A. N. Osiptsov

Heat transfer in the boundary layer of a gas-evaporating drops two-phase mixture

Abstract A mist flow in a laminar boundary layer over a hot flat plate is studied by asymptotic and numerical methods. A two-continuum approximation is used to describe the ‘gas-evaporating drops’ twophase medium. The Saffman force, acting on the drops and causing their deposition, is taken into account. The mechanism of heat transfer enhancement by the drops evaporating in the boundary layer has been studied, and similarity criteria have been found. The predicted overall heat transfer coefficient for a plate segment is in good agreement with the familiar experimental data.

MATHEMATICAL MODELING OF NEAR-WALL FLOWS OF TWO- PHASE MIXTURE WITH EVAPORATING DROPLETS

In the framework of the two-continuum approach, using the matched asymptotic expansion method, the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved. The similarity criteria controlling the mist flows were determined. For the flow along a curvilinear surface, the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition. The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body. It is demonstrated that, due to evaporation, a droplet-free region develops near the wall inside the boundary layer. On the upper edge of this region, the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream. The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream.

Self-Similar Regimes of Liquid-Layer Spreading along a Superhydrophobic Surface

Within the Stokes film approximation, unsteady spreading of a thin layer of a heavy viscous fluid along a horizontal superhydrophobic surface is studied in the presence of a given localized mass supply in the film. The forced (induced by the mass supply) spreading regimes are considered, for which the surface tension effects are insignificant. Plane and axisymmetric flows along the principal direction of the slip tensor of the superhydrophobic surface are studied, when the corresponding slip tensor component is either a constant or a power function of the spatial coordinate, measured in the direction of spreading. An evolution equation for the film thickness is derived. It is shown that this equation has self-similar solutions of a source type. The examples of self-similar solutions are constructed for power and exponential time dependences of mass supply. In the final part of the paper, some of the solutions constructed are generalized to the case of a weak dependence of the flow on the second spatial coordinate, caused by a slight variability of the slip coefficient in the direction normal to that of spreading. The constructed self-similar solutions can be used for experimental determination of the parameters important for hydrodynamics, e.g. the slip tensor components of commercial superhydrophobic surfaces.

Limits of the inertial particle deposition regime and heat transfer in supersonic viscous-dusty-gas flow past bodies

Supersonic steady dusty-gas flow past a blunt body at moderate and large Reynolds numbers Re is considered. Using the complete Navier-Stokes equations for the carrier phase, the effect of viscosity on the limits of the inertial particle deposition regime and the two-phase flow pattern near the frontal surface of the body is studied numerically for 102 ≤ Re ≤ 105. The dependence of the limits of the inertial particle deposition regime on the phase velocity slip ahead of the bow shock is investigated. For large Re, the flow near the stagnation point is studied in the boundary layer approximation. On the basis of numerical calculations over a wide range of variation of the Reynolds number and the particle inertia parameter, the maximum increase in the heat fluxes at the stagnation point due to the presence of dispersed particles in the free-stream is estimated.

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop ...

Viscous fluid streamlet flow down an inclined superhydrophobic surface

The problem of a steady flow of a viscous streamlet down an inclined plane superhydrophobic surface in a gravity field is investigated. A nonlinear partial differential equation for determining the unknown form of the streamlet cross section is derived. A class of nonuniform superhydrophobic surfaces, which are characterized by an effective slip tensor, for which the construction of self-similar solutions of the problem under consideration is possible, is found. The necessary conditions for the existence of self-similar solutions are found. The self-similar shapes of the wetting region and the streamlet cross section are found numerically for two examples of superhydrophobic surfaces. The results of the investigation can be used when experimentally determining the effective characteristics of superhydrophobic surfaces, namely, the components of the effective slip tensor.

Aerosol Flow Through a Micro-Capillary

A combined theoretical/experimental study of micron size aerosol flows through micro-capillaries of diameter about 100 μm and length about 1 cm is presented. It is shown that under proper conditions at a relatively high velocity of about 100 m/s such an aerosol flow reveals a new manifestation of microfluidics: the Saffman force acting on aerosol particles in gas flowing through a micro-capillary becomes significant thereby causing noticeable migration of particles toward the center line of the capillary. This finding opens up new opportunities for aerosol focusing, which is in stark contrast to the classical aerodynamic focusing methodologies where only particle inertia and the Stokes force of gas-particle interaction are typically used to control particle trajectories. A mathematical model for aerosol flow through a micro-capillary accounting for complicated interactions between particles and carrier gas is presented. This model describes the experimental observables obtained via shadowgraphy for aerosol beams exiting micro-capillaries. It is further shown that it is possible to design a micro-capillary system capable of generating a Collimated Aerosol Beam (CAB) in which aerosol particles stay very close to a capillary center line. The performance of such a CAB system for direct-write fabrication on a substrate is demonstrated. The lines deposited by CAB for direct-write fabrication are shown to exhibit widths of less than 5 μm — superior to ink-jet. Materials deposition based upon directed aerosol flow has the potential of finding application in the fields of flexible electronics, sensors, and solar cells. In this paper, the genesis of a new materials deposition method termed Collimated Aerosol Beam Direct-Write (CAB-DW) is discussed.Copyright

Shock-Induced Dust Cloud Over a Deposit Layer of Fine Particles

The present paper investigates particle density profiles of a dust cloud induced by a normal shock wave moving at a constant speed along a flat surface deposited with fine particles. In shock-fixed coordinates, numerical simulation of flow structures of the carrier- and dispersed-phases was performed for the M = 2 case. The fineness and non-uniformity of the particle size are taken into account and their effects on the dust cloud are discussed in detail.

THE DISTRIBUTION OF PARTICLES IN A SHOCK-INDUCED BOUNDARY LAYER OF A DUSTY GAS OVER A SOLID SURFACE

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied. The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account. A method for calculating the density profile of dispersed phase near the wall is proposed and some numerical results are given. It is shown that behind the shock wave, there exists a curved thin layer where the density of particles is many times higher than the original one. This dust collection effect may be of essential importance to the problem of dust explosion in industry.