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We develop a novel boundary integral formulation for the steady linearized form of Grad's 13-moment (G13) equations applied to a uniform flow of rarefied gas past solid objects at low Mach numbers. Changing variables leads to a system of boundary integral equations that combines integral equations from Stokes flow and potential theory. The strong coupling between the stress deviator and heat flux featured by the G13 equations demands adding a boundary integral equation for the pressure. We specialize the integral equations for an axisymmetric flow with no swirl and derive the axisymmetric fundamental solutions for the pressure equation, seemingly absent in the Stokes-flow literature. Using the boundary element method to achieve a numerical solution, we apply this formulation to streaming flow of rarefied gas past prolate or oblate spheroids with their axis of symmetry parallel to the free stream, considering various aspect ratios and Knudsen numbers—the ratio of the molecules' mean free path to the macroscopic length scale. After validating the method, we obtain the surface profiles of the deviations from the unperturbed state of the traction, heat flux, pressure, temperature, and slip velocity, as well as the drag on the spheroid, observing convergence with the number of elements. Rarefaction phenomena, such as temperature jump and polarization, Knudsen effects in the drag, and velocity slippage, are predicted. This method opens a new path for investigating other gas non-equilibrium phenomena that can be modeled by the same set of equations, such as thermophoresis, and has application in nano- and microfluidics.

Thin-film evaporation from nanoporous membranes is a promising cooling technology employed for the thermal management of modern electronic devices. We propose an effective one-dimensional analytical approach that can accurately predict the temperature and density jump relations, and evaporation rates, for arbitrary nanoporous membrane configurations. This is accomplished through the specification of an effective evaporation coefficient that encompasses the influence of different system parameters, such as porosity, meniscus shape, evaporation coefficient, and receding height. Our proposed approach can accurately predict all the typical output evaporation parameters of interest like mass flux, and temperature and density jumps, without the need to carry out computationally demanding numerical simulations. Several exemplar cases comprising of nanoporous configurations with a wide range of parameters have been considered to demonstrate the feasibility and accuracy of this analytic approach. This work thus enables a quick, efficient, and accurate means of aiding the design and engineering analysis of nanoporous membrane-based cooling devices.\ud

Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation free-surface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquiddrops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed.\ud