MRI studies of the evaporation of a single liquid droplet from porous surfaces

A combination of in situ one-dimensional profiling and two-dimensional 1H magnetic resonance imaging has been applied to study the shape and subsequent dynamic evaporation behavior of a single liquid droplet after impact onto a porous surface in a carefully controlled atmosphere. Aspects of the porous media permeability and particle shape are shown to affect considerably the observed drying regime. Variation in the shape, spread ratio, and penetration depth of the liquid droplet following impact are attributed to the different types of porous media used. A comparison of numerical simulations with the MRI data for the droplet shape, spread factor, and penetration depth show good agreement though larger deviations between simulated and experimental results occur in certain cases where the surface of the porous medium is disrupted by the impact of the liquid droplet. Initial results examining the effect of a reduced liquid surface tension show a significantly increased evaporation rate.     

微管道内两相流数值算法及在电浸润液滴控制中的应用

叙述了一种模拟电介质电润湿(electrowetting on dielectric，EWOD)下的微液滴的运动的数值方法. 采用二阶投影法求解N-S方程和level set 函数，并利用零level set函数俘获液滴运动界面，在液体与固体接触的边界上，通过引入动态接触角表征电介质表面润湿性随电势的改变. 数值计算基于MAC网格，模拟了2维微管道内与固体壁面接触的变润湿性的两种液体的分界面形状、平板上的微液滴在不同电势作用下处于不同湿润性的形态，以及微管道内改变接触角液滴的运动变形过程等算例. 关键词： 电浸润 接触角 level set函数 投影法     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

Controlled Production of Emulsions Using a Crossflow Membrane

A method for manufacturing emulsions — crossflow membrane emulsification has been studied. This involves the formation of emulsions by breaking up the discontinuous phase into droplets in a controlled manner without the use of turbulent eddies. This is achieved by passing the discontinuous phase through a suitable microporous medium and injecting the droplets so formed directly into a moving continuous phase. This paper presents two examples of experimental data for droplet formation using a single pore (capillary tube) and a membrane tube. A high-speed video camera (up to 1000 frames per second) was used to record the formation of droplet from a single pore and thus measure droplet growth and the detachment processes as a function of process parameters such as transmembrane pressure drop, membrane pore size, continuous phase crossflow velocity etc. Real emulsions were prepared using a membrane tube.     

Absorption of external thermal radiation in asymmetrically illuminated droplets

A theoretical model of thermal radiation absorption in semi-transparent droplets at the surface and inside a fuel spray is presented. Asymmetry of droplet illumination is taken into account. Results of Mie calculations of thermal radiation absorption inside large spherical droplets illuminated from a hemisphere are presented. Simple approximations for the angular and radial dependencies of the absorbed radiation power are suggested. These approximations are generalisations of the approximations suggested earlier by the authors for the case of symmetric illumination of droplets. They predict the results close to those which follow from the Mie calculations. Results of approximate calculations for a typical diesel fuel droplet at the periphery of the spray are presented. As in the case of symmetrical droplet illumination, an increased absorption of thermal radiation in the central area of the droplet is predicted. Also, at the illuminated side of the droplet, the absorption of radiation in a thin layer near the surface of the droplet is predicted, as in the case of symmetrical droplet illumination. Absorption of radiation in the central area of the droplet is related to the contribution of radiation in the spectral ranges of semi-transparency. The maximum of radiation absorption near the droplet surface is linked to the contribution of radiation in the vicinity of the diesel fuel absorption peak .     

Unsteady MHD Non-Darcian Flow over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model

An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.     

A finite difference method for a coupled model of wave propagation in poroelastic materials

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.     

