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We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. While the flow in a funnel may be related to a number of other flow configurations as limiting cases, understanding its stability is complicated due to the presence of additional azimuthal curvature, as well as due to convergent flow effects imposed by the geometry. The convergent nature of the flow leads to thickening of the film, therefore influencing its stability properties. In this work, we analyse these stability properties by combining physical experiments, asymptotic modelling, self-similar type of analysis and numerical simulations. We show that an appropriate long-wave-based model, supported by the input from experiments, simulations and linear stability analysis that originates from the flow down an incline plane, provides a basic insight allowing an understanding of the development of contact line instability and emerging length scales. 

We study the influence of a membrane filter's internal pore structure on its flow and adsorptive fouling behaviour. Membrane performance is measured via (1) comparison between volumetric flow rate and throughput during filtration and (2) control of concentration of foulants at membrane pore outlets. Taking both measures into account, we address the merits and drawbacks of selected membrane pore structures. We first model layered planar membrane structures with intra-layer pore connections, and present comparisons between non-connected and connected structures. Our model predicts that membrane filters with connected pore structures lead to higher total volumetric throughput than those with non-connected structures, over the filter lifetime. We also provide a sufficient criterion for the concentration of particles escaping the filter to achieve a maximum in time (indicative of a membrane filter whose particle retention capability can deteriorate). Additionally, we find that the influence of intra-layer heterogeneity in pore-size distribution on filter performance depends on the connectivity properties of the pores. 

Model hard colloids have a great deal of relevance to physics and in particular the study of their phase behavior which can mimic that of simple atomic liquids and solids. "Nearly hard colloidal sphere" suspensions were formulated 35 years ago by the Ottewill group (Univ. of Bristol) and Imperial Chemical Industries Ltd., which were used by Pusey and van Megen in their seminal study of the phase behavior of hard-sphere colloids. We report on our efforts to reproduce and refine this benchmark polymer colloid, including the recent synthesis of hard ellipsoids for random and ordered packing studies in microgravity*. The custom-made samples are composed of linear polymer chains of poly(methyl methacrylate), functionalized with photo-crosslinkable moieties and fluorescent molecules. The resulting ellipsoidal shapes are about 1 micron in size and stabilized with surface-grafted poly(12-hydroxystearic acid) chains. The particles are dispersed in a refractive index matching fluid and particle aspect ratios vary from 1 to 4. * Launched March 2020 aboard SpaceX CRS-20 resupply service mission to the International Space Station. *NASA NNX13AR67G (NYU); NSF GOALI 1832291 (NYU); NSF GOALI 1832260 (NJIT) 

In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate–film thermal conductivity ratio are large so that the effect of substrate thermal diffusion is retained at leading order in the long-wave approximation. As a result, the system dynamics is described by a nonlinear partial differential equation for the film thickness that is non-locally coupled to the full substrate heat equation. Perturbing about a steady quiescent state, we find that its stability is described by a non-self-adjoint eigenvalue problem. We show that, under appropriate model parameters, the linearized eigenvalue problem admits complex eigenvalues that physically correspond to oscillatory (in time) instabilities of the thin-film height. As the principal results of our work, we provide a complete picture of the susceptibility to oscillatory instabilities for different model parameters. Using this description, we conclude that oscillatory instabilities are more relevant experimentally for films heated by insulating substrates. Furthermore, we show that oscillatory instability where the fastest-growing (most unstable) wavenumber is complex, arises only for systems with sufficiently large substrate thicknesses. Finally, we discuss adaptation of our model to a practical setting and make predictions of conditions at which the reported instabilities can be observed.