Related papers: Radius and surface tension of microscopic bubbles …
We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied…
This paper concerns global existence for arbitrary nonzero surface tension of bubbles in a Hele-Shaw cell that translate in the presence of a pressure gradient. When the cell width to bubble size is sufficiently large, we show that a unique…
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…
The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical…
These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a…
It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also {\it{buoyancy}} can play an important role at breakup. In order to better understand this role,…
Bubble formation and detachment at a submerged orifice exists widely in both daily life and academic research, and the influence of solid surface on bubble formation and detachment has also been extensively investigated. For example, it has…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
We employ a novel fluid-particle model to study the shearing behavior of granular soils under different saturation levels, ranging from the dry material via the capillary bridge regime to higher saturation levels with percolating clusters.…
Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived…
In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…
The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally…
The classical continuum mechanical model of granular media of rational thermodynamics results in a Coulomb-Mohr type equilibrium stress-strain relation. The proof is based on a two component material model introducing a scalar internal…
We describe experiments on B{\'e}nard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a…
Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole…
The study of gas bubble dynamics in liquids is justified by the numerous applications and natural phenomena where this two-phase flow is encountered. Gas bubbles move as forces are applied to them; their dynamics are full of nuances that…
This paper deals with the controllability of the second grade fluids, a class of non-Newtonian of differentiel type, on a two-dimensional torus. Using the method of Agrachev-Sarychev [1], [2] and of Sirikyan [26], we prove that the system…
Surface bubbles are present in many industrial processes and in nature, as well as in CO$_2$ beverage. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of…
By means of a relativistic microscopic approach we calculate the expansion velocity of bubbles generated during a first-order electroweak phase transition. In particular, we use the gradient expansion of the Kadanoff-Baym equations to set…
We performed numerical simulations of a homogeneous swarm of bubbles rising at large Reynolds number, Re = 760 with volume fractions ranging from 1% to 10%. We consider a simplified model in which the interfaces are not resolved, but which…