气孔分布特性对含水多孔介质气体扩散的影响

本文基于多孔介质的气孔分布特性,计算了多孔介质在含水状态下的扩散性能,并且比较了采用两种方式计算相对渗透率时的相对扩散性能。其结果表明,基于气孔分布的计算结果低于与气孔分布无关的计算结果。另外,疏水性含水多孔介质的扩散性能低于亲水性含水多孔介质的扩散性能,基于气孔分布计算含水多孔介质的气体扩散性能时,Wyllie公式并不适用。     

A stochastic theory for deep bed filtration accounting for dispersion and size distributions

We develop a stochastic theory for filtration of suspensions in porous media. The theory takes into account particle and pore size distributions, as well as the random character of the particle motion, which is described in the framework of the theory of continuous-time random walks (CTRW). In the limit of the infinitely many small walk steps we derive a system of governing equations for the evolution of the particle and pore size distributions. We consider the case of concentrated suspensions, where plugging the pores by particles may change porosity and other parameters of the porous medium. A procedure for averaging of the derived system of equations is developed for polydisperse suspensions with several distinctive particle sizes. A numerical method for solution of the flow equations is proposed. Sample calculations are applied to compare the roles of the particle size distribution and of the particle flight dispersion on the deposition profiles. It is demonstrated that the temporal flight dispersion is the most likely mechanism forming the experimentally observed hyperexponential character of the deposition profiles.     

Fluctuations of the number of neighboring pores and appearance of multiple nonergodic states of a nonwetting liquid confined in a disordered nanoporous medium

Multiple nonergodic states have been observed for nonwetting liquid in the Fluka100 C18 and Fluka100 C8 porous media with broad pore size distributions having different widths. The dispersion transition where the volume of confined liquid depends critically on the degree of filling of the porous medium and temperature is observed in the temperature range 293–343 K under study for the Fluka100 C18 porous medium and is not observed for the Fluka100 C8 porous medium. A mechanism of the appearance of multiple nonergodic states has been proposed. It has been shown that fluctuations of the number of the nearest neighbors in the disordered system are mainly responsible for the features of confinement of nonwetting liquid and nonergodic states of nonwetting liquid in the nanoporous media under investigation with wide pore size distributions.     

Low-frequency surface wave propagation along plane boundaries in fluid-saturated porous media

A method of the mechanics of a fluid-saturated porous medium is used to study the propagation of harmonic surface waves along the free boundary of such a medium, along the boundary between a porous medium and a fluid, and along the boundary between two porous half-spaces. It is shown that, at low frequencies (i.e., for waves with frequencies lower than the Biot characteristic frequency), the corresponding dispersion equations in zero-order approximation are reduced to the equations for an “equivalent” elastic medium. For the wave numbers of surface waves, corrections taking into account the generation of longitudinal waves of the second kind at the boundary are calculated. Examples of numerical solutions of dispersion equations for rock are presented.     

Pores resolving simulation of Darcy flows

A theoretical formulation and corresponding numerical solutions are presented for microscopic fluid flows in porous media with the domain sufficiently large to reproduce integral Darcy scale effects. Pore space geometry and topology influence flow through media, but the difficulty of observing the configurations of real pore spaces limits understanding of their effects. A rigorous direct numerical simulation (DNS) of percolating flows is a formidable task due to intricacies of internal boundaries of the pore space. Representing the grain size distribution by means of repelling body forces in the equations governing fluid motion greatly simplifies computational efforts. An accurate representation of pore-scale geometry requires that within the solid the repelling forces attenuate flow to stagnation in a short time compared to the characteristic time scale of the pore-scale flow. In the computational model this is achieved by adopting an implicit immersed-boundary method with the attenuation time scale smaller than the time step of an explicit fluid model. A series of numerical simulations of the flow through randomly generated media of different porosities show that computational experiments can be equivalent to physical experiments with the added advantage of nearly complete observability. Besides obtaining macroscopic measures of permeability and tortuosity, numerical experiments can shed light on the effect of the pore space structure on bulk properties of Darcy scale flows.     

Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range

A model is developed for the hemispherical transmittance of direct and scattered solar radiation from a cloudless atmosphere by a mist layer of water droplets in order to investigate the potential of water misting systems to serve as a protection from solar irradiation with particular emphasis on harmful UV radiation. The proposed model is based on published spectral experimental data for solar irradiation, Mie theory for interaction of the radiation with single spherical droplets, and radiative transfer theory. Known limiting solutions are employed to simplify the Mie calculations. The modified two-flux approximation is used to account for both direct and diffuse irradiation in lieu of a numerical solution for the full radiative transfer equation in anisotropically scattering media. The role of the governing parameters of a disperse water curtain of water droplets, water content, and droplet size for sample conditions is studied in some detail, particularly in the near-ultraviolet part of the spectrum where radiation can result in human tissue damage.     

On the structure of the steady-state flow velocity field near the interface between a homogeneous liquid and a Brinkman porous medium

The structure of a homogeneous liquid flow at the interface with a porous medium saturated with the same liquid has been studied in the boundary layer approximation. The porous medium is described by the Brinkman model. Self-similar equations of motion in the form of Blasius equation have been found, and their numerical solutions have been presented. An expression for the force exerted by the flow on the porous medium is derived.     

液滴溅落问题的光滑粒子动力学模拟

对传统的光滑粒子动力学方法进行了改进, 改进的光滑粒子动力学方法对传统粒子方法中的核近似式和粒子近似式进行了修正, 采用Riemann 算法求解光滑粒子动力学流体控制方程, 添加了表面张力的计算程序, 考虑了表面张力对液滴溅落的影响. 应用改进的光滑粒子动力学方法对液滴静止状态下冲击液面的飞溅过程进行了数值模拟. 计算结果表明, 改进的光滑粒子动力学方法能够有效地描述液滴溅落液面的动力学特性和自由表面变化特征, 能够得到稳定精度的结果.     

Vaporization and combustion in three-dimensional droplet arrays

The quasi-steady vaporization and combustion of multiple-droplet arrays is studied numerically. Utilizing the Shvab–Zeldovich formulation, a transformation of the governing equations to a three-dimensional Laplace’s equation is performed, and the solution to Laplace’s equation is obtained numerically to find the effects of droplet interactions in symmetric, multiple-droplet arrays. Vaporization rates, flame surface shapes, and flame locations are found for different droplet array configurations and fuels. The number of droplets, the droplet arrangement within the arrays, and the droplet spacing within the arrays are varied to determine the effects of these parameters. Computations are performed for uniformly spaced three-dimensional arrays of up to 216 droplets, with center-to-center spacing ranging from 3 to 25 droplet radii. As a result of the droplet interactions, the number of droplets and relative droplet spacing significantly affect the vaporization rate of individual droplets within the array, and consequently the flame shape and location. For small droplet spacing, the individual droplet vaporization rate decreases below that obtained for an isolated droplet by several orders of magnitude. A similarity parameter which correlates vaporization rates with array size and spacing is identified. Individual droplet flames, internal group combustion, and external group combustion can be observed depending on the droplet geometry and boundary conditions.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Simulation of impact of a hollow droplet on a flat surface

Despite many theoretical and experimental works dealing with the impact of dense continuous liquid droplets on a flat surface, the dynamics of the impact of hollow liquid droplets is not well addressed. In an effort to understand dynamics of the hollow droplet impingement, a numerical study for the impact of a hollow droplet on a flat surface is presented. The impingement model considers the transient flow dynamics during impact and spreading of the droplet using the volume of fluid surface tracking method (VOF) coupled with the momentum transport model within a one-domain continuum formulation. The model is used to simulate the hydrodynamic behaviour of the impact of glycerin hollow droplet. It is found that the impact and spreading of the hollow droplet on a flat surface is distinctly different from the conventional dense droplet and has some new hydrodynamic features. A phenomenon of formation of a central counter jet of the liquid is predicted. With the help of simulations the cause of this phenomenon is discussed. Comparison of the predicted length of the central counter jet and the velocity of the counter jet front shows good agreements with the experimental data. The influence of the droplet initial impact velocity and the hollow droplet shell thickness on the impact behaviour is highlighted.     

Tracer dispersion in a percolation network with spatial correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolationlike porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We find that the resulting statistical properties of the tracer show a transition from a subdiffusion regime at low Peclet number to an enhanced diffusion regime at high Peclet number.