H. T. Davis

Microwave heating: an evaluation of power formulations

Abstract Microwave heating of food systems have conventionally been modeled based on a Lambert law formulation of the absorbed power. However this is strictly valid for semi-infinite samples only. The correct power dissipation must be computed from maxwells equations. To determine the conditions of the approximate applicability of Lamberts law for finite slabs, we have compared it with the microwave heating predicted by Maxwells equations. We have found that the critical slab thickness L crit (in cm) above which the Lambert law limit is valid can be estimated from L crit = 2.7 β −1 - 0.08, where the penetration depth, β −1 , is the distance in cm from the sample surface where the field reduces to 1/ e of its incident intensity. Temperature profiles calculated with the Lambert law limit for slabs thicker than L crit are within 0.5% of those predicted with the power calculated from Maxwells equations. Using Maxwells equations we have developed a general formulation for power absorbed in a homogeneous, isotropic multilayered medium exposed to plane waves from both faces. We report temperature profiles obtained by solving the transient heat conduction equation with the microwave power as a source term. Thermal and dielectric properties are assumed to be temperature-independent.

Monte Carlo simulation of model amphiphile‐oil–water systems

A square‐lattice model of amphiphile‐oil–water systems is developed in which oil and water molecules occupy single sites and amphiphiles occupy chains of sites. Energies and free energies estimated by Monte Carlo sampling of configuration space show that when the head, or water‐loving portion, of the amphiphile has no tendency to hydrate or surround itself with water, as opposed to surrounding itself with other heads, the capability of even long amphiphiles to solubilize repellant oil and water into a single phase is weak. Although the Monte Carlo free energies deviate markedly from those given by quasichemical theory, the deviation of the phase behavior is modest. Computer drawings of typical equilibrium configurations show highly irregular interfaces, apparently caused by capillary waves which are pronounced in two dimensions.

Molecular dynamics of flow in micropores

The method of nonequilibrium molecular dynamics is used to study the viscosity and flow properties of strongly inhomogeneous liquids, a particular case of which is a liquid confined in a micropore only a few molecular diameters wide. Fluid inhomogeneity is introduced by imposing an external potential that in one case simulates flat solid walls and in the other case causes density peaks in the middle of a thin liquid film. For comparison a homogeneous fluid is also simulated. In both types of inhomogeneous fluid, the shear stress and effective viscosity are smaller than in the homogeneous fluid. The density profiles and the diffusivities in the micropore were found to be independent of flow, even at the extremely high rates, 1010–1011 s−1 of the simulation. The Green–Kubo relation is found to be valid for the diffusivity under the flow studied. We propose a local average density model (LADM) of viscosity and diffusivity, in which the local transport coefficients are those of homogeneous fluid at a mean den...

Percolation theory of two phase flow in porous media

The simultaneous flow of two phases through porous media has long lacked a sound theoretical description, due, in large measure, to the complex geometry and topology of the pore space, and the chaotic, nearly random spatial distribution of the fluids. For some 20 years, a theory of flow through random media, percolation theory, has existed in the field of mathematical physics. In this paper, it is demonstrated that percolation theory describes the distribution of non-wetting fluid in common sandstones and limestones during capillary pressure and relative permeability measurements. In particular, the theory predicts the relative amounts of non-wetting fluid in each of three distinct fluid configurations: isolated, dead-end, and flow effective fluid. Porous media are herein idealized as random mixtures of solid and void to which concepts of percolation theory apply. For sinter-bodies a critical porosity, φc ⋍ 112, exists, below which the void space is not continuous across the sample. For many natural porous materials, e.g. sandstones and limestones, the dependence of residual non-wetting saturation upon porosity is roughly that which corresponds to the existence of a critical porosity, whose value is again 112. The distribution of the non-wetting phase during two phase flow, in particular, the amount of isolated and dead-end fluid, can be qualitatively predicted by simple graph models. The concepts of dead end and isolated fluid must be considered if relative permeability, capillary pressure, and other descriptors of two phase flow are to be understood.

Tracer diffusion in polyatomic liquids. III

Tracer diffusion measurements taken over a wide range of temperature (25.0–142.7° C) are reported for nine solutes (Ar, CH4, Kr, Xe, R4 Sn: R = Me, Et, n‐Pr, n‐Bu) in cyclohexane. The measurements were made in a Taylor dispersion apparatus modified for pressurization and temperature control. Rough‐hard‐sphere theory, in which the diffusion coefficient is the product of a constant rotational factor, Enskog’s diffusivity of hard spheres, and a computer‐generated backscattering coefficient, agrees well with the observed results. The theory furnishes new insights into the origins of the energy of activation of diffusion and explains trends not previously understood.

