Thomas A. Baer

Rapid prototyping of patterned functional nanostructures

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.

A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Computational fluid mechanics techniques for examining free surface problems in two-dimensional form are now well established. Extending these methods to three dimensions requires a reconsideration of some of the difficult issues from two-dimensional problems as well as developing new formulations to handle added geometric complexity. This paper presents a new finite element formulation for handling three-dimensional free surface problems with a boundary-fitted mesh and full Newton iteration, which solves for velocity, pressure, and mesh variables simultaneously. A boundary-fitted, pseudo-solid approach is used for moving the mesh, which treats the interior of the mesh as a fictitious elastic solid that deforms in response to boundary motion. To minimize mesh distortion near free boundary under large deformations, the mesh motion equations are rotated into normal and tangential components prior to applying boundary conditions. The Navier–Stokes equations are discretized using a Galerkin–least square/pressure stabilization formulation, which provides good convergence properties with iterative solvers. The result is a method that can track large deformations and rotations of free surface boundaries in three dimensions. The method is applied to two sample problems: solid body rotation of a fluid and extrusion from a nozzle with a rectangular cross-section. The extrusion example exhibits a variety of free surface shapes that arise from changing processing conditions. Copyright

Hierarchically Structured Functional Porous Silica and Composite Produced by Evaporation-Induced Self-Assembly

Abstract Recently so-called soft lithography approaches [Angew. Chem. Int. Ed. 37 (1998) 550] have been combined with surfactant [Adv. Mater. 9 (1997) 811, Nature 390 (1997) 674] and particulate [Science 282 (1998) 2244] templating procedures to create oxides 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. Using self-assembling inks we have combined evaporation-induced (silica/surfactant) self-assembly [Adv. Mater. 11 (1999) 579] with rapid prototyping techniques like micro-pen lithography [Science 283 (1999) 661, Mat. Res. Soc. Symp. Proc. 542 (1999) 159], ink-jet printing [Adv. Mater. 11 (1999) 734, Mat. Sci. Eng. C5 (1998) 289], and dip coating on micro-contact printed substrates to form hierarchically organized structures in seconds. By co-condensation of tetrafunctional silanes (Si(OR) 4 ) with tri-functional organosilanes ((RO) 3 SiR ′ ) [Chem. Commun. (1999) 1367, Chem. Commun. (1997) 1769, J. Am. Chem. Soc. 119 (1997) 4090] or bridged silsesquioxanes (RO) 3 Si–R ′ –Si(OR) 3 ) or by inclusion of organic additives, we have selectively derivatized the silica framework with functional R ′ ligands or molecules. The rapid-prototyping procedures we describe are simple, employ readily available equipment, and provide a link between computer-aided design and self-assembled functional 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.

NMR measurements and simulations of particle migration in non-newtonian fluids

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.

Iterative Solvers and Preconditioners for Fully-Coupled Finite Element Formulations of Incompressible Fluid Mechanics and Related Transport Problems

Finite element discretization of fully-coupled, incompressible flow problems with the classic mixed velocity-pressure interpolation produces matrix systems that render the best and most robust iterative solvers and preconditioners ineffective. The indefinite nature of the discretized continuity equation is the root cause and is one reason for the advancement of pressure penalty formulations, least-squares pressure stabilization techniques, and pressure projection methods. These alternatives have served as admirable expedients and have enabled routine use of iterative matrix solution techniques; but all remain plagued by exceedingly slow convergence in the corresponding nonlinear problem, lack of robustness, or limited range of accuracy. The purpose of this paper is to revisit matrix systems produced by this old mixed velocity-pressure formulation with two approaches: (1) deploying well-established tools consisting of matrix system reordering, GMRES, and ILU preconditioning on modern architectures with substantial distributed or shared memory, and (2) tuning the preconditioner by managing the condition number using knowledge of the physical causes leading to the large condition number. Results obtained thus far using these simple techniques are very encouraging when measured against the reliability (not efficiency) of a direct matrix solver. Here we demonstrate routine solution for an incompressible flow problem using the Galerkin finite element method, Newton-Raphson iteration, and the robust and accurate LBB element. We also critique via an historical survey the limitations of pressure-stabilization strategies and all other commonly used alternatives to the mixed formulation for acceleration of iterative solver convergence. The performance of the new iterative solver approaches on other classes of problems, including fluid-structural interaction, multi-mode viscoelasticity, and free surface flow is also demonstrated.

A level set approach to 3D mold filling of Newtonian fluids.

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.Copyright

Large deformation solid-fluid interaction via a level set approach.

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.

3D Numerical Modelling of Mould Filling of a Coat Hanger Distributer and Rectangular Cavity

Filling processes occur in a wide range of industries, ranging from packaging of consumer products to manufacturing processes for making polymeric, metal and ceramic components. These processes involve the complex interplay of extrusion of a viscous liquid into a mould or container where it displaces a gas phase. Numerical modelling based on computational fluid dynamics can be useful for understanding the filling process. However, complexity arises in that the fluid dynamics in both the viscous liquid and gas phase must be resolved while concurrently determining the location of the fluid-gas interface and the interaction of this interface with the solid surface, i.e., the wetting behaviour. Determining the free surface location and wetting behaviour is an integral part of the numerical method.

Hydrodynamic Effects on Coalescence

The goal of this project was to design, build and test novel diagnostics to probe the effect of hydrodynamic forces on coalescence dynamics. Our investigation focused on how a drop coalesces onto a flat surface which is analogous to two drops coalescing, but more amenable to precise experimental measurements. We designed and built a flow cell to create an axisymmetric compression flow which brings a drop onto a flat surface. A computer-controlled system manipulates the flow to steer the drop and maintain a symmetric flow. Particle image velocimetry was performed to confirm that the control system was delivering a well conditioned flow. To examine the dynamics of the coalescence, we implemented an interferometry capability to measure the drainage of the thin film between the drop and the surface during the coalescence process. A semi-automated analysis routine was developed which converts the dynamic interferogram series into drop shape evolution data.