Crown formation from a cavitating bubble close to a free surface

A rapidly growing bubble close to a free surface induces jetting: a central jet protruding outwards and a crown surrounding it at later stages. While the formation mechanism of the central jet is known and documented, that of the crown remains unsettled. We perform axisymmetric simulations of the problem using the free software program BASILISK, where a finite-volume compressible solver has been implemented, which uses a geometric volume-of-fluid (VoF) method for the tracking of the interface. We show that the mechanism of crown formation is a combination of a pressure distortion over the curved interface, inducing flow focusing, and of a flow reversal, caused by the second expansion of the toroidal bubble that drives the crown. The work culminates in a parametric study with the Weber number, the Reynolds number, the pressure ratio and the dimensionless bubble distance to the free surface as control parameters. Their effects on both the central jet and the crown are explored. For high Weber numbers, we observe the formation of weaker ‘secondary crowns’, highly correlated with the third oscillation cycle of the bubble.

Thermal fracture of functionally graded thermal barrier coatings with pre-existing edge cracks and multiple internal cracks imitating a curved interface

This work is devoted to the problem of thermal fracture of a functionally graded coating on a homogeneous substrate (FGC/H) with an emphasis on the analysis of a special system of cracks that simulates a curved interface. The FGC/H structure contains the pre-existing crack system in the FGC, both edge cracks (which are often seen in FGC/H structures) and internal cracks. The stress intensity factors are calculated. (Generally, both Mode I and Mode II are nonzero.) Then, using the appropriate fracture criterion for mixed-mode fracture conditions, the crack propagation direction (so-called fracture angles) and critical loads, when this propagation is initiated, are determined. The application of fracture criteria requires knowledge of the fracture toughness near the crack tips. Thus, it is assumed that the fracture toughness of an FGC, as well as other material properties, continuously varies through the thickness of the coating. For multiple cracks, it is also important to know the weakest crack that starts to propagate first, and the initial direction of this growth. Therefore, the main attention is paid to the evaluation of the fracture angles for the cracks for different parameters of the FGC/H structure. Both cases of a homogeneous semi-infinite medium with a system of cracks imitating a curved interface and FGC/H structures with identical crack systems are studied.

Capillary force on an 'inert' colloid: a physical analogy to dielectrophoresis

''Inert'' colloids are μm-scale particles that create no distortion when trapped at a planar fluid-fluid interface. When placed in a curved interface, however, such colloids can create interfacial distortions of...

Stability analysis of a nanopatterned bimaterial interface

In the article it is shown that the nanopatterned interface of bimaterial is unstable due to the diffusion atom flux along the interface. The main goal of the research is to analyze the conditions of interface stability. The authors developed a model coupling thermodynamics and solid mechanics frameworks. In accordance with the Gurtin—Murdoch theory of surface/interface elasticity, the interphase between two materials is considered as a negligibly thin layer with the elastic properties differing from those of the bulk materials. The growth rate of interface roughness depends on the variation of the chemical potential at the curved interface, which is a function of interface and bulk stresses. The stress distribution along the interface is found from the solution of plane elasticity problem taking into account plane strain conditions. Following this, the linearized evolution equation is derived, which describes the amplitude change of interface perturbation with time.

Amplitude and phase changes for reflected and transmitted waves from a curved interface in anisotropic media

Summary It is well known that seismic data that have been recorded in complex geological environments must be compensated for geometrical spreading before AVO/AVA analysis, in order to avoid erroneous imaging interpretation. By investigating analytically both the effect of the geometrical spreading and the effect of the reflector curvature on amplitude and phase changes for reflected and transmitted waves between anisotropic media, using ray theory, we show that these data should be compensated for interface effects as well. In order to gain insight more specifically in the focusing effect of the interface, the special case of homogeneous isotropic media separated by a curved interface of syncline type is discussed and compared to the case of a plane interface. 3D numerical simulations of wave reflection from curved interfaces using a Spectral-Element Method validate our analytical derivations. In particular, numerical seismograms obtained at a vertical receiver array highlight that the effect of interface curvature on the reflected events is much more pronounced in a restricted area associated with the existence of caustics, which is consistent with our analytical predictions. Moreover, comparisons between the numerical and the analytical results confirm the fact that using plane-wave reflection coefficients without correction for the interface effect may lead to wrong interpretation of AVA/AVO analysis.

Oscillating PDE in a rough domain with a curved interface: homogenization of an optimal control problem

Homogenization of an elliptic PDE with periodic oscillating coefficients and an associated optimal control problems with energy type cost functional is considered. The domain is a 3-dimensional region (method applies to any $n$ dimensional region) with oscillating boundary, where the base of the oscillation is curved and it is given by a Lipschitz function. Further, we consider a general elliptic PDE with oscillating coefficients. We also include very general type cost functional of Dirichlet type given with oscillating coefficients which can be different from the coefficient matrix of the equation. We introduce appropriate unfolding operators and approximate unfolded domain to study the limiting analysis. The present article is new in this generality.