Physics of oil entrapment in water-wet rock

Displacement of oil from an initially oil-filled porous rock by water consists of advancement of menisci and rupture of oil connections. In displacements controlled by capillarity, which are typical of oil reservoir floods, these pore-level events are governed by the local pore geometry, pore topology, and fluid properties, but the pressure field initiates these pore-level events and integrates them with the externally imposed Darcy flow. This paper reports the physics of the pore-level and their integration on a computationally simple model of rock: a square network of pores. The novelty of the approach lies in keeping track of the evolution of the displacement front and in constructing an approximation of the entire pressure field that carries the information essential for predicting the evolution. The result gives insight into the state of the residual oil saturation and its dependence on pore geometry and the capillary number, N/sub ca/, of displacement. As the capillary number increases, the residual oil saturation decreases and the residual oil blobs tend to be smaller. As the pore size distribution becomes wider, the decrease of residual oil saturation with capillary number becomes smoother.

Efficient molecular simulation of chemical potentials

This paper evaluates methods of estimating chemical potential—actually fugacity coefficient—from molecular simulations. These methods are based on formulas given by Widom, by Bennett, and by Shing and Gubbins. They are tested with molecular dynamics simulations of Lennard‐Jones liquids along the isotherm kT/e=1.2 for densities from 0.65σ−3 to 0.90σ−3. A new test molecule sampling method, excluded volume map sampling, is found to be as much as 2 orders of magnitude more efficient than uniform test molecule sampling; it is more efficient and reliable than restricted umbrella sampling proposed by Shing and Gubbins. Several difficulties of estimating the variance of the fugacity coefficient estimates are surmounted by novel application of standard statistical methods. The statistical analysis shows that Bennett’s method yields estimates with the least variance and Widom’s method yields estimates with the greatest variance although all methods are consistent to within statistical error. Pressure and fugacity c...

Visualization of blob mechanics in flow through porous media

Two fluids are placed inside a porous medium, one in the form of disconnected blobs, or ganglia. Motions of individual blobs are observed by means of a three-dimensional flow visualization arrangement with the refractive indices of solid matrix and continuous liquid matched. Liquid velocities needed to mobilize non-wetting blobs are measured versus blob length and liquid viscosity. Velocities accord with the theory of blob mechanics, as do the critical values of the capillary number μυσ. The latter agree satisfactorily with reported values (ca. 0.005) for virtually complete displacement of residual non-wetting phase. The largest vertical length of stationary blobs is measured versus density difference and also accords with the theory.

A tractable molecular theory of flow in strongly inhomogeneous fluids

A recently introduced model is used to study several flows in fluids with large density variations over distances comparable to their molecular dimensions (strongly inhomogeneous fluids). According to our model, the local average density model (LADM), local viscosity coefficients can be assigned at each point in a strongly inhomogeneous fluid and the stress tensor retains its Newtonian form provided that the properly defined local viscosities are used. The model has been previously shown to agree with the results of molecular dynamics simulations on diffusion and flow properties in plane Couette flow. Application of this model requires determination of the molecular density profiles in the flow region. Using a successful closure for the pair distribution function, we solve the Yvon–Born–Green (YBG) equation of fluid structure in order to determine the density profiles of a fluid confined between planar micropore walls only a few molecular diameters apart. The fluid confinement produces a strongly inhomoge...

Displacement of residual nonwetting fluid from porous media

Abstract Percolation theory of transport in random composites is used to explain the correlation between the residual saturation of nonwetting phase in porous media after displacement by a wetting phase and the capillary number, this number being a measure of the ratio of Darcy-law viscous force in the wetting liquid to interfacial tension force in curved menisci between the two phases. Statistical concepts of percolation theory give estimates of the length distribution of blobs created when the nonwetting phase loses continuity because of displacement by the wetting phase. These estimates agree with the few experimental data. Simple blob mobilization theory and experiments establish that the capillary number required to mobilize a blob is inversely proportional to its length in the direction of the Darcy-law pressure gradient; this and the predictions of percolation theory account for the observed capillary number correlation.