Equations Of Motion For Liquid Research Articles

Poro-Thermoelastic Waves in a Homogeneous Anisotropic Plate Plunged in the Inviscid Fluid

This paper inspects the behavior of thermoelastic waves in the homogeneous, transversely isotropic plate containing voids immersed in the inviscid fluid in reference to the one-temperature generalized model of thermoelasticity. The basic governing equations for the solid plate have been developed in the context of the linear theory of poro-thermoelasticity. Helmholtz decomposition principle has been employed to solve the equations of motion for liquid. For the stress-free solid-liquid interfaces, the isothermal and thermally insulated boundary conditions have been applied simultaneously on the obtained solutions. The solutions of governing equations reveal that there exists a coupled system of waves namely thermal waves, void wave motion, and elastic waves, and a decoupled purely transverse wave. Apart from that, one mechanical wave in each liquid layer also exists. The secular equation for anti-symmetric and symmetric modes of vibration has been derived which better explains wave motion. To unveil the wave characteristics, the numerical–functional iteration technique has been employed for generating numerical data and results have been validated by tracing out the various graphs. The effects of temperature change, as well as voids in the solid plate and inviscid liquid in the neighborhood of the plate, have been noticed on phase velocity, attenuation coefficient, etc

Analyzing the influence of a particle's linear and angular velocity on the equations of liquid motion

This paper has analyzed the equation of motion in terms of stresses (Navier), as well as its two special cases for an incompressible viscous current. One is the Stokes (Navier-Stokes) equation, and the other was derived with fewer restrictions. It has been shown that the Laplace equation of linear velocity can be represented as a function of two variables ‒ the linear and angular speed of particle rotation. To describe the particle acceleration, all motion equations employed a complete derivative from speed in the Gromeka-Lamb form, which depends on the same variables. Taking into consideration the joint influence of linear and angular velocity allows solving a task of the analytical description of a turbulent current within the average model. A given method of analysis applies the provision of general physics that examines the translational and rotational motion. The third type of mechanical movement, oscillatory (pulsation), was not considered in the current work. A property related to the Stokes equation decomposition has been found; a block diagram composed of equations and conditions has been built. It is shown that all equations for viscous liquid have their own analog in a simpler model of non-viscous fluid. That makes it easier to find solutions to the equations for the viscous flow. The Stokes and Navier equations were used to solve two one-dimensional problems, which found the distribution of speed along the normal to the surface at the flow on a horizontal plate and in a circular pipe. Both solution methods produce the same result. No solution for the distribution of speed along the normal to the surface in a laminar sublayer could be found. A relevant task related to the mathematical part is to solve the problem of closing the equations considered. A comparison of the theoretical and empirical equations has been performed, which has made it possible to justify the assumption that a rarefied gas is the Stokes liquid

Numerical investigation of shock induced bubble collapse in water

A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.

Linear stability analysis of reaction fronts in liquids

The propagation of a reaction front for liquid-to-solid reaction is studied. The model includes the heat equation, an equation for the concentration of the liquid reactant, and the equations of liquid motion under the Boussinesq approximation. The linear stability of the reaction front is studied, and conditions for cellular and oscillatory instability are determined.