arXiv subjects

Stéphane Zaleski

Publications and source records attributed to Stéphane Zaleski.

At least 19 recordsLinked to original sources

arXiv2026

Shear-driven arrest of dip-coating film entrainment

A plate withdrawn from a bath of partially wetting liquid entrains a film above a critical velocity. Here, we show that this critical threshold can be substantially increased by the presence of a laminar gas flow opposed to the plate velocity that exerts a tangential shear stress on the liquid-gas interface. Using two-phase immiscible Navier-Stokes simulations and confining the gas to a narrow channel, we derive a closed-form expression for the interfacial stress, which combined with lubrication theory relates the thickness of the film and the contact line velocity to the applied shear stress. As the gas velocity is increased, the film thins and the contact line velocity slows down, until the imposed shear overcomes the drag of the moving plate and entrainment is arrested. As in the quiescent case, the velocity mismatch between plate and contact line is independent of the plate velocity and is set by the applied shear alone. We find that one set of varying gas flow simulations, with constant critical plate velocity, therefore determines the critical gas flow for every smaller plate velocity.

cond-mat.soft↗

arXiv2026

A Three-dimensional Edge-Based Interface Tracking (EBIT) Method for Multiphase-flow Simulations

The Edge-Based Interface Tracking (EBIT) method is a novel Front-Tracking method in which the markers are located on grid edges, and their connectivity is implicitly represented by a color vertex field. This localized representation simplifies topology changes and allows for automatic parallelization. In this work, we propose a simplified extension of EBIT to three dimensions (3D). The directional split scheme used for interface advection in the two-dimensional (2D) version is generalized to 3D by decomposing each 3D directional advection step into 2D advection problems on the two corresponding cube faces. The same dimension-reduction strategy is applied to connectivity representation, allowing the main 2D algorithms and data structures to be reused and thereby reducing the algorithmic and implementation complexity. For coupling with the Navier--Stokes equations, volume fractions are reconstructed from the EBIT markers and color vertex field using the Front2VOF geometric method. The resulting volume fractions are then used to compute the fluid properties and surface-tension forces with the Height-Function method. The 3D EBIT method has been implemented in the free Basilisk framework, with the documented source code available in the online repository. The method is verified against five benchmark cases: translation with uniform velocity, 3D deformation test, oscillating drop, rising bubble, and bubble merging. The results show good agreement with reference solutions and with the Volume-of-Fluid (VOF) method implemented in Basilisk, demonstrating the effectiveness of the simplified extension. In addition, the 3D EBIT method exhibits excellent weak scalability, highlighting its potential advantage over traditional front-tracking methods for large-scale parallel computations.

physics.flu-dyn↗

arXiv2026

Scale- and Structure-Dependent Fractal Dimensions in a Two-Dimensional Atomizing Liquid Jet

Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct numerical simulations, VOF-DNS, of a liquid jet with adaptive mesh refinement in Basilisk. Box counting of the full resolved interface does not yield a single scale-independent exponent. Instead, two scaling ranges appear, separated by a crossover near box-counting level Lbox about 7: coarser boxes measure the folded connected jet envelope, whereas finer boxes increasingly sample ligaments, droplets, and nearly smooth local interface segments. Decomposing the interface into detached droplets, ligaments, and the connected main body shows that the relevant effective dimension is structure dependent. Droplets remain near Euclidean at fine scales, ligaments occupy an intermediate level, and the main body carries the largest coarse-scale dimension. This hierarchy persists for liquid Reynolds numbers from 100 to 10000 at fixed gas Weber number 200. Thus, in this two-dimensional VOF-DNS setting, fractal dimension is best interpreted not as a single global exponent, but as a scale- and structure-resolved state variable for interfacial folding and breakup.

physics.flu-dyn↗

arXiv2026

Holes in Sheets: Double-Threshold Rupture of Draining Liquid Films

Classical rupture is attributed to molecular (van der Waals) forces acting at nanometric thicknesses. Nonetheless, micron-thick liquid sheets routinely perforate far above the scale where these molecular forces act, yet the mechanism that selects opening versus healing has remained unclear. Using direct numerical simulations of a draining sheet with an entrained air bubble (cavity), we show that irreversible rupture occurs only when a deterministic double-threshold is crossed: (i) the outward driving (from airflow or inertia) is strong enough and (ii) the cavity is distorted enough. If either condition falls short, surface tension heals the cavity and the sheet reseals. The time for this process is set by the balance between inertia and viscosity -- fast for inertia-dominated sheets and slower for viscous ones. This double-threshold mechanism explains why micrometer-thick films perforate and offers practical control options -- driving strength and defect geometry -- for predicting and controlling breakup in spray formation processes, wave breaking, and respiratory films.

physics.flu-dyn↗

arXiv2026

Applying contact angles based on a continuously moving contact line in 2D VOF simulations

A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature estimation in the contact line cell, where the interface normal is constrained to the prescribed angle to ensure smooth contact line motion. On flat solid surfaces, the proposed model achieves higher accuracy than the conventional vertical height-function method for enforcing very small and very large contact angles. Moreover, it extends naturally to curved solid surfaces represented by the embedded boundary method, enabling the imposition of arbitrary contact angles without inducing significant spurious currents near the contact line. Numerical validations confirm the accuracy and robustness of the proposed method, demonstrating its applicability to multiphase flows involving complex wall geometries and contact-line dynamics.

