Retention of Rising Oil Droplets in Density Stratification

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification, with the goal of quantifying and parametrizing the impact of stratification on timescales that describe the delay in rising. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and these are the first experiments to study single liquid droplets as opposed to solid particles or bubbles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two new timescales which quantitatively describe this slowdown: an entrainment timescale and a retention timescale. These timescales measure dynamics that were not captured in previous timescale discussions, which primarily focused on the timescale to the velocity minimum (Umin). The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the duration over which the droplet\u27s rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. These two timescales are interconnected by the magnitude of the slowdown (Uu−Umin) relative to the upper-layer terminal velocity (Uu), as well as a constant that reflects the approximately universal form of the recovery of a droplet\u27s velocity from Uminto Uu. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr =Uu/(Nd) and Re =ρuUud/ν. We find that both timescales are only significantly large for Fr ≲1, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the force enhancement Γ, the ratio between the maximum stratification-induced force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622 (2019)] on the force enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach

Retention of rising droplets in density stratification

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and are the first experiments to study single liquid droplets as opposed to solid particles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two timescales which quantitatively describe this slowdown: an entrainment timescale, and a retention timescale. The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the length of time over which the droplet's rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr $=U_u/(Nd)$ and Re $=\rho_u U_u d/\nu$. We find that both timescales are only significantly large for Fr $\lesssim1$, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the drag enhancement $\Gamma$, the ratio between the maximum stratification force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622-656 (2019)] on the drag enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence

Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to $N=3\times 10^6$) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density

Dancing disclinations in confined active nematics

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to achieve structured flows and ordered disclinations is of particular importance in the design and control of active systems. By confining an active nematic fluid within a channel, we find a regular motion of disclinations, in conjunction with a well defined and dynamic vortex lattice. As pairs of moving disclinations travel through the channel, they continually exchange partners producing a dynamic ordered state, reminiscent of Ceilidh dancing. We anticipate that this biomimetic ability to self-assemble organised topological disclinations and dynamically structured flow fields in engineered geometries will pave the road towards establishing new active topological microfluidic devices

Gestion des déjections de bovins et pollution par les nitrates: Diversité des pratiques dans les élevages laitiers du plateau lorrain

National audienceThe author monitored the management practices of cattle excreta on some 20 farms selected for their diversity on the Plateau Lorrain in eastern France. A relation was found between the type of cattle housing, the type of basic ration of the herd during indoor wintering, and dung spreading practices. On the basis of current knowledge on nitrogen cycling he is able to predict the consequences of these practrices on the mineralisation rate of dung spread on the fields, on the risks of leaching of the nitrates produced and on the possibilities of their utilisation and uptaked by the sward.L'auteur a observé les pratiques de gestion des déjections de gros bovins dans une vingtaine d'exploitations du Plateau Lorrain choisis pour leur diversité. Il en déduit une relation entre le type de bâtiment d'élevage, le type de ration de base du troupeau pendant la période de stabulation en hiver et les pratiques d'épandages des déjections. Il se réfère aux connaissances actuelles sur le cycle de l'azote pour prévoir les conséquences de ces pratiques sur la cinétique de la minéralisation des déjections épandues, sur les risques de lessivage des nitrates produits et sur les possibilités de leur valorisation par les couverts végétaux

A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids – Application to shape optimization

We present a numerical method for solving the equations of linear elasticity on irregular domains in two and three spatial dimensions. We combine a finite volume and a finite difference approaches to derive discretizations that produce second-order accurate solutions in the L^∞-norm. Our discretization is 'sharp' in the sense that the physical boundary conditions (mixed Dirichlet/Neumann-type) are imposed at the interface and the solution is computed inside the irregular domain only, without the need of smearing the solution across the interface. The irregular domain is represented implicitly using a level-set function so that this approach is applicable to free moving boundary problems; we provide a simple example of shape optimization to illustrate this capability. In addition, we provide an extension of our method to the case of adaptive meshes in both two and three spatial dimensions: we use non-graded quadtree (2D) and octree (3D) data structures to represent the grid that is automatically refined near the irregular domain’s boundary. This extension to quadtree/octree grids produces second-order accurate solutions albeit non-symmetric linear systems, due to the node-based sampling nature of the approach. However, the linear system can be solved with simple linear solvers; in this work we use the BICGSTAB algorithm