The interaction between moving bubbles, vapor voids in liquid, can arguably represent the simplest dynamical system in continuum mechanics as only a liquid and its vapor phase are involved. Surprisingly, and perhaps because of the ephemeral nature of bubbles, there has been no direct measurement of the time-dependent force between colliding bubbles which probes the effects of surface deformations and hydrodynamic flow on length scales down to nanometers. Using ultrasonically generated microbubbles (∼100 μm size) that have been accurately positioned in an atomic force microscope, we have made direct measurements of the force between two bubbles in water under controlled collision conditions that are similar to Brownian particles in solution. The experimental results together with detailed modeling reveal the nature of hydrodynamic boundary conditions at the air/water interface, the importance of the coupling of hydrodynamic flow, attractive van der Waals-Lifshitz forces, and bubble deformation in determining the conditions and mechanisms that lead to bubble coalescence. The observed behavior differs from intuitions gained from previous studies conducted using rigid particles. These direct force measurements reveal no specific ion effects at high ionic strengths or any special role of thermal fluctuations in film thickness in triggering the onset of bubble coalescence.bubble collision | colloidal forces | hydrodynamic interaction | soft matter | thin films B ubble dynamics has attracted scientific interest since the time of Leonardo da Vinci (1), yet the observation that some simple salts can prevent bubble coalescence at high concentrations whereas others cannot remains unexplained even after over a decade of systematic study (2). In themselves, bubble-bubble interactions are very important because they feature in diverse situations, from the basis of the bends in deep-sea divers, to the development of effective ultrasonic imaging contrast agents, through to enhancing the quality of champagne. However, the delicate and ephemeral nature of bubbles poses significant technical challenges to the precise quantification of the force-displacement characteristics of bubble collisions.As a vapor phase in a liquid, the interaction between bubbles should be amenable to a simple explanation in terms of basic physical and chemical principles. A detailed understanding of the interaction between moving bubbles can provide the foundation on which to study the fundamental coupling between forces and deformations that defines the dynamic interaction on the nanoscale between soft-matter materials, such as bubbles, drops, emulsions, biological cells, soft tissues, and gels. Here we report direct measurements of the dynamic force between two deformable microbubbles in water under a variety of accurately controlled collision protocols. The typical collision velocities are in the regime of Brownian particles of comparable dimensions. The experimental conditions are such that only attractive van der Waals-Lifshitz forces and hydrodynami...

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.

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In this paper, we consider a predator–prey model with herd behavior and prey‐taxis subject to the homogeneous Neumann boundary condition. First, by analyzing the characteristic equation, the local stability of the positive equilibrium is discussed. Then, choosing prey‐tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of nonconstant solutions bifurcating from the positive equilibrium by an abstract bifurcation theory, and find the stable bifurcating solutions near the bifurcation point under suitable conditions. We have shown that prey‐taxis can destabilize the uniform equilibrium and yields the occurrence of spatial patterns. Furthermore, some numerical simulations to illustrate the theoretical analysis are also carried out, Turing patterns such as spots pattern, spots–strip pattern, strip pattern, stable nonconstant steady‐state solutions, and spatially inhomogeneous periodic solutions are obtained, which also expand our theoretical results.