A coarse-grained molecular dynamics method coupled with umbrella sampling is developed to study the desorption process of SDS and CTAC surfactants from spherical micelles. The influence mechanisms of aggregation number, salt species and concentrations on the desorption process of surfactant from spherical micelles are revealed. We find that the radius and eccentricity of spherical micelles both increase with aggregation number rising, and the effects of salt concentration depend on the ionic radius and adsorption characteristics of the counterions. Larger salicylate ions with stronger adsorption ability have more significant effect on the micellar structures. Based on umbrella sampling method, we obtain the desorption free energy and time of surfactants from micelles. we find that the desorption free energy and desorption time of surfactant both show a non-monotonic variation with the increase of aggregation number and salt concentration, whose mechanisms are attributed to the electrostatic shielding induced by ion adsorption on micelle surface. Moreover, we reveal that the free energy plays a leading role in surfactant desorption process. Combing the theory of micelle thermodynamics, we further develop the critical micelle concentration prediction method, and obtain the distribution range of micelle size under the critical micelle concentration of surfactants.

Variational methods are used in a unified coordinate system.The mesh spacing, smoothness,orthogonality and regularity of grids are considered to obtain an elliptic equation for h.Typical examples demonstrate that it is possible to use variational methods in a unified coordinate system,and the distribution of h satisfies different boundary conditions.

The stability analysis and transition prediction are proceeded for one-order compression ramp,which is the valuable configuration for the hypersonic vehicles.The finite volume method is used to solve the NS equations to get the basic flow field.The solution of the eigenvalue problem is obtained by using the linear stability theory under the assumption of local parallel flows.The first mode and the second mode unstable waves are found at the Mach number of 6.With the relation of the temporal and spatial amplification rates,the transition position is predicted by the EN method.

Numerical method for stability analysis and transition prediction for supersonic flow around a blunt cone is investigated. In order to meet the required accuracy of the numerical values in the basal flow field, the result of the flow field is obtained by solving Euler equations where the pressure attribution on the surface of the cone is used as the outer edge pressure attribution of the viscous boundary layer. The Rayleigh inverse-iteration method and boundary layer asymptotic expansion method are used to solve the blunt cone boundary layer stability equation to get reliable boundary layer transition data. This method improves the numerical precision, and saves the computation time. It is also useful for stability analysis of blunt cone supersonic flow.

It assesses the Rayleigh inverse-iteration method and boundary layer asymptotic expansion method, and uses them into the stability equations of compressible boundary layer and the numerical method for forecasting the transition point. It gives also a stability analysis on the first mode of the boundary layer of flat plane and a forecasting of transition point. Results are discussed and compared with observations.