A solution to the upward migration of an intrusion

The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.

Two Bubbles Thermocapillary Migration Experimental System

An experimental investigation will be performed on the thermocapillary motion of two bubbles in Chinese return-satellite. The experiment will study the migration process of bubble caused by thermocapillary effect in microgravity environment, and their interaction between two bubbles. The bubble is driven by the thermocapillary stress on the surface on account on the variation of the surface tension with temperature. The interaction between two bubbles becomes significant as the separation distance between them is reduced drastically so that the bubble interaction has to be considered. Recently, the problem has been discussed on the method of successive reflections, and accurate migration velocities of two arbitrarily oriented bubbles were derived for the limit of small Marangoni and Reynolds numbers. Numerical results for the migration of the two bubbles show that the interaction between two bubbles has significant influence on their thermocapillary migration velocities with a bubble approaching another. However, there is a lack of experimental validate for the theoretic results. Now the experimental facility is designed for experimenting time after time. A cone-shaped top cover is used to expel bubble from the cell after experiment. But, the cone-shaped top cover can cause temperature uniformity on horizontal plane in whole cell. Therefore, a metal board with multi-holes is fixed under the top cover. The board is able to let the temperature distribution on the board uniform because of their high heat conductivity, and the bubble can pass through it. In the system two bubbles are injected into the test cell respectively by two sets of cylinder. And the bubbles sizes are controlled by two sets of step-by-step motor. It is very important problem that bubble can be divorced from the injecting mouth in microgravity environment. Thus, other two sets of device for injecting mother liquid were used to push bubble. The working principle of injecting mother liquid is to utilize pressure difference directly between test cell and reservoir

Influence of Wind and Grain Size on Migration of Asymmetric Sand Waves

Large parts of shallow seas are covered by regular seabed patterns and sand wave is one kind of these patterns. The instability of the sedimentary structures may hazard pipelines and the foundations of offshore structures. In the last decade or so, it's a focus for engineers to investigate the movement mechanism of sand waves. Previous theoretical studies of the subject have developed a general model to predict the growth and migration of sand waves, which is based on the two-dimensional vertical shallow water equations and the bed-form deformation equations. Although the relation between wave-current flow and sand bed deformation has been established, the topographic influence has not been considered in the model. In this paper some special patterns, which are asymmetric and close to the reality, are represent as the perturbed seabed and the evolution of sand waves is calculated. The combination of a steady flow induced by wind and a sinusoidal tidal flow is considered as the basic flow. Finally the relations of some parameters (grain size, etc.) and sand waves' growth and migration are discussed, and the growth rate and migration speeds of asymmetric sand waves are carried out.