Macroscopic capillarity without a constitutive capillary pressure function

This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions of nonpercolating phases. The resulting equations of motion open the possibility to describe flow processes where drainage and imbibition occur simultaneously. The theory predicts hysteresis and process dependence of capillary phenomena. The traditional theory is recovered as a special case in the residual decoupling approximation. Explicit calculations are presented for quasistatic equilibrium profiles near hydrostatic equilibrium. The results are found to agree with experiment.     

Shape instabilities in vesicles: A phase-field model

A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also derived. With this model it is possible to see the vesicle shape deformation dynamically, when some external agent instabilizes the membrane, for instance, inducing an inhomogeneous spontaneous curvature. The numerical scheme used is detailed and some stationary shapes are shown together with a shape diagram for vesicles of spherical topology and no spontaneous curvature, in agreement with known results.     

Short-time dynamics of partial wetting

When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.     

An extension to the Wheeler phase-field model to allow decoupling of the capillary and kinetic anisotropies

The formulation of the phase-field problem due to Wheeler et al. [Physica D 66, 243 (1993)] has been adopted and extended as a tool for solidification research by many groups around the World. However, an intrinsic problem of this model is that it couples two physically distinct anisotropies, those associated with the surface energy of the solid-liquid interface and attachment kinetics, into a single anisotropy parameter. In this paper we present a simple extension to the Wheeler model in which we show that introducing a complex form of the anisotropy function allows these two physical parameters to be decoupled.Received: 16 June 2004, Published online: 21 October 2004PACS: 81.10.-h Methods of crystal growth; physics of crystal growth - 81.30.Fb Solidification - 64.70.Dv Solid-liquid transitions     

Morphological stability analysis of partial wetting

We develop a macroscopic static theory of the morphological stability of partial wetting. The system we studied consist of a smooth horizontal solid surface and some non-volatile liquid on it. A necessary condition for the stable equilibrium of such systems is known as the Young condition on the contact angle made at the contact line where the free surface of liquid meets the solid surface. But this condition is local and is not sufficient for the stability. We present a formulation for studying the stability of systems which satisfy the Young condition. Then we apply this to several morphologies of wetting. We find that there are at least two fundamental morphologies that we call a hole and a ridge, which are thermodynamically unstable against certain infinitesimal deformations of the contact lines. The hole type instability has also been found recently [D. J. Srolovitz and S. A. Safran, J. Appl. Phyys., 60 (1986), 1]. We also derived a reduced expression for the wetting energy as a functional of the contact line positions under the assumption of almost flat free surface of the liquid. This serves us to understand the characteristic length scale which appears in the ridge type instability. Besides these instabilities there is another category of morphological instability in which the system becomes unstable against an infinitesimal deformation of the free surface of liquid. We show this by an illustrating example in which the instability is described as the so-called tangent bifureation in nonlinear systems.     

汽化滞后的毛细管内流动模型与计算

基于均相流模型,建立了制冷剂在毛细管内绝热流动的数学模型,同时考虑了管内流动过程中实际存在的汽化滞后问题。针对工质为R22的制冷系统,开发了程序进行流动模拟计算,该程序对于制冷系统毛细管的匹配具有实用价值。     

Micrometric granular ripple patterns in a capillary tube

The oscillatory motion of a fluid carrying micron-sized particles inside a capillary tube is investigated experimentally. It is found that initially uniformly distributed particles can segregate and accumulate to form regularly spaced micron-sized particle clusters. The wavelength of the microclusters is compared to data for macroscale sand-ripple patterns and found to obey the same universal scaling as these. A dimensional analysis is performed that confirms the universality of the experimentally observed scaling. The experimental data for the microripple clusters further suggest the existence of a minimum particle length scale for which patterns can form and below which the Brownian motion associated with the molecules of the matrix fluid inhibits pattern formation.     

Corner wetting in a far-from-equilibrium magnetic growth model

The irreversible growth of magnetic films is studied in three-dimensional confined geometries of size L×L×M, where M≫L is the growing direction. Competing surface magnetic fields, applied to opposite corners of the growing system, lead to the observation of a localization-delocalization (weakly rounded) transition of the interface between domains of up and down spins on the planes transverse to the growing direction. This effective transition is the precursor of a true far-from-equilibrium corner wetting transition that takes place in the thermodynamic limit. The phenomenon is characterized quantitatively by drawing a magnetic field-temperature phase diagram, firstly for a confined sample of finite size, and then by extrapolating results, obtained with samples of different size, to the thermodynamic limit. The results of this work are a nonequilibrium realization of analogous phenomena recently investigated in equilibrium systems, such as corner wetting transitions in the Ising model.     

The wetting transition in a random surface model

We continue our analysis of the phase diagram of a discrete random surface, with no downward fingers, lying above a flat two-dimensional substrate. The surface is closely related to the 2D Ising model and its free energy is exactly solvable in much (but not all) of the phase diagram. There is a transition at temperatureT _w from a high-T infinite height or wet phase to a low-T finite height or partially wet phase. Previously it was shown that when a parameterb, related to the contact interaction, is positive,T _w is independent ofb and there is a logarithmic specific heat divergence asT _w is approached fromeither side. Here we show that forb<0,T _w does depend onb and there isno thermodynamic singularity from the wet phase. The partially wet phases forb0 andb>0 differ in the absence or presence of a monolayer covering the entire substrate; this results in a first-order transition across the lineb=0,T<T _w.This paper is dedicated to Jerry Percus.     

Non-equilibrium wetting transition in a magnetic Eden model

Magnetic Eden clusters (Ausloos et al., Europhys. Lett. 24, 629 (1993)) with ferromagnetic interaction between nearest-neighbor spins are grown in a confined 2d-geometry with short range magnetic fields acting on the surfaces. The change of the growing interface curvature driven by the field and the temperature is identified as a non-equilibrium wetting transition and the corresponding phase diagram is evaluated. Received 27 March 2000     

Unsteady crack motion and branching in a phase-field model of brittle fracture

Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability at a fraction of the wave speed.     

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.     

Ultrasonic detection of resonant cavitation bubbles in a flow tube by their second-harmonic emissions

During low-power exposures, biophysical effects of ultrasonic cavitation are induced primarily by resonant bubbles, and there is a need for a new method of detecting these small bubbles. Bubble pulsation theory indicates that second-harmonic emissions emanate from resonant bubbles even at low amplitudes. A device was constructed to detect resonant bubbles passing through it in a flowing liquid by monitoring second-harmonic responses to a low amplitude, 1.64 MHz ultrasonic field. During testing, 4.2 μm diameter resonant bubbles produced signals 40 times larger than 500 μm diameter bubbles, and this technique was much better than a first-harmonic scattering technique for counting resonant bubbles.     

An exactly solved model with a wetting transition

A model of a binary mixture, showing a wetting transition, is examined. No prewetting phenomena are found. The scaling functions are obtained for the film thickness and for the correlation lengths.     

Macroscopic model of plasma accelerator

A simple macroscopic model of plasma accelerator, well describing the process of the plasma cluster acceleration in the accelerator and being directly derived from the physical principles of activity of the accelerator performance, is presented in the present paper.