arXiv subjects

Omar K. Matar

Publications and source records attributed to Omar K. Matar.

At least 19 recordsLinked to original sources

arXiv2026

Numerical simulation of a two-frequency-driven superlattice Faraday-wave pattern

The formation of a superlattice pattern in two-frequency-driven Faraday waves discovered and named SSS-I by Arbell & Fineberg (1998, 2002) is investigated by means of Direct Numerical Simulations (DNS) of the full three-dimensional Navier--Stokes equations with a free surface. Two simulations with distinct quasi-hexagonal initial conditions run at a forcing amplitude $25\%$ above the Faraday-wave onset followed quite different routes, but both led eventually to the same superlattice pattern after around 250 forcing periods. This regime is inaccessible to the approximations of weak nonlinearity or viscosity. The standing-wave pattern contain rows of patches, alternating in time between hills and lakes that are connected by a long skeleton resembing the backbone of DNA strands. The patches and skeleton of the pattern can be related to its spatial Fourier decomposition, which combines hexagonal modes with a spatially and temporally subharmonic mode. One of the transition routes passes through several fairly long-lived transients including different hexagonal patterns and another superlattice pattern; the other passes only through erratic and disordered states. After another 100 periods, the pattern became unstable and was succeeded by a dynamic version of SSS-I in which the superlattice is modulated and drifts in the direction of the backbone, while preserving its basic shape. Convergence to SSS-I states both experimentally in a large geometry and numerically from two different initial conditions and in a minimal geometry demonstrates the robustness of the SSS-I pattern.

physics.flu-dyn↗

arXiv2026

Translation dynamics of evaporating sessile binary-mixture droplet populations

The translation dynamics of two binary mixture droplets is investigated theoretically and is corroborated with experiments. The proposed model accounts for the effects of Marangoni stresses generated by evaporative cooling and concentration gradients, as well as vapour diffusion, for both components of the binary mixture. We consider thin droplets, allowing us to use the lubrication theory to derive the evolution equation for the droplet profiles. We numerically solve the evolution equations using the finite element method and examine various cases of pure and binary droplet pairs exhibiting translational behaviours like attraction, repulsion, and 'chasing'. The results show that the combined effect of solutal Marangoni, capillary effect, and thermal Marangoni determines the movement of the droplets. The non-uniform evaporation generated from 'vapour shielding' creates such effects. We observe that for droplets with the same initial composition, solutal Marangoni and capillary forces induce droplet attraction, while thermal Marangoni effects drive their repulsion. For droplets with different initial compositions, the drop with a higher concentration of the more volatile component pushes, or `chases', the drop with a lower initial concentration of this component, completely driven by the solutal Marangoni. We carried out experiments involving water-morpholine binary mixture droplets to validate the results predicted by our model.

physics.flu-dyn↗

arXiv2026

Interfacial standing wave-patterns disentangle dilatational and shear surface viscous effects

Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the three-dimensional interfacial standing waves as a means to decouple the influence of dilatational and shear surface viscosities. Two dimensionless controlling parameters are introduced: $Bq$, the total Boussinesq number, which quantifies the the relative importance of surface viscous stresses compared with bulk viscous stresses, and $\tan χ$, which quantifies the ratio of surface dilatational viscosity to surface shear viscosity. The growth rates and threshold accelerations are independent of $χ$, consistent with previous theoretical predictions. Nonlinear analyses of square and hexagonal patterns reveal that Fourier decomposition of wave-patterns can effectively decouple the intricate dynamics into axial modes, where the waves are weakly dependent on $χ$, and oblique modes, where additional damping occurs in the shear surface viscous dominant interface. These results demonstrate that Faraday wave-patterns provide a route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities.

physics.flu-dyn↗

arXiv2025

Direct numerical simulation of two-phase flows with surfactant-induced surface viscous effects

Direct numerical simulations of interfacial flows with surfactant-induced complexities involving surface viscous stresses are performed within the framework of the Level Contour Reconstruction Method (LCRM); this hybrid front-tracking/level-set approach leverages the advantages of both methods. In addition to interface-confined surfactant transport that results in surface diffusion and Marangoni stresses, the interface, endowed with shear and dilatational viscosities; these act to resist deformation arising from velocity gradients in the plane of the two-dimensional manifold of the interface, and interfacial compressibility effects, respectively. By adopting the Boussinesq-Scriven constitutive model, We provide a mathematical formulation of these effects that accurately captures the interfacial mechanics, which is then implemented within the LCRM-based code by exploiting the benefits inherent to the underlying front-tracking/level-sets hybrid approach. We validate our numerical predictions against a number of benchmark cases that involve drops undergoing deformation when subjected to a flow field or when rising under the action of buoyancy. The results of these validation studies highlight the importance of adopting a rigorous approach in modelling the interfacial dynamics. We also present results that demonstrate the effects of surface viscous stresses on interfacial deformation in unsteady parametric surface waves and atomisation events.

