Physics of Fluids publishes in traditional areas of fluid dynamics as well as in novel and emerging areas of the field including dynamics of gases, liquids, and complex or multiphase liquids. Physics of Fluids is published with the cooperation of the APS Division of Fluid Dynamics.
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We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a HeleShaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsitypromoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the leastsquares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the ℓ1norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm wellsuited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we study a 2D convection problem in which viscosity depends on temperature by abruptly changing its value by a factor of 400 within a narrow temperature gap. We conduct a study which combines bifurcation analysis and timedependent simulations. Solutions such as limit cycles are found that are fundamentally related to the presence of symmetry. Spontaneous platelike behaviors that rapidly evolve towards a stagnant lid regime emerge sporadically through abrupt bursts during these cycles. The platelike evolution alternates motions towards either the right or the left, thereby introducing temporary asymmetries on the convecting styles. Further timedependent regimes with stagnant and platelike lids are found and described.

The results of an experimental study involving low Reynolds number, countercurrent flows of glycerol and air on an inclined glass substrate inside a rectangular channel are presented. The interface forms a thickened front immediately upstream of a thin, precursor layer region. This front is vulnerable to spanwise perturbations, which, under certain conditions, grow to acquire the shape of “fingers.” Decreasing the inclination angle has a stabilizing effect on the front; complete stability is achieved below a critical angle whose value depends on the remaining system parameters. Regions of transient finger formation are also observed. It is also found that increasing the ratio of the precursor to the inlet film thickness, and increasing the liquid and air flowrates also exerts a stabilizing effect on the interface. Analyses of the initial finger growthrate corroborate the findings of previous theoretical work, showing this growthrate to be independent of inclination angle and liquid film Reynolds number, and weaklydependent on the air flowrate for low inclination angles. Both qualitative and quantitative agreement with theoretical studies from the literature was also found, in terms of the effects of flow parameters and the observed dynamics of the developing fingers.

We study the stability of a static liquid column rising from an infinite pool, with its top attached to a horizontal plate suspended at a certain height above the pool's surface. Two different models are employed for the column's contact line. Model 1 assumes that the contact angle always equals Young's equilibrium value. Model 2 assumes a functional dependence between the contact angle and the velocity of the contact line, and we argue that, if this dependence involves a hysteresis interval, linear perturbations cannot move the contact line. It is shown that, within the framework of Model 1, all liquid columns are unstable. In Model 2, both stable and unstable columns exist (the former have larger contact angles θ and/or larger heights H). For Model 2, the marginal stability curve on the (θ, H)plane is computed. The mathematical results obtained imply that, if the plate to which a stable liquid column is attached is slowly lifted up, the column's contact line remains pinned while the contact angle is decreasing. Once it reaches the lower boundary of the hysteresis interval, the column breaks down.