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Register a new userExact solutions of the problem of dynamics of a fluid with a free surface located between two approaching vertical walls
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Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the sides) by two solid vertical walls approaching each other with a constant velocity. The solutions are obtained for a situation where the capillary and gravity forces are absent, and the fluid motion is completely determined by the motion of the walls. The solutions contain an arbitrary function, which allows one to describe the nonlinear evolution of perturbations of an arbitrary shape for an initially flat horizontal surface of the fluid. Examples of exact solutions corresponding to the formation of bubbles, cuspidal points, and droplets are considered.
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The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and its magnitude is much larger then the instability threshold, the asymptotic behavior of the system can be described by the well-known 3D Laplacian growth equations. The integrability of these equations in 2D geometry makes it possible to described the evolution of the surface up to the formation of singularities, viz., cuspidal point at which the electric field strength, the velocity of the liquid, and the curvature of its surface assume infinitely large values. The exact solutions obtained for the problem of the electrocapillary wave profile at the boundary of liquid helium indicate the tendency to a charge in the surface topology as a result of formation of charged bubbles.
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.
In the present study, simulations are directed to capture the dynamics of evacuating inner gas of a bubble bursting at the free surface, using Eulerian based volume of fluid (VOF) method. The rate by which surrounding air rushing inside the bubble cavity through the inner gas evacuation is estimated and compared by the collapsing bubble cavity during the sequential stages of the bubble bursting at the free surface. Further, the reachability of inner gas over the free surface is evaluated by establishing the comparison of the same through various horizontal planes, lying at different altitudes above the unperturbed surface. The evacuating inner gas accompanies vortex rings, which entrains the surrounding gas-phase. During the successive stages of air entrainment, spatiotemporal characteristics of the vortex ring are obtained. At low Bond numbers (< 1), after comparing the phase contours of evacuating inner gas from the bubble cavity, the consequences at the axial growth of gas jet and the radial expansion of the jet tip is discussed separately. Furthermore, under the respiration process, the axial growth of rising inner gas over the free surface and the radial expansion of vortex rings of a bubble bursting at the free surface is compared with the quiescent surrounding air. At last, the effects of various possible asymmetric perforation of the bubble cap keeping the same Bo are studied. The cause of bent gas jet, as a consequence of perforation of the bubble cap, asymmetrically, is explained by plotting the velocity vectors.
A physical model of a three-dimensional flow of a viscous bubbly fluid in an intermediate regime between bubble formation and breakage is presented. The model is based on mechanics and thermodynamics of a single bubble coupled to the dynamics of a viscous fluid as a whole, and takes into account multiple physical effects, including gravity, viscosity, and surface tension. Dimensionle
In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent atoms are determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid which isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here we report the creation of a cohesive two-dimensional chiral liquid consisting of millions of spinning colloidal magnets and study its flows. We find that dissipative viscous edge pumping is a key and general mechanism of chiral hydrodynamics, driving uni-directional surface waves and instabilities, with no counterpart in conventional fluids. Spectral measurements of the chiral surface dynamics reveal the presence of Hall viscosity, an experimentally long sought property of chiral fluids. Precise measurements and comparison with theory demonstrate excellent agreement with a minimal but complete chiral hydrodynamic model, paving the way for the exploration of chiral hydrodynamics in experiment.
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