physics.flu-dyn↗

arXiv2025

Drop size distribution from laboratory experiments based on single-drop fragmentation and comparison with aerial in-situ measurements

Laboratory experiments and theoretical modelling are conducted to determine the raindrop size distribution (DSD) resulting from distinct fragmentation processes under various upward airstreams. Since weather radar echoes are proportional to the sixth power of the average droplet diameter, understanding the fragmentation mechanisms that lead to different breakup sizes is crucial for accurate rainfall predictions. We utilize a two-parameter gamma distribution for theoretical modelling and estimate the average droplet diameter from the theoretically obtained characteristic sizes, often treated as assumed input parameters for different rain conditions in rainfall modelling. Our experimental and theoretical findings demonstrate a close agreement with the DSD predicted by the Marshall and Palmer relationship for steady rain conditions. Additionally, in situ DSD measurements at different altitudes were obtained through research flights equipped with advanced sensors, further validating our rainfall model. This study underscores the effectiveness of laboratory-scale experiments and the critical importance of accurately characterizing DSD to enhance rainfall predictions.

physics.flu-dyn↗

arXiv2025

A novel hybrid approach for accurate simulation of compressible multi-component flows across all-Mach number

Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics. Thus, this work presents a novel approach that combines the Godunov-type scheme for high-speed flows with the projection solution procedure for incompressible flows to address this challenge. The proposed hybrid approach begins by splitting the inviscid flux into the advection part and the pressure part. The solution variables are first updated to their intermediate states by solving the advection part with the all-speed AUSM (Advection Upwind Splitting Method) Riemann solver. The advection flux in AUSM is modified to eliminate the pressure flux term that deteriorates the accuracy at the low Mach region. To prevent the advection flux from causing spurious velocities when surface tension is present, the pressure-velocity coupling term is modified to ensure it vanishes at material interfaces. Then, we derive the pressure Helmholtz equation to solve the final pressure and update the intermediate states to the solution variables at the next time step. The proposed hybrid approach retains the upwind property of the AUSM scheme for high Mach numbers while recovering central schemes and the standard projection solution for low Mach limits. To accurately resolve the complex flow structures including shock waves and material interfaces without numerical oscillations, a newly proposed homogenous ROUND (Reconstruction Operator on Unified Normalised-variable Diagram) reconstruction strategy is employed in this work. By simulating high-speed compressible multiphase flows and incompressible multiphase flows, this study demonstrates the ability of the proposed method to accurately handle flow regimes across all Mach numbers.

physics.flu-dyn↗

arXiv2025

Marangoni-driven patterns, ridges, and hills in surfactant-covered parametric surface waves

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, like squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday wave patterns. We use a quantity $B$, that assesses the relative importance of Marangoni stresses as compared to the the surface wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$. For a surfactant-free interface, a square wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes, and ultimately to ridges and hills. These hills are a consequence of the bi-directional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.

physics.flu-dyn↗

arXiv2024

Thin film flow over a spinning disc: Experiments and direct numerical simulations

The dynamics of thin liquid films flowing over a spinning disc is studied through a combination of experiments and direct numerical simulations. We consider a comprehensive range of interfacial flow regimes from waveless through to three-dimensional (3D) waves, and for previously unexplored inertia-dominated conditions that have practical relevance. The transition between these regimes is categorised within a phase map based on two governing parameters that correspond to modified inverse Weber ($λ$) and Ekman numbers ($r_{disc}$). Our findings show that stationary two-dimensional (2D) spiral waves, which unfold in the direction of rotation from the Coriolis effect, transition to 3D waves with the emergence of small perturbations on the wavefronts. These non-stationary structures grow asymmetrically in the 2D-3D transitional region, and detach from the parent spiral wave to form wavelets or so-called $Λ$ solitons. We show that during and after this wave formation process, flow circulations unique to the spinning disc arrangement are present within the main wave hump. Furthermore, when combined with observations of wall strain rates and topology within the film, these findings elucidate the mechanisms that underpin the apparent wave-induced interfacial turbulence effects observed for spinning disc flows.

physics.flu-dyn↗

arXiv2024

On the convection boundedness of numerical schemes across discontinuities

This short note introduces a novel diagnostic tool for evaluating the convection boundedness properties of numerical schemes across discontinuities. The proposed method is based on the convection boundedness criterion and the normalised variable diagram. By utilising this tool, we can determine the CFL conditions for numerical schemes to satisfy the convection boundedness criterion, identify the locations of over- and under-shoots, optimize the free parameters in the schemes, and develop strategies to prevent numerical oscillations across the discontinuity. We apply the diagnostic tool to assess representative discontinuity-capturing schemes, including THINC, fifth-order WENO, and fifth-order TENO, and validate the conclusions drawn through numerical tests. We further demonstrate the application of the proposed method by formulating a new THINC scheme with less stringent CFL conditions.

