An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Effect of convection on domain growth during demixing transitions in fluids

Current analytical work on the effect of convection on the late stages of spinodal decomposition in liquids is briefly described. The morphology formed during the spinodal decomposition process depends on the relative composition of the two species. Droplet spinodal decomposition occurs when the concentration of one of the species is small. Convective transport has a significant effect on the scaling laws in the late-stage coarsening of droplets in translational or shear flows. In addition, convective transport could result in an attractive interaction between non-Brownian droplets which could lead to coalescence. The effect of convective transport for the growth of random interfaces in a near-symmetric quench was analysed using an area distribution function, which gives the distribution of surface area of the interface in curvature space. It was found that the curvature of the interface decreases proportional to time t in the late stages of spinodal decomposition, and the surface area also decreases proportional to t.

Freezing of classical fluids in a quenched random potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.

Techniques for realistic visualization of fluids: A survey

Visualization of fluids has wide applications in science, engineering and entertainment. Various methodologies Of visualizing fluids have evolved which emphasize on capturing different aspects of the fluids accurately. In this survey the existing methods for realistic visualization of fluids are reviewed. The approaches are classified based on the key concept they rely on for fluid modeling. This classification allows for easy selection of the method to be adopted for visualization given an application. It also enables identification of alternative techniques for fluid modeling.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Instabilities of soft elastic microtubes filled with viscous fluids: Pearls, wrinkles, and sausage strings

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro-or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y = gamma/(G(e)R) > 6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y > 2, where gamma, G(e), and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

Effect of capillarity and heterogeneity in the numerical modelling of multiphase flow of fluids in unsaturated porous medium

The multiphase flow of fluids in the unsaturated porous medium is considered as a three phase flow of water, NAPL, and air simultaneously in the porous medium. The adaptive solution fully implicit modified sequential method is used for the numerical modelling. The effect of capillarity and heterogeneity effect at the interface between the media is studied and it is observed that the interface criteria has to be taken into account for the correct prediction of NAPL migration especially in heterogeneous media. The modified Newton Raphson method is used for the linearization and Hestines and Steifel Conjugate Gradient method is used as the solver.

Effect of convection and viscoelasticity on spinodal decomposition in fluids

Current analytical work on the effect of convection and viscoelasticity on the early and late stages of spinodal decomposition is briefly described. In the early stages, the effect of viscoelastic stresses was analysed using a simple Maxwell model for the stress, which was incorporated in the Langevin equation for the momentum field. The viscoelastic stresses are found to enhance the rate of decomposition. In the late stages, the pattern formed depends on the relative composition of the two species. Droplet spinodal decomposition occurs when the concentration of one of the species is small. Convective transport does not have a significant effect on the growth of a single droplet, but it does result in an attractive interaction between non - Brownian droplets which could lead to coalescence. The effect of convective transport for the growth of random interfaces in a near symmetric quench was analysed using an 'area distribution function', which gives the distribution of surface area of the interface in curvature space. It was found that the curvature of the interface decreases proportional to t in the late stages of spinodal decomposition, and the surface area also decreases proportional to t.

Evaporation Heat Transfer Coefficient in a Capillary Pumped Loop and Loop Heat Pipe for Different Working Fluids

Capillary pumped loop (CPL) and loop heat pipe (LHP) are passive two-phase heat transport devices. They have been gaining importance as a part of the thermal control system of spacecraft. The evaporation heat transfer coefficient at the tooth-wick interface of an LHP or CPL has a significant impact on the evaporator temperature. It is also the main parameter in sizing of a CPL or LHP. Experimentally determined evaporation heat transfer coefficients from a three-port CPL with tubular axially grooved (TAG) evaporator and a TAG LHP with acetone, R-134A, and ammonia as working fluids are presented in this paper. The influences of working fluid, hydrodynamic blocks in the core, evaporator configuration (LHP or CPL), and adverse elevation (evaporator above condenser) on the heat transfer coefficient are presented.

