Francois Blanchette

High‐resolution numerical simulations of resuspending gravity currents: Conditions for self‐sustainment

Received 21 February 2005; revised 30 June 2005; accepted 29 August 2005; published 22 December 2005. [1] We introduce a computational model for high-resolution simulations of particle-laden gravity currents. The features of the computational model are described in detail, and validation data are discussed. Physical results are presented that focus on the influence of particle entrainment from the underlying bed. As turbulent motions detach particles from the bottom surface, resuspended particles entrained over the entire length of the current are transferred to the current’s head, causing it to become denser and potentially accelerating the front of the current. The conditions under which turbidity currents may become self-sustaining through particle entrainment are investigated as a function of slope angle, current and particle size, and particle concentration. The effect of computational domain size and initial aspect ratio of the current on the evolution of the current are also considered. Applications to flows traveling over a surface of varying slope angle, such as turbidity currents spreading down the continental slope, are modeled via a spatially varying gravity vector. Particular attention is given to the resulting particle deposits and erosion patterns.

Dynamics of drop coalescence at fluid interfaces

Drop coalescence was studied using numerical simulations. Liquid drops were made to coalesce with a body of the same liquid, either a reservoir or a drop of different size, each with negligible impact velocity. We considered either gas or liquid as a surrounding fluid, and experimental results are discussed for the gas-liquid set-up. Under certain conditions, a drop will not fully coalesce with the liquid reservoir, leaving behind a daughter drop. Partial coalescence is observed for systems of low viscosity, characterized by a small Ohnesorge number, where capillary waves remain sufficiently vigourous to distort the drop significantly. For drops coalescing with a flat interface, we determine the critical Ohnesorge number as a function of Bond number, as well as density and viscosity ratios of the fluids. Studying the coalescence of two drops of different sizes reveals that partial coalescence may occur in low-viscosity systems provided the size ratio of the drops exceeds a certain threshold. We also determine the extent to which the process of partial coalescence is self-similar and find that the viscosity of the drop has a large effect on the droplets vertical velocity after pinch off. Finally, we report on the formation of satellite droplets generated after a first pinch off and on the ejection of a jet of tiny droplets during coalescence of a parent drop significantly deformed by gravity.

Igneous Layering in Basaltic Magma Chambers

Layering is a common feature in mafic and ultramafic layered intrusions and generally consists of a succession of layers characterized by contrasted mineral modes and/or mineral textures, including grain size and orientation and, locally, changing mineral compositions. The morphology of the layers is commonly planar, but more complicated shapes are observed in some layered intrusions. Layering displays various characteristics in terms of layer thickness, homogeneity, lateral continuity, stratigraphic cyclicity, and the sharpness of their contacts with surrounding layers. It also often has similarities with sedimentary structures such as cross-bedding, trough structures or layer termination. It is now accepted that basaltic magma chambers mostly crystallize in situ in slightly undercooled boundary layers formed at the margins of the chamber. As a consequence, most known existing layering cannot be ascribed to a simple crystal settling process. Based on detailed field relationships, geochemical analyses as well as theoretical and experimental studies, other potential mechanisms have been proposed in the literature to explain the formation of layered igneous rocks. In this study, we review important mechanisms for the formation of layering, which we classify into dynamic and non-dynamic layer-forming processes.

Simulations of surfactant effects on the dynamics of coalescing drops and bubbles

We present simulations of coalescence in the presence of surfactant. We consider a fluid-fluid interface where we track surfactant concentration. Our model is applicable to a soap bubble merging with a suspended soap film and to a surfactant covered liquid drop merging with a reservoir. In both cases, we determine the regime in which coalescence is only partial. Along with viscous effects, represented by the Ohnesorge number, the elasticity of the surface tension relative to the surfactant concentration is seen to play a key role and exhibits a surprising nonmonotonic influence, for which we present a physical mechanism. The effects of gravity are also simulated, along with effects of differing initial conditions, as well as those of uneven initial surfactant concentration, as are likely to arise in physical applications. We describe how the presence of surfactants can influence a coalescence cascade.

