arXiv subjects

Linda J. Cummings

Publications and source records attributed to Linda J. Cummings.

At least 19 recordsLinked to original sources

arXiv2026

Denoising 3D images: robustness of persistent homology measures

When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the computation of PH of large 3D images, and any analysis of PH that incorporates the number of generators. As such, it is often necessary to denoise the data before computing its PH. We analyze the PH of synthetic 3D images of porous media in the presence of spatially uncorrelated noise, and perform a comparative analysis of various topological measures (e.g. bottleneck distance, Wasserstein distance, persistence statistics and persistence images) to assess their robustness to both noise and the denoising process (i.e. adding spatially uncorrelated Gaussian noise, and denoising by either a Gaussian convolution or a machine learning approach).

cs.CG↗

arXiv2026

Using surface acoustic waves to drive thin film flow over an obstacle

We study a new paradigm for ultrasonic driven object coating by using a model system where MHz-level surface acoustic waves (SAWs) drive the spreading of a silicone oil film atop topographical obstacles. We use experiments to show that nanometer-amplitude SAWs, propagating in the substrate of a piezoelectric actuator, propel macroscopic oil films to climb and traverse solid obstacles placed on the actuator. The oil dynamics reveal rich coupling between ultrasonic forcing, capillarity, and gravity; the balance of which determines coating success. We formulate a simplified two-dimensional theoretical model that incorporates obstacle geometry directly in the oil thin-film evolution equation, introducing a new representation of acoustic streaming in the presence of substrate height variations. Despite the simplifications inherent in the modeling, simulations show qualitative agreement with the experiments, providing evidence that the model captures the key physics.

physics.flu-dyn↗

arXiv2026

Using wetting and ultrasonic waves to extract oil from oil/water mixtures

Oil and water placed atop of a solid surface respond differently to a MHz-level surface acoustic wave (SAW) propagating in the solid due to their different surface wetting properties. We observe that, under SAW excitation, oil films, whether non-organic silicon oil or organic sunflower oil, are extracted continuously from sessile drops, comprising emulsions of the oil in question in a solution of water and surfactants. The mechanism responsible for the extraction of oil from the mixtures is the acoustowetting phenomenon: the low surface tension oil phase leaves the mixture in the form of 'fingers' that, away from the drop, spread opposite the path of the SAW. The high surface tension water phase remains at rest. Increasing either the SAW intensity or the oil content in the mixture enhances the rate at which oil leaves the emulsion. We further observe acoustic-capillary flow instabilities at the free surface of the oil film and the formation of spatial gradients in the emulsion oil-concentrations in the presence of SAW. Our study suggests the potential for using SAW for heterogeneous removal of oil from oil-in-water mixtures to complement current phase separation methods.

physics.flu-dyn↗

arXiv2025

Stochastic Modeling of Filtration with Sieving in Graded Pore Networks

We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving of large particles, two fouling mechanisms typically observed during the early stages of commercial filtration applications. In our model, first-principles continuum partial differential equations model transport of the small particles and adsorptive fouling in each pore, while sieving particles are assumed to follow a discrete Poisson arrival process with a biased random walk through the pore network. Our goals are to understand the relative influences of each fouling mode and highlight the effect of their coupling on the performance of filters with a pore-size gradient (specifically, we consider a banded filter with different pore sizes in each band). Our results suggest that, due to the discrete nature of pore blockage, sieving alters qualitatively the rate of the flux decline. Moreover, the difference between sieving particle sizes and the initial pore size (radius) in each band plays a crucial role in indicating the onset and disappearance of sieving-adsorption competition. Lastly, we demonstrate a phase transition in the filter lifetime as the arrival frequency of sieving particles increases.

physics.flu-dyn↗

arXiv2025

Monte-Carlo based model for the extraction of oil from oil-water mixtures using wetting and surface acoustic waves

This work presents a Monte Carlo (MC) based microscopic model for simulating the extraction of oil from oil-in-water emulsions under the influence of surface acoustic waves (SAWs). The proposed model is a two-dimensional Ising-lattice gas model that employs Kawasaki dynamics to mimic the interactions between oil, water, and air, as well as external forces such as gravity and acoustic stress. By incorporating both acoustic streaming and acoustic radiation pressure, the model captures key experimental observations, including selective oil extraction and droplet motion under SAW excitation. The results highlight the critical role of acoustic radiation pressure in enabling oil film formation and detachment, governed by the balance between capillary and acoustic stresses. The study provides qualitative agreement with experimental findings and offers insights into the essential mechanisms driving acoustowetting-induced phase separation, demonstrating the utility of discrete modeling for complex fluid dynamics problems.

