Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field

We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

Three-Dimensional Membrane Imaging with X-ray Ptychography: Determination of Membrane Transport Properties for Membrane Distillation

Membrane distillation (MD) is a desalination technique that uses a membrane to thermally separate potable water from sea or brackish water. The mass transport processes through the membrane are commonly described by the dusty gas model. These processes are modeled assuming uniform, ideally cylindrical capillaries and are adjusted for the membrane geometry by including porosity and tortuosity. The tortuosity is usually set to 2 or is used as an adjusting parameter to fit theoretical models to experimentally measured data. In this work, ptychographic X-ray computed tomography is employed to map the three-dimensional (3D) structure of three commercial state-of-the-art PTFE membranes in MD. The porosity, tortuosity and permeability (viscous flow coefficient) of the samples are computed using the lattice Boltzmann method. The intrinsic permeability is compared to the dusty gas model and an apparent permeability is proposed which is corrected for Knudsen slip effects at the membrane structure. Article Highlights 3D structure of membranes for distillation measured at full height at an unprecedented detail using X-ray ptychography for the first time. Comparison of the dusty gas model to 3D direct numerical simulation: permeability and Knudsen effects. Membrane characterization and calculation of the hydraulic tortuosity factor from 3D flow field simulations.