Matthew G. Hennessy

A Unified Approach for Patterning via Frontal Photopolymerization.

A unified patterning strategy via frontal photopolymerization (FPP) that is robust to a wide range of radical photopolymerizing systems, including thiol-ene and acrylic monomers is reported. The factors governing the spatiotemporal solidification process, including front position, profile shape, and thermal effects, are investigated and modeled theoretically, resulting in the predictive FPP patterning of polymer networks with prescribed dimensions.

A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection

This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a nonvolatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Benard--Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a nonautonomous linearized system which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite-dimensional approximation of the linearized problem. This is determined to leading and to next order. The corrections indicate that the validity of the expan...

A Two-Phase Model for Evaporating Solvent-Polymer Mixtures

Evaporating solvent-polymer mixtures play an important role in a number of modern industrial applications. We focus on developing a two-phase model for a fluid composed of a volatile solvent and a nonvolatile polymer in a thin-film geometry. The model accounts for density differences between the phases as well as evaporation at a fluid-air interface. We use the model in one dimension to explore the interplay between evaporation and compositional buoyancy; the former promotes the growth of a polymer-rich skin at the free surface while the latter tends to pull the denser polymeric phase to the substrate. We also examine how these mechanisms influence the drying time of the film. In the limit of dilute polymer, the model can be reduced to a single nonlinear boundary value problem. The nondilute problem has a rich asymptotic structure. We find that the shortest drying times occur in the limit of strong gravitational effects due to the rapid formation of a bilayer with a polymer-rich lower layer and a solvent-rich upper layer. In addition, gravity plays a key role in inhibiting the formation of a skin and can prevent substantial increases in the drying time of the film.

Controlled Topological Transitions in Thin-Film Phase Separation

In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.

The primary flow transition in a differentially heated rotating channel of fluid with O(2) symmetry

Abstract The primary flow transition in a periodic differentially heated rotating channel of fluid with O(2) symmetry is studied. This transition occurs when a time-independent flow that is uniform along the channel bifurcates to a stationary wave flow. The fluid is modelled using the Navier–Stokes equations in the Boussinesq approximation and the flow transition is found using linear stability analysis. The computation of the flow transition curve is performed efficiently by replacing the relevant eigenvalue problem with an equivalent bordered linear system, and by implementing a pseudoarclength continuation strategy that is appropriate for large-scale systems. The dynamics of the fluid near the transition are deduced by applying centre manifold reduction and normal form theory. The reduction produces analytical expressions for the normal form coefficients in terms of functions that must be computed numerically. The results indicate that the transition to stationary wave flow occurs via a supercritical pitchfork bifurcation to a group orbit, sometimes referred to as a pitchfork of revolution. Furthermore, at several points along the transition curve two such pitchfork bifurcations occur simultaneously, which physically corresponds to the interaction of two stationary wave modes. An analysis of the normal form equations that are associated with the steady-state mode interactions shows the possibility of bistability and hysteresis of the stationary waves. Many of the results obtained in the channel model show a remarkable quantitative similarity to those of theoretical and experimental studies of analogous experiments using a cylindrical annulus, even though the difference in the symmetries of the systems ensure certain qualitative differences. This suggests that the dynamics of the fluid are dominated by the differential heating and the rotation, and not by the curvature of the system.

Mathematical modelling of Tyndall star initiation

The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid-liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.