Physics of beer tapping

The popular bar prank known in colloquial English as beer tapping consists in hitting the top of a beer bottle with a solid object, usually another bottle, to trigger the foaming over of the former within a few seconds. Despite the trick being known for long time, to the best of our knowledge, the phenomenon still lacks scientific explanation. Although it seems natural to think that shock-induced cavitation enhances the diffusion of CO$_2$ from the supersaturated bulk liquid into the bubbles by breaking them up, the subtle mechanism by which this happens remains unknown. Here we show that the overall foaming-over process can be divided into three stages where different physical phenomena take place in different time-scales, namely: bubble-collapse (or cavitation) stage, diffusion-driven stage and buoyancy-driven stage. In the bubble-collapse stage, the impact generates a train of expansion-compression waves in the liquid that leads to the fragmentation of pre-existing gas cavities. Upon bubble fragmentation, the sudden increase of the interface-area-to-volume ratio enhances mass transfer significantly, which makes the bubble volume grow by a large factor until CO$_2$ is locally depleted. At that point buoyancy takes over, making the bubble clouds rise and eventually form buoyant vortex rings whose volume grows fast due to the feedback between the buoyancy-induced rising speed and the advection-enhanced CO$_2$ transport from the bulk liquid to the bubble. The physics behind this explosive process might also be connected to some geological phenomena.Comment: 7 pages, 4 figures, 4 movies Accepted in Physical Review Letter

The physics of Beer Tapping

The popular bar prank known in colloquial English as beer tapping consists in hitting the top of a beer bottle with a solid object, usually another bottle, to trigger the foaming over of the former within a few seconds. Despite the trick being nown for a long time, to the best of our knowledge, the phenomenon still lacked scientific explanation. Although it seems natural to think that shock-induced cavitation enhances the diffusion of CO2 from the supersaturated bulk liquid into the bubbles by breaking them up, the subtle mechanism by which this happens remains unknown. Here, we show that the overall foaming-over process can be divided into three stages where different physical phenomena take place in different time scales: namely, the bubble- collapse (or cavitation) stage, the diffusion-driven stage, and the buoyancy-driven stage. In the bubble-collapse stage, the impact generates a train of expansion-compression waves in the liquid that leads to the fragmentation of preexisting gas cavities. Upon bubble fragmentation, the sudden increase of the interface-area-to-volume ratio enhances mass transfer significantly, which makes the bubble volume grow by a large factor until CO2 is locally depleted. At that point buoyancy takes over, making the bubble clouds rise and eventually form buoyant vortex rings whose volume grows fast due to the feedback between the buoyancy-induced rising speed and the advection-enhanced CO2 transport from the bulk liquid to the bubble. The physics behind this explosive process sheds insight into the dynamics of geological phenomena such as limnic eruptions.Máster en Hidráulica Ambienta

Bubbles dynamics in microchannels: inertial and capillary migration forces

This work focuses on the dynamics of a train of unconfined bubbles flowing in microchan- nels. We investigate the transverse position of a train of bubbles, its velocity and the associated pressure drop when flowing in a microchannel depending on the internal forces due to viscosity, inertia and capillarity. Despite the small scales of the system, inertia, referred to as inertial migration force, play a crucial role in determining the transverse equilibrium position of the bubbles. Beside inertia and viscosity, other effects may also affect the transverse migration of bubbles such as the Marangoni surface stresses and the surface deformability. We look at the influence of surfactants in the limit of infinite Marangoni effect which yields rigid bubble interface. The resulting migration force may balance external body forces if present such as buoyancy, Dean or magnetic ones. This balance not only determines the transverse position of the bubbles but, consequently, the surrounding flow structure, which can be determinant for any mass/heat transfer process involved. Finally, we look at the influence of the bubble deformation on the equilibrium position and compare it to the inertial migration force at the centred position, explaining the stable or unstable character of this position accordingly. A systematic study of the influence of the parameters - such as the bubble size, uniform body force, Reynolds and capillary numbers - has been carried out using numerical simulations based on the Finite Element Method, solving the full steady Navier-Stokes equations and its asymptotic counterpart for the limits of small Reynolds and/or capillary numbers.Comment: Submitted to JF

Molecular dynamics simulations of Ibuprofen release from pH-gated silica nanochannels

The iboprufen delivery process from cylindrical silica pores of diameter 3~nm, with polyamine chains anchored at the pore outlets,was investigated by means of massive molecular dynamics simulations. Effects from pH were introduced by considering polyamine chains with different degree of protonation. High, low and intermediate pH environments were investigated. The increment of the acidity of the environment leads to a significant decrease of the pore aperture,  yielding an effective diameter, for the lowest pH case, that is 3.5~times smaller than the one associated to the highest pH one. Using a biased sampling procedure, Gibbs free energy profiles for the ibuprofen delivery process were obtained. The joint analysis of the corresponding profiles, time evolution of the ibuprofen position within the channel, orientation of the molecule and instantaneous effective diameter of the gate, suggests a 3-steps mechanism for ibuprofen delivery. A complementary analysis of the translational mobility of ibuprofen along the axial direction of the channel revealed a sub-diffusive dynamics in the low and intermediate pH cases.Deviations from Brownian diffusive dynamics are discussed and compared with direct experimental results. Fil: Rodriguez, Javier. Comisión Nacional de Energía Atómica; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo de Investigación en Educacion Ciencia y Tecnologia; ArgentinaFil: Elola, Maria Dolores. Comisión Nacional de Energía Atómica; Argentin

On the von Neumann and Frank-Wolfe Algorithms with Away Steps

The von Neumann algorithm is a simple coordinate-descent algorithm to determine whether the origin belongs to a polytope generated by a finite set of points. When the origin is in the of the polytope, the algorithm generates a sequence of points in the polytope that converges linearly to zero. The algorithm's rate of convergence depends on the radius of the largest ball around the origin contained in the polytope. We show that under the weaker condition that the origin is in the polytope, possibly on its boundary, a variant of the von Neumann algorithm that includes generates a sequence of points in the polytope that converges linearly to zero. The new algorithm's rate of convergence depends on a certain geometric parameter of the polytope that extends the above radius but is always positive. Our linear convergence result and geometric insights also extend to a variant of the Frank-Wolfe algorithm with away steps for minimizing a strongly convex function over a polytope