Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.
Filling operations, in which a viscous fluid displaces a gas in a complex geometry, occur with surprising frequency in many manufacturing processes. Difficulties in generating accurate models of these processes involve accurately capturing the interfacial boundary as it undergoes large motions and deformations, preventing dispersion and mass-loss during the computation, and robustly accounting for the effects of surface tension and wetting phenomena. This paper presents a numerical capturing algorithm using level set theory and finite element approximation. Important aspects of this work are addressing issues of mass-conservation and the presence of wetting effects. We have applied our methodology to a three-dimension model of a complicated filling problem. The simulated results are compared to experimental flow visualization data taken for filling of UCON oil in the identical geometry. Comparison of simulation and experiment indicates that the simulation conserved mass adequately and the simulated interface shape was in approximate agreement with experiment. Differences seen were largely attributed to inaccuracies in the wetting line model.
Shear-induced migration of particles is studied during the slow flow of suspensions of neutrally buoyant spheres, at 50% particle volume fraction, in an inelastic but shear-thinning, suspending fluid. The suspension is flowing in between a rotating inner cylinder and a stationary outer cylinder. The conditions are such that nonhydrodynamic effects are negligible. Nuclear magnetic resonance (NMR) imaging demonstrates that the movement of particles away from the high shear rate region is more pronounced than for a Newtonian suspending liquid. We test a continuum constitutive model for the evolution of particle concentration in a flowing suspension proposed by Phillips et al., but extended to shear-thinning, suspending fluids. The fluid constitutive equation is Carreau-like in its shear-thinning behavior but also varies with the local particle concentration. The model captures many of the trends found in the experimental data, but does not yet agree quantitatively. In fact, quantitative agreement with a diffusive flux constitutive equation would be impossible without the addition of another fitting parameter that may depend on the shear-thinning nature of the suspending fluid. Because of this, we feel that the Phillips model may be fundamentally inadequate for simulating flows of particles in non-Newtonian suspending fluids without the introduction of a normal stress correction or other augmenting terms.
Living systems exhibit form and function on multiple length scales and at multiple locations. In order to mimic such natural structures, it is necessary to develop efficient strategies for assembling hierarchical materials. Conventional photolithography, although ubiquitous in the fabrication of microelectronics and microelectromechanical systems, is impractical for defining feature sizes below 0.1 micrometres and poorly suited to pattern chemical functionality. Recently, so-called 'soft' lithographic approaches have been combined with surfactant and particulate templating procedures to create materials with multiple levels of structural order. But the materials thus formed have been limited primarily to oxides with no specific functionality, and the associated processing times have ranged from hours to days. Here, using a self-assembling 'ink', we combine silica-surfactant self-assembly with three rapid printing procedures-pen lithography, ink-jet printing, and dip-coating of patterned self-assembled monolayers-to form functional, hierarchically organized structures in seconds. The rapid-prototyping procedures we describe are simple, employ readily available equipment, and provide a link between computer-aided design and self-assembled nanostructures. We expect that the ability to form arbitrary functional designs on arbitrary surfaces will be of practical importance for directly writing sensor arrays and fluidic or photonic systems.
We describe parallel simulations of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact lines. The Galerlin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of problem unknowns. Issues concerning the proper constraints along the solid-fluid dynamic contact line in three dimensions are discussed. Parallel computations are carried out for an example taken from the coating flow industry, flow in the vicinity of a slot coater edge. This is a three-dimensional free-surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another part of the flow domain. Discussion focuses on parallel speedups for fixed problem size, a class of problems of immediate practical importance.