Confined fluids in a Janus pore: influence of surface asymmetry on structure and solvation forces

Density distribution, fluid structure and solvation forces for fluids confined in Janus slit-shaped pores are investigated using grand canonical Monte Carlo simulations. By varying the degree of asymmetry between the two smooth surfaces that make up the slit pores, a wide variety of adsorption situations are observed. The presence of one moderately attractive surface in the asymmetric pore is sufficient to disrupt the formation of frozen phases observed in the symmetric case. In the extreme case of asymmetry in which one wall is repulsive, the pore fluid can consist of a frozen contact layer at the attractive surface for smaller surface separations (H) or a frozen contact layer with liquid-like and gas-like regions as the pore width is increased. The superposition approximation, wherein the solvation pressure and number density in the asymmetric pores can be obtained from the results on symmetric pores, is found to be accurate for H > 4 sigma(ff), where sigma(ff) is the Lennard-Jones fluid diameter and within 10% accuracy for smaller surface separations. Our study has implications in controlling stick slip and overcoming static friction `stiction' in micro and nanofluidic devices.

Application of a Class of Nano fluids to improve the Loadability of Power Transformers

It is generally known that addition of conducting or insulating particles to mineral transformer oil, lowers its breakdown strength, E-d. However, if the particulates are of molecular dimensions, or nanoparticles, (NPs), as they are called, the breakdown strength is seen to increase considerably. Recent experiments by the authors on oil cooled power equipment such as transformers showed that, nanofluids comprising NPs of selected oxides of iron, such as Fe(3)o(4), called magnetite, added to transformer oil increased the breakdown voltage of the virgin oil and more importantly a remarkable enhancement in the thermal conductivity and the viscosity and hence an increased loadability of the transformer for a given top oil temperature (TOT).

Evaluation of isopentane, R-245fa and their mixtures as working fluids for organic Rankine cycles

Low grade thermal energy from sources such as solar, geothermal and industrial waste heat in the temperature range of 380-425 K can be converted to electrical energy with reasonable efficiency using isopentane and R-245fa. While the former is flammable and the latter has considerable global warming potential, their mixture in 0.7/0.3 mole fraction is shown to obviate these disadvantages and yet retain dominant merits of each fluid. A realistic thermodynamic analysis is carried out wherein the possible sources of irreversibilities such as isentropic efficiencies of the expander and the pump and entropy generation in the regenerator, boiler and condenser are accounted for. The performance of the system in the chosen range of heat source temperatures is evaluated. A technique of identifying the required source temperature for a given output of the plant and the maximum operating temperature of the working fluid is developed. This is based on the pinch point occurrence in the boiler and entropy generation in the boiling and superheating regions of the boiler. It is shown that cycle efficiencies of 10-13% can be obtained in the range investigated at an optimal expansion ratio of 7-10. (C) 2012 Elsevier Ltd. All rights reserved.

Evaluation of carbon dioxide blends with isopentane and propane as working fluids for organic Rankine cycles

The main theme of this paper is to study the flammability suppression of hydrocarbons by blending with carbon dioxide, and to evaluate these mixtures as possible working fluids in organic Rankine cycle for medium temperature concentrated solar power applications. The analysis takes into account inevitable irreversibilities in the turbine, the pump, and heat exchangers. While the isopentane + CO2 mixture suffers from high irreversibility mainly in the regenerator owing to a large temperature glide, the propane + CO2 mixture performs more or less the same as pure propane albeit with high cycle pressures. In general, large temperature glides at condensing pressures extend the heat recovery into the two-phase dome, which is an advantage. However, at the same time, the shift of the pinch point towards the warm end of the regenerator is found to be a major cause of irreversibility. In fact, as the number of carbon atoms in alkanes decreases, their blend with CO2 moves the pinch point to the colder end of the regenerator. This results in lower entropy generation in the regenerator and improved cycle efficiency of propane + CO2 mixtures. With this mixture, real cycle efficiencies of 15-18% are achievable at a moderate source temperature of 573 K. Applicability for a wide range of source temperatures is found to be an added advantage of this mixture.

Nanodiamond-Based Thermal Fluids

Dispersions of nanodiamond (average size similar to 6 nm) within dielectric insulator mineral oil are reported for their enhanced thermal conductivity properties and potential applications in thermal management. Dynamic and kinematic viscosities-very important parameters in thermal management by nanofluids-are investigated. The dependence of the dynamic viscosity is well-described by the theoretical predictions of Einstein's model. The temperature dependence of the dynamic viscosity obeys an Arrhenius-like behavior, where the activation energy and the pre-exponential factor have an exponential dependence on the filler fraction of nanodiamonds. An enhancement in thermal conductivity up to 70% is reported for nanodiamond based thermal fluids. Additional electron microscopy, Raman spectroscopy and X-ray diffraction analysis support the experimental data and their interpretation.