physics.flu-dyn↗

arXiv2024

Using Thermal Crowding to Direct Pattern Formation on the Nanoscale

Metal films and other geometries of nanoscale thickness, when exposed to laser irradiation, melt and evolve as fluids as long as their temperature is sufficiently high. This evolution often leads to pattern formation, which may be influenced strongly by material parameters that are temperature dependent. In addition, the laser heat absorption itself depends on the time-dependent metal thickness. Self-consistent modeling of evolving metal films shows that, by controlling the amount and geometry of deposited metal, one could control the instability development. In particular, depositing additional metal leads to elevated temperatures through the `thermal crowding' effect, which strongly influences the metal film evolution. This influence may proceed via disjoint metal geometries, by heat diffusion through the underlying substrate. Fully self-consistent modeling focusing on the dominant effects, as well as accurate time-dependent simulations, allow us to describe the main features of thermal crowding and provide a route to control fluid instabilities and pattern formation on the nanoscale.

cond-mat.mtrl-sci↗

arXiv2022

Flow through Pore-Size Graded Membrane Pore Networks

Pore-size gradients are often used in the design of membrane filters to increase filter lifetime and ensure fuller use of the initial membrane pore volume. In this work, we impose pore-size gradients in the setting of a membrane filter with an internal network of interconnected tube-like pores. We model the flow and foulant transport through the filter using the Hagen-Poiseuille framework coupled with advection equations via conservation of fluid and particle flux, with adsorption as the sole fouling mechanism. We study the influence of pore-size gradient on performance measures such as total filtrate throughput and accumulated contaminant concentration at the membrane downstream pore outlets. Within the limitations of our modeling assumptions we find that there is an optimal pore-radius gradient that maximizes filter efficiency independent of maximum pore length (an input parameter that influences the structure of the pore network), and that filters with longer characteristic pore length perform better.

physics.flu-dyn↗

arXiv2022

A Graphical Representation of Membrane Filtration

We analyze the performance of membrane filters represented by pore networks using two criteria: 1) total volumetric throughput of filtrate over the filter lifetime and 2) accumulated foulant concentration in the filtrate. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant volumetric flow rates at each pore junction (network vertex). Such a setup yields a system of partial differential equations on the network. We study the influence of three geometric network parameters on filter performance: 1) average number of neighbors of each vertex; 2) initial total void volume of the pore network; and 3) tortuosity of the network. We find that total volumetric throughput depends more strongly on the initial void volume than on average number of neighbors. Tortuosity, however, turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration in the filtrate shows an exponential decay as tortuosity increases.

physics.flu-dyn↗

arXiv2022

Network-based membrane filters: Influence of network and pore size variability on filtration performance

We model porous membrane filters as networks of connected cylindrical pores via a random network generation protocol, and their initial pore radii via a uniform distribution of widths that vary about some mean value. We investigate the influence of network and pore size (radius) variations on the performance of membrane filters that undergo adsorptive fouling. We find that membrane porosity variations, independently of whether induced by variations of the pore radii or of the random pore network, are an important factor determining membrane filter performance. Network and pore size variations still play a role, in particular if pore radii variations are significant. To quantify the influence of these variations, we compare the performance metrics of networks built from pores of variable radii to their (equal porosity) counterparts built from pores of uniform radius. We show that the effect of pore radii variations is to increase throughput, but also to reduce foulant control.

cond-mat.soft↗

arXiv2021

The influence of thermal effects on the breakup of thin films of nanometric thickness

We apply a previously developed asymptotic model (J. Fluid. Mech. 915, A133 (2021)) to study instabilities of free surface films of nanometric thickness on thermally conductive substrates in two and three spatial dimensions. While the specific focus is on metal films exposed to laser heating, the model itself applies to any setup involving films on the nanoscale whose material parameters are temperature-dependent. For the particular case of metal films heated from above, an important aspect is that the considered heating is volumetric, since the absorption length of the applied laser pulse is comparable to the film thickness. In such a setup, absorption of thermal energy and film evolution are closely correlated and must be considered self-consistently. The asymptotic model allows for a significant simplification, which is crucial from both modeling and computational points of view, since it allows for asymptotically correct averaging of the temperature over the film thickness. We find that the properties of the thermally conductive substrate -- in particular its thickness and rate of heat loss -- play a critical role in controlling the film temperature and dynamics. The film evolution is simulated using efficient GPU-based simulations which, when combined with the developed asymptotic model, allow for fully nonlinear time-dependent simulations in large three-dimensional computational domains. In addition to uncovering the role of the substrate and its properties in determining the film evolution, one important finding is that, at least for the considered range of material parameters, strong in-plane thermal diffusion in the film results in negligible spatial variations of temperature, and the film evolution is predominantly influenced by temporal variation of film viscosity and surface tension (dictated by average film temperature), as well as thermal conductivity of the substrate.

physics.flu-dyn↗

arXiv2021

Filtration with multiple species of particles

Filtration of feed containing multiple species of particles is a common process in the industrial setting. In this work we propose a model for filtration of a suspension containing an arbitrary number of particle species, each with different affinities for the filter membrane. We formulate a number of optimization problems pertaining to effective separation of desired and undesired particles in the special case of two particle species and we present results showing how properties such as feed composition affect the optimal filter design (internal pore structure). In addition, we propose a novel multi-stage filtration strategy, which provides a significant mass yield improvement for the desired particles, and, surprisingly, higher purity of the product as well.