math.NA↗

arXiv2024

Surfactant-laden bubble bursting: dynamics of capillary waves and Worthington jet at large Bond number

We present a numerical study of the main sub-stages preceding aerosol formation via bursting bubbles: capillary wave propagation along the bubble, convergence at the bubble's apex, the ascent of a Worthington jet and its break-up to release liquid drops. We focus on two crucial yet overlooked aspects of the system: the presence of surface-active agents and dynamics driven by non-negligible gravitational effects, quantified by the Bond number. Our results propose, for the first time, a mechanism explaining capillary wave retardation in the presence of surfactants, involving the transition from bi- to uni-directional Marangoni stresses, which pull the interface upwards, countering the motion of the waves. We also quantitatively elucidate the variable nature of the waves' velocity with various surfactant parameters, including surfactant solubility and elasticity, a departure from the constant behaviour well-documented in clean interfaces.

physics.flu-dyn↗

arXiv2024

The fluid dynamics of a viscoelastic fluid dripping onto a substrate

Extensional flows of complex fluids are pivotal in industrial applications like spraying, atomisation, and microfluidic drop deposition. The Dripping-on-Substrate (DoS) technique is a conceptually simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. DoS involves capillary-driven thinning of a liquid bridge formed by a slowly dispensed drop onto a partially-wetting solid substrate. By following the filament thinning and pinch-off, the extensional viscosity and relaxation time can be determined. Importantly, DoS enables measurements for lower viscosity solutions than commercially available capillary break-up extensional rheometers. To understand DoS operation, we employ a computational rheology approach via adaptively-refined, time-dependent axisymmetric simulations using the open-source Eulerian code, \textit{Basilisk}. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable viscoelastic solution. We focus on understanding the roles of surface tension, elasticity, and finite chain extensibility in the Elasto-Capillary (EC) regime. Additionally, we explore perturbative effects of gravity and substrate wettability in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model capturing the initial thinning rates, balancing inertia and capillarity. This model also describes the structure of the transition region to the nonlinear EC regime, where elastic stresses counteract capillary pressure in the thread as the filament thins toward breakup. Finally, we propose a fitting methodology based on the analytical solutions for FENE-P fluids to enhance accuracy in determining the effective relaxation time for unknown fluids.

physics.flu-dyn↗

arXiv2024

Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.

physics.flu-dyn↗

arXiv2023

Transition to elasto-capillary thinning dynamics in viscoelastic jets

We perform simulations of an impulsively-started, axisymmetric viscoelastic jet exiting a nozzle and entering a stagnant gas phase using the open-source code Basilisk. This code allows for efficient computations through an adaptively-refined volume-of-fluid technique that can accurately capture the deformation of the liquid-gas interface. We use the FENE-P constitutive equation to describe the viscoelasticity of the liquid and employ the log-conformation transformation, which provides stable solutions for the evolution of the conformation tensor as the jet thins down under the action of interfacial tension. For the first time, the entire jetting and breakup process of a viscoelastic fluid is simulated, including the pre-shearing flow through the nozzle, which results in an inhomogeneous initial radial stress distribution in the fluid thread that affects the subsequent breakup dynamics. The evolution of the velocity field and the elastic stresses in the nozzle are validated against analytical solutions where possible, and the early-stage dynamics of the jet evolution are compared favourably to the predictions of linear stability theory. We study the effect of the flow inside the nozzle on the thinning dynamics of the viscoelastic jet (which develops distinctive "beads-on-a-string" structures) and on the spatio-temporal evolution of the polymeric stresses in order to systematically explore the dependence of the filament thinning and breakup characteristics on the initial axial momentum of the jet and the extensibility of the dissolved polymer chains.