Modeling Huddling Penguins

We present a systematic and quantitative model of huddling penguins. In this mathematical model, each individual penguin in the huddle seeks only to reduce its own heat loss. Consequently, penguins on the boundary of the huddle that are most exposed to the wind move downwind to more sheltered locations along the boundary. In contrast, penguins in the interior of the huddle neither have the space to move nor experience a significant heat loss, and they therefore remain stationary. Through these individual movements, the entire huddle experiences a robust cumulative effect that we identify, describe, and quantify. This mathematical model requires a calculation of the wind flowing around the huddle and of the resulting temperature distribution. Both of these must be recomputed each time an individual penguin moves since the huddle shape changes. Using our simulation results, we find that the key parameters affecting the huddle dynamics are the number of penguins in the huddle, the wind strength, and the amount of uncertainty in the movement of the penguins. Moreover, we find that the lone assumption of individual penguins minimizing their own heat loss results in all penguins having approximately equal access to the warmth of the huddle.

Electrically induced drop detachment and ejection

A deformed droplet may leap from a solid substrate, impelled to detach through the conversion of surface energy into kinetic energy that arises as it relaxes to a sphere. Electrowetting provides a means of preparing a droplet on a substrate for lift-off. When a voltage is applied between a water droplet and a dielectric-coated electrode, the wettability of the substrate increases in a controlled way, leading to the spreading of the droplet. Once the voltage is released, the droplet recoils, due to a sudden excess in surface energy, and droplet detachment may follow. The process of drop detachment and lift-off, prevalent in both biology and micro-engineering, has to date been considered primarily in terms of qualitative scaling arguments for idealized superhydrophobic substrates. We here consider the eletrically-induced ejection of droplets from substrates of finite wettability and analyze the process quantitatively. We compare experiments to numerical simulations and analyze how the energy conversion efficiency is affected by the applied voltage and the intrinsic contact angle of the droplet on the substrate. Our results indicate that the finite wettability of the substrate significantly affects the detachment dynamics, and so provide new rationale for the previously reported large critical radius for drop ejection from micro-textured substrates.

Drops settling in sharp stratification with and without Marangoni effects

We present numerical simulations of drops settling in a layered ambient fluid. We focus on nearly spherical drops with Reynolds numbers of order 10. The ambient is composed of miscible fluids, with the top layer lighter than the lower one, representing fluid stratified through temperature or salinity variations, while the drop itself is heavier than both layers. The surface tension between the ambient and the drop may or may not be different for each layer. Such a system can be used to model oil droplets settling or rising in the ocean. When surface tension is uniform, the drop slows down significantly as it encounters the transition region, due to entrained fluid from the upper layer, before accelerating again in the lower layer. We characterize this effect in terms of the sharpness of the transition, and the drops Reynolds number. When the upper and lower surface tensions are not matched, the drop may either suddenly accelerate through the transition region if the lower surface tension is less than the...

Modeling the vertical motion of drops bouncing on a bounded fluid reservoir

We present a first-principles model of drops bouncing on a liquid reservoir. We consider a nearly inviscid liquid reservoir and track the waves that develop in a bounded domain. Bouncing drops are modeled as vertical linear springs. We obtain an expression for the contact force between drop and liquid surface and a model where the only adjustable parameter is an effective viscosity used to describe the waves on the reservoir’s surface. With no adjustable parameters associated to the drop, we recover experimental bouncing times and restitution coefficients. We use our model to describe the effect of the Bond, Ohnesorge, and Weber numbers on drops bouncing on a stationary reservoir. We also use our model to describe drops bouncing on an oscillated reservoir, describing various bouncing modes and a walking threshold.

Stability of a stratified fluid with a vertically moving sidewall

We present the results of a combined theoretical and experimental study of the stability of a uniformly stratified fluid bounded by a sidewall moving vertically with constant velocity. This arrangement is perhaps the simplest in which boundary effects can drive instability and, potentially, layering in a stratified fluid. Our investigations reveal that for a given stratification and diffusivity of the stratifying agent, the sidewall boundary-layer flow becomes linearly unstable when the wall velocity exceeds a critical value. The onset of instability is clearly observed in the experiments, and there is good quantitative agreement with some predictions of the linear stability analysis.

The influence of suspended drops on peristaltic pumping

We present a numerical investigation of peristaltic pumping in the presence of suspended drops, the latter serving as a model for deformable obstructions. We impose a sinusoidal motion to an elastic tube thereby driving flow. Inertial and curvature effects are both accounted for, and we track streamlines and transport within the tube. It is found that drops of radius less than half that of the tube have little effect on the overall flow. Larger drops are found to become more easily trapped by the traveling wave and therefore to enhance transport. Inertial effects are seen to increase the size of the trapped region, but to limit the regime in which fluid may be trapped at all.