math.OC↗

arXiv2021

On efficient asymptotic modelling of thin films on thermally conductive substrates

We consider a free surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a setup where the heat absorption depends on the local film thickness. Our focus is on modeling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a setup commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered setup the Marangoni (thermocapillary) effect turns out to be insignificant.

physics.flu-dyn↗

arXiv2020

Dielectrowetting of a thin nematic liquid crystal layer

We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equation is coupled to a boundary value problem that describes the interaction between the local molecular orientation of the NLC (the director field) and the electric potential. We investigate numerically the behavior of an initially flat film for a range of film heights and surface anchoring conditions.

cond-mat.soft↗

arXiv2019

Modeling and design optimization for pleated membrane filters

Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work (Sanaei & Cummings 2016) used a highly-simplified membrane model to investigate how the pleating effect and membrane geometry affect this performance differential. In this work, we extend this line of investigation and use asymptotic methods to couple an outer problem for the flow within the pleated structure to an inner problem that accounts for the pore structure within the membrane. We use our new model to formulate and address questions of optimal membrane design for a given filtration application.

physics.flu-dyn↗

arXiv2019

Oscillatory thermocapillary instability of a film heated by a thick substrate

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, system dynamics are described by a nonlinear partial differential equation for the film thickness that is nonlocally 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.

physics.flu-dyn↗

arXiv2018

Computing dynamics of thin films via large scale GPU-based simulations

We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based on the alternate direction implicit (ADI) method, with the main part of the compu- tational work carried out in the GPU computing environment. Efficient and accurate computations allow for simulations on large computational domains in three spatial dimensions (3D) and for long computational times. We apply the methods developed to the particular problem of instabilities of thin fluid films of nanoscale thickness. The large scale of the simulations minimizes the effects of boundaries, and also allows for simulating domains of the size encountered in published experiments. As an outcome, we can analyze the development of instabilities with an unprecedented level of detail. A particular focus is on analyzing the manner in which instability develops, in particular regarding differences between spinodal and nucleation types of dewetting for linearly unstable films, as well as instabilities of metastable films. Simulations in 3D allow for consideration of some recent results that were previously obtained in the 2D geometry (J. Fluid Mech. 841, 925 (2018)). Some of the new results include using Fourier transforms as well as topological invariants (Betti numbers) to distinguish the outcomes of spinodal and nucleation types of instabilities, describing in precise terms the complex processes that lead to the formation of satellite drops, as well as distinguishing the shape of the evolving film front in linearly unstable and metastable regimes. We also discuss direct comparison between simulations and available experimental results for nematic liquid crystal and polymer films.

physics.flu-dyn↗

arXiv2017

Stability of thin fluid films characterised by a complex form of structural/effective disjoining pressure

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic liquid crystal films; however we note that similar instability mechanisms, and forms of the effective disjoining pressure, appear in other contexts, such as the well-studied problem of polymeric films on two-layered substrates. The analysis is carried out within the framework of the long-wave approximation, which leads to a fourth order nonlinear partial different equation for the film thickness. Within the considered formulation, the nematic character of the film leads to an additional contribution to the disjoining pressure, changing its functional form. This effective disjoining pressure is characterised by the presence of a local maximum for non-vanishing film thickness. Such a form leads to complicated instability evolution that we study by analytical means, including application of marginal stability criteria, and by extensive numerical simulations that help us develop a better understanding of instability evolution in the nonlinear regime. This combination of analytical and computational techniques allows us to reach novel understanding of relevant instability mechanisms, and of their influence on transient and fully developed fluid film morphologies.

cond-mat.soft↗

arXiv2015

Interfacial deformation and jetting of a magnetic fluid

An attractive technique for forming and collecting aggregates of magnetic material at a liquid--air interface by an applied magnetic field gradient was recently addressed theoretically and experimentally [Soft Matter, (9) 2013, 8600-8608]: when the magnetic field is weak, the deflection of the liquid--air interface has a steady shape, while for sufficiently strong fields, the interface destabilizes and forms a jet that extracts magnetic material. Motivated by this work, we develop a numerical model for the closely related problem of solving two-phase Navier--Stokes equations coupled with the static Maxwell equations. We computationally model the forces generated by a magnetic field gradient produced by a permanent magnet and so determine the interfacial deflection of a magnetic fluid (a pure ferrofluid system) and the transition into a jet. We analyze the shape of the liquid--air interface during the deformation stage and the critical magnet distance for which the static interface transitions into a jet. We draw conclusions on the ability of our numerical model to predict the large interfacial deformation and the consequent jetting, free of any fitting parameter.

physics.flu-dyn↗