on the trapping mechanism and flow conditions close to critical, when the drop squeezes with high resistance. The problem is a close prototype of drop-solid interactions for emulsion flow through a granular material; such interactions are much more lubrication-sensitive than drop-drop interactions and require advanced numerical tools to succeed. The algorithm is based on the Hebeker representation for the solid-particle contribution, leading to a well-behaved system of second-kind integral equations, combined with novel regularization techniques for singular and near-singular boundary integrals; high-order near-singularity subtraction for the solid-to-drop double-layer contribution is the most crucial element. Simulations are performed for drop squeezing between (i) two close spheres, (ii) two parallel spheroidal disks, and (iii) three close spheres forming an equilateral triangle (including the case of close solid-solid contact). The drop non-deformed diameter is from two to several times larger than the inner constriction diameter and, in some simulations, the drop decelerates 103-104 times in the throat before being able to pass through. The effects of the constriction type, capillary number, and viscosity ratio on the drop velocity in the throat, exit time, and drop-solid spacing (of the order of 1% of the particle size) are explored in detail; critical capillary numbers (below which trapping occurs) are accurately determined. Even for a substantially supercritical capillary number, the drop has to nearly coat solid particles to be able to pass through a tight constriction. The ability of the algorithm to simulate both supercritical and subcritical conditions (when the drop is trapped, with a small but non-zero drop-solid spacing) is vital for future applications to large-scale simulations of emulsion flow through granular media. © 2006 Cambridge University Press.