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In this paper, we discuss the well‐posedness of impinging flow through a semi‐infinitely long nozzle and impacting on a plane. More precisely, given the semi‐infinitely long nozzle with finite inlet, the plane, and the positive incoming horizontal velocity, then there exists a unique smooth solution to the impinging flow. Moreover, there exists a smooth free interface that separates the fluid such that it flows out of different outlets in the downstream. [ABSTRACT FROM AUTHOR]

In this work, the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional (2D) immersed boundary-multiphase lattice Boltzmann flux solver (IB-MLBFS). The fluid domain is discretized by finite volume discretization, and the flux on the grid interface is evaluated by lattice Boltzmann equations. Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure. First, the water entry of a circular cylinder is simulated and the results are compared with the experiment, which considered the length-diameter ratio of the circular cylinder. The reliability of 2D simulation is verified and the deformation of the free interface is well investigated. Afterward, the water exit of a circular cylinder with constant velocity is simulated, which is less researched. In addition, the results show the advantage of present IB-MLBFS to some extent. Finally, the water exit and re-entry of a circular cylinder are presented, and the results present the complex deformation of the free interface and the dynamic response of the moving structure. Based on the numerical results, the free interface of the multiphase fluids is well captured, and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS. [ABSTRACT FROM AUTHOR]

Microorganisms often swim within heterogeneous fluid media composed of multiple materials with very different properties. The swimming speed is greatly affected by the composition and rheology of the fluidic environment. In addition, biological locomotions are also strongly influenced by the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary significantly. Using a two-fluid immersed boundary method, we investigate the classical Taylor's swimming sheet problem near interfaces within multi-fluid media. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and phase separation in the multi-fluid mixture are closely coupled with the movement of the swimmer. Depending on the interface location, the frictional coefficient, and the multi-fluid composition, the swimmer can move faster or slower than that in a single phase fluid. [ABSTRACT FROM AUTHOR]

In this paper, we study the global existence of steady subsonic flows with collision, where the collision is caused by a confluence of two semi‐infinitely incoming flows that are nonmiscible steady subsonic irrotational Euler flows come from two different infinitely nozzles. First, we prove that when the total flux of two incoming flows is less that the critical mass flux, there exists a unique global smooth subsonic flow with collision. Meanwhile, the interface between two flows is a smooth free interface, which is determined uniquely by the mass fluxes of incoming flows. Second, by using the blowup argument, we establish the asymptotic behaviors for the stream function. Finally, we prove that the position of free interface can be determined uniquely by the mass fluxes of incoming flows. Moreover, we establish the monotonicity of the relation between the position of free interface and the mass fluxes of incoming flows. [ABSTRACT FROM AUTHOR]

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'. [ABSTRACT FROM AUTHOR]

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G. I. Sivashinsky. Our approach is twofold: (I) We eliminate the front and get to a fully nonlinear system with boundary conditions; (II) We use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations is presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II). [ABSTRACT FROM AUTHOR]

The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented. [ABSTRACT FROM AUTHOR]

solution was put forward to predicate the flow pattern of gas penetration in gas-assisted injection molding. The differential equations that governed the flow field and gas/melt free-interface evolution were analyzed and discretized by Galerkin finite element method, and the free interface was located by the volume of fluid method. The gas was assumed as a fluid phase of constant density and viscosity instead of being simply treated as boundary conditions. The non-Newtonian property of polymer melt was characterized by Carreau model with four parameters. As a case study, different kinds of gas channel were modeled. The gas/melt free interface was captured. The gas front velocity and the pressure of gas/melt front were also computed. The edge shape of gas channel was discussed, which are helpful for the design of gas-assisted injection molding. [ABSTRACT FROM AUTHOR]