physics.flu-dyn↗

arXiv2023

Data-driven modelling for drop size distributions

The prediction of the drop size distribution (DSD) resulting from liquid atomization is key to the optimization of multi-phase flows, from gas-turbine propulsion, through agriculture, to healthcare. Obtaining high-fidelity data of liquid atomization, either experimentally or numerically, is expensive, which makes the exploration of the design space difficult. First, to tackle these challenges, we propose a framework to predict the DSD of a liquid spray based on data as a function of the spray angle, the Reynolds number, and the Weber number. Second, to guide the design of liquid atomizers, the model accurately predicts the volume of fluid contained in drops of specific sizes whilst providing uncertainty estimation. To do so, we propose a Gaussian process regression (GPR) model, which infers the DSD and its uncertainty form the knowledge of its integrals, and of its first moment, i.e., the mean drop diameter. Third, we deploy multiple GPR models to estimate these quantities at arbitrary points of the design space from data obtained from a large number of numerical simulations of a flat fan spray. The kernel used for reconstructing the DSD incorporates prior physical knowledge, which enables the prediction of sharply peaked and heavy-tailed distributions. Fourth, we compare our method with a benchmark approach, which estimates the DSD by interpolating the frequency polygon of the binned drops with a GPR. We show that our integral approach is significantly more accurate, especially in the tail of the distribution (i.e., large, rare drops), and it reduces the bias of the density estimator by up to ten times. Finally, we discuss physical aspects of the model's predictions and interpret them against experimental results from the literature. This work opens opportunities for modelling drop size distribution in multiphase flows from data.

physics.flu-dyn↗

arXiv2023

A machine learning approach to the prediction of heat-transfer coefficients in micro-channels

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation.

physics.flu-dyn↗

arXiv2023

Discovery of mixing characteristics for enhancing coiled reactor performance through a Bayesian Optimisation-CFD approach

Processes involving the manufacture of fine/bulk chemicals, pharmaceuticals, biofuels, and waste treatment require plug flow characteristics to minimise their energy consumption and costs, and maximise product quality. One such versatile flow chemistry platform is the coiled tube reactor subjected to oscillatory motion, producing excellent plug flow qualities equivalent to well-mixed tanks-in-series 'N'. In this study, we discover the critical features of these flows that result in high plug flow performance using a data-driven approach. This is done by integrating Bayesian optimisation, a surrogate model approach, with Computational fluid dynamics that we treat as a black-box function to explore the parameter space of the operating conditions, oscillation amplitude and frequency, and net flow rate. Here, we correlate the flow characteristics as a function of the dimensionless Strouhal, oscillatory Dean, and Reynolds numbers to the reactor plug flow performance value 'N'. Under conditions of optimal performance (specific examples are provided herein), the oscillatory flow is just sufficient to limit axial dispersion through flow reversal and redirection, and to promote Dean vortices. This automated, open-source, integrated method can be easily adapted to identify the flow characteristics that produce an optimised performance for other chemical reactors and processes.

physics.flu-dyn↗

arXiv2023

Analyzing drop coalescence in microfluidic device with a deep learning generative model

Predicting drop coalescence based on process parameters is crucial for experiment design in chemical engineering. However, predictive models can suffer from the lack of training data and more importantly, the label imbalance problem. In this study, we propose the use of deep learning generative models to tackle this bottleneck by training the predictive models using generated synthetic data. A novel generative model, named double space conditional variational autoencoder (DSCVAE) is developed for labelled tabular data. By introducing label constraints in both the latent and the original space, DSCVAE is capable of generating consistent and realistic samples compared to standard conditional variational autoencoder (CVAE). Two predictive models, namely random forest and gradient boosting classifiers, are enhanced on synthetic data and their performances are evaluated on real experimental data. Numerical results show that considerable improvement in prediction accuracy can be achieved by using synthetic data and the proposed DSCVAE clearly outperforms the standard CVAE. This research clearly brings more insight into handling imbalanced data for classification problems, especially in chemical engineering

cs.CE↗

arXiv2022

Drop encapsulation and bubble bursting in surfactant-laden flows in capillary channels

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles travelling through liquid-filled square capillaries under high Weber number conditions. These conditions consistently induce the formation of a re-entrant jet at the back of the bubble that commonly gives way to a deep liquid cavity. Subsequent steps include pinch-off events in the cavity to generate one or multiple encapsulated drops which may coalesce, in conjunction with the bursting of the bubble-liquid interface by either the cavity or the drops. Some of these interfacial instabilities have previously been reported experimentally (Olbricht 1996) and numerically (Izbassarov & Muradoglu 2016) for liquid-liquid flow in microchannels. We carry out three-dimensional direct numerical simulations based on a hybrid interface-tracking/level-set method capable of accounting for the presence and dynamic exchange of surfactants between the liquid bulk phase and the liquid-gas interface. Our results indicate that the delicate interplay amongst inertia, capillarity, viscosity, surfactant adsorption/desorption kinetics, and Marangoni stresses has a dramatic influence over the non-axisymmetric morphological structures of the encapsulated drops-elongated bubble. This strong coupling also influences the pinch-off time, penetration depth of the cavity, and number, size, and velocity of the encapsulated drops across the bubble. The observed phenomena are summarised in three main morphological regimes based on surfactant-related parameters and dimensionless groups. A discussion of the flow regime maps is also provided.

physics.flu-dyn↗