Jorge F. Willemsen

Bio: Jorge F. Willemsen is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Nonlinear system & Hagen–Poiseuille equation. The author has an hindex of 9, co-authored 15 publications receiving 1176 citations. Previous affiliations of Jorge F. Willemsen include University of California, Santa Cruz.

Molecular Dynamics of Fluid Flow at Solid Surfaces

Abstract: We use molecular dynamics techniques to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids we find the no-slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow-independent slip-length boundary condition. We examine the trajectories of individual molecules in Poiseuille flow, and also find that their average behavior is given by Taylor-Aris hydrodynamic dispersion. An immiscible two-fluid system is simulated by a species-dependent intermolecular interaction. We observe a static meniscus whose contact angle agrees with simple estimates and, when motion occurs, velocity- dependent advancing and receding angles. The local velocity field near a moving contact line shows a breakdown of the no-slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan

Capillary displacement and percolation in porous media

Abstract: We consider capillary displacement of immiscible fluids in porous media in the limit of vanishing flow rate. The motion is represented as a stepwise Monte Carlo process on a finite two-dimensional random lattice, where at each step the fluid interface moves through the lattice link where the displacing force is largest. The displacement process exhibits considerable fingering and trapping of displaced phase at all length scales, leading to high residual retention of the displaced phase. Many features of our results are well described by percolation-theory concepts. In particular, we find a residual volume fraction of displaced phase which depends strongly on the sample size, but weakly or not at all on the co-ordination number and microscopic-size distribution of the lattice elements.

Molecular dynamics of Poiseuille flow and moving contact lines.

Abstract: We report on molecular-dynamics simulations of the low--Reynolds-number flow of Lennard-Jones fluids through a channel. Application of a pressure gradient to a single fluid produces Poiseuille flow with a no-slip boundary condition and Taylor-Aris hydrodynamic dispersion. For an immiscible two-fluid system we find a (predictable) static contact angle and, when accelerated, velocity-dependent advancing and receding contact angles. The approximate local velocity field is obtained, in which the no-slip condition appears to break down near the contact line.

Surface relaxation and pore sizes in rocks—a nuclear magnetic resonance analysis

Abstract: The pulsed gradient nuclear magnetic resonance technique has been applied to the measurement of pore sizes in rocks. The measurements also yield an estimate of the strength of the magnetization relaxation at the pore‐rock interface.

Wetting and Spreading

Abstract: Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

Nonlinear dynamics and breakup of free-surface flows

Abstract: Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems.

Micro-electro-mechanical-systems (mems) and fluid flows

Abstract: The micromachining technology that emerged in the late 1980s can provide micron-sized sensors and actuators. These micro transducers are able to be integrated with signal conditioning and processing circuitry to form micro-electromechanical-systems (MEMS) that can perform real-time distributed control. This capability opens up a new territory for flow control research. On the other hand, surface effects dominate the fluid flowing through these miniature mechanical devices because of the large surface-to-volume ratio in micron-scale configurations. We need to reexamine the surface forces in the momentum equation. Owing to their smallness, gas flows experience large Knudsen numbers, and therefore boundary conditions need to be modified. Besides being an enabling technology, MEMS also provide many challenges for fundamental flow-science research.

Invasion percolation: a new form of percolation theory

Abstract: A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance. The name invasion percolation is proposed for this new process. Similarities to, and differences from, ordinary percolation theory are discussed.

A general boundary condition for liquid flow at solid surfaces

Abstract: Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.