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Droplet migration in a Hele-Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and high mesh resolution is only used near the interface. Parametric studies are performed on the droplet horizontal radius and the capillary number. For droplets with an horizontal radius larger than half the channel height, the droplet overfills the channel and exhibits a pancake shape. A lubrication film is formed between the droplet and the wall and particular attention is paid to the effect of the lubrication film on the droplet velocity. The computed velocity of the pancake droplet is shown to be lower than the average inflow velocity, which is in agreement with experimental measurements. The numerical results show that both the strong shear induced by the lubrication film and the three-dimensional flow structure contribute to the low mobility of the droplet. In this low-migration-velocity scenario, the interfacial flow in the droplet reference frame moves toward the rear on the top and reverses direction moving to the front from the two side edges. The velocity of the pancake droplet and the thickness of the lubrication film are observed to decrease with capillary number. The droplet velocity and its dependence on capillary number cannot be captured by the classic Hele-Shaw equations, since the depth-averaged approximation neglects the effect of the lubrication film. [ABSTRACT FROM AUTHOR]

We investigate theoretically and numerically a model of a supersolid in a dipole-blockaded Bose-Einstein condensate. The dependence of the superfluid fraction with an imposed thermal bath and a uniform boost velocity on the condensate is considered. Specifically, we observe a critical velocity for the nucleation of vortices in our system that is strongly linked to a steplike decrease in the superfluid fraction. We are able to use a scaling argument based on the energy required to activate a vortex, relating the critical temperature to the critical velocity, and find that this relationship is in good agreement with the numerical simulations carried out on the nonlocal Gross-Pitaevskii equation. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) capillary retraction of a viscous liquid film is studied using numerical and analytical approaches for both diphasic and free surface flows. Full 2D Navier-Stokes equations are integrated numerically for the diphasic case, while one-dimensional (1D) free surface model equations are used for free surface flows. No pinch-off is observed in the film in any of these cases. By means of an asymptotic matching method on the 1D model, we derive an analytical expansion of the film profile for large times. Our analysis shows that three regions with different timescales can be identified during retraction: the rim, the film, and an intermediate domain connecting these two regions. The numerical simulations performed on both models show good agreement with the analytical results. Finally, we report the appearance of an instability in the diphasic retracting film for small Ohnesorge number. We understand this as a Kelvin-Helmholtz instability arising due to the formation of a shear layer in the neck region during the retraction. [ABSTRACT FROM AUTHOR]

In order to test the rheology of granular flows, we performed series of numerical simulations of nearly monodisperse stationary chute flows from rapid to slow and very slow flow regime, namely, close to the jamming transition. We check how existing rheological models (i.e., Bagnold's model and the I-model) capture the behavior of the numerical flows, and perform an acute characterization of the structure of the flow in terms of grains velocity fluctuations close to the jamming transition. The simulations show that both Bagnold's and the I-model fail to describe the data points in the slow regime, namely, when I≤2×10-2. Turning to the analysis of grains velocity fluctuations, we compute the associated correlation length λ and show its dependence on the inertial number: λ/d∝I-0.32. The amplitude of the grains velocity fluctuations, namely, the granular temperature, exhibits a power-law dependence on the shear rate and allows for an efficient prediction of the shape of the velocity profiles. The main result consists of a scaling merging all data points for all flow regimes onto the same master curve, and relating granular temperature, shear rate, and the variation of stress between the considered depth and the bottom wall. This scaling can be written as a relation between local stress, local shear rate, and local temperature, provided the introduction of a characteristic length scale ξ=d(H-z)/z where both the distance to the surface and the distance to the bottom wall are involved. This scaling strongly suggests a nonlocal behavior, valid in the flow regime and extending close to the jamming transition, and hints at granular temperature as the variable at the origin of the nonlocality. [ABSTRACT FROM AUTHOR]

We study the transverse instability of a retracting liquid rim using a long wavelength approximation model and full numerical simulations. We observe that the instability of the rim is driven both by the Rayleigh-Taylor mechanism because of the initial rim acceleration, and by the Rayleigh-Plateau one. The coupling between the rim and the sheet stabilizes the rim at long wavelength. Full numerical simulations are in good agreement with the model and the subsequent break-up of droplets is observed in the numerical simulations when the instability is strong enough. [ABSTRACT FROM AUTHOR]

Abstract: We describe computations performed using the Gerris code, an open-source software implementing finite volume solvers on an octree adaptive grid together with a piecewise linear volume of fluid interface tracking method. The parallelisation of Gerris is achieved by domain decomposition. We show examples of the capabilities of Gerris on several types of problems. The impact of a droplet on a layer of the same liquid results in the formation of a thin air layer trapped between the droplet and the liquid layer that the adaptive refinement allows to capture. It is followed by the jetting of a thin corolla emerging from below the impacting droplet. The jet atomisation problem is another extremely challenging computational problem, in which a large number of small scales are generated. Finally we show an example of a turbulent jet computation in an equivalent resolution of cells. The jet simulation is based on the configuration of the Deepwater Horizon oil leak. [Copyright &y& Elsevier]