physics.flu-dyn↗

arXiv2025

A consistent treatment of dynamic contact angles in the sharp-interface framework with the generalized Navier boundary condition

In this work, we revisit the Generalized Navier Boundary condition (GNBC) introduced by Qian et al.\ in the sharp interface Volume-of-Fluid context. We replace the singular uncompensated Young stress by a smooth function with a characteristic width $\varepsilon > 0$ that is understood as a physical parameter of the model. Therefore, we call the model the ``Contact Region GNBC'' (CR-GNBC). We show that the model is consistent with the fundamental kinematics of the contact angle transport described by Fricke, Köhne and Bothe. We implement the model in the geometrical Volume-of-Fluid solver Basilisk using a ``free angle'' approach. This means that the dynamic contact angle is not prescribed but reconstructed from the interface geometry and subsequently applied as an input parameter to compute the uncompensated Young stress. We couple this approach to the two-phase Navier Stokes solver and study the withdrawing tape problem with a receding contact line. It is shown that the model allows for grid-independent solutions and leads to a full regularization of the singularity at the moving contact line, which is in accordance with the thin-film equation subject to this boundary condition. In particular, it is shown that the curvature at the moving contact line is finite and mesh converging. As predicted by the fundamental kinematics, the parallel shear stress component vanishes at the moving contact line for quasi-stationary states (i.e. for $\dotθ_d=0$) and the dynamic contact angle is determined by a balance between the uncompensated Young stress and an effective contact line friction. Furthermore, a non-linear generalization of the model is proposed, which aims at reproducing the Molecular Kinetic Theory of Blake and Haynes for quasi-stationary states.

physics.flu-dyn↗

arXiv2025

Three-dimensional numerical study on hydrogen bubble growth at electrode

Three-dimensional direct numerical simulation of electrolysis is applied to investigate the growth and detachment of bubbles at electrodes. The moving gas-liquid interface is modeled employing the VOF-based method. To ensure the accuracy of the simulations, a mesh-independence study has been performed. The simulations include the growth phase of the bubbles, followed by their detachment from the electrode surface, and the results are validated with analytical models and experimental data. The bubble growth is diffusion-controlled, leading to the scaling $R\propto t^{1/2}$, but our simulation overpredicts the growth exponent during the initial stage. We further demonstrate that the number of nucleation sites significantly affects gas transport, as quantified by the Sherwood number. The influences of contact angle and nucleation site on bubble detachment are also examined. The predicted detachment radius varies linearly with contact angle, consistent with Fritz's linear relation between the volume-equivalent radius and contact angle, confirming that the surface tension is the dominant attachment force. Finally, as the nucleation sites increase, the induced bubble coalescence accelerates the bubble detachment. Taken together, these findings give us valuable insights into improving gas bubble removal and enhancing overall electrolysis efficiency.

physics.flu-dyn↗

arXiv2025

A multiscale numerical approach to investigate interfacial mass transfer in three phase flow: application to metallurgical bottom-blown ladles

We use direct numerical simulation (DNS) to investigate mass transfer between liquid steel and slag during a metallurgical secondary refinement process through two reduced-scale water experiments, which reproduce the dynamics seen in an industrial bottom-blown ladle. A container is filled with water and topped by a thin layer of oil, representing the molten steel and slag, respectively. The system is agitated by a bubble plume that impinges on the oil layer and forms an open-eye. A tracer species, dissolved in the water, acts as a passive scalar that is progressively absorbed into the oil layer. Both the hydrodynamics and mass transfer in the system are studied and compared with experiments from the literature of different size and geometry. The numerical simulation of mass transfer is challenging due to the high Péclet number, leading to extremely thin species boundary layers at the interface. Resolving the boundary layer is prohibitive even with adaptive grid techniques. A subgrid-scale (SGS) boundary layer model corrects the scalar transport equation, allowing us to solve convection-dominated transport on relatively coarse grids. The hydrodynamics is investigated, and we analyze how the resultant flow field governs mass transport. The numerical results recover two flow regimes: a quasi-steady regime at low flow rates with small deformations of the oil-water interface and an atomizing regime at large flow rates. Interfacial species transport is determined to be dominated in an annulus surrounding the open eye caused by a shear layer at the oil-water interface. It is observed that we achieve grid-independent macroscopic quantities that match relatively well with those observed in experiments, allowing use of simulation techniques as a complementary tool going forward.

physics.flu-dyn↗

arXiv2025

Mass diffusion and bending in dynamic wetting by phase-field and sharp-interface models

Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring empirical fitting for the slip length. On the other hand, this paradox does not appear in phase-field models as the contact line moves through diffusive mass transport. In this work, we present a toy model that accounts for mass diffusion at the contact line within a sharp-interface framework. This model is based on a theoretical relation derived from the Cahn-Hilliard equations, which links the total diffusive mass transport to the curvature at the wall. From an estimate of the chemical potential on a curved interface, we obtain an expression for the width of the highly curved region $δ$ and the apparent angle. In the sharp-interface model, we then introduce a fictitious boundary, displaced by a distance $δ$ into the domain, where a Navier boundary condition is applied along a dynamic apparent contact angle that accounts for the local interface bending. The robustness of the model is assessed by comparing the toy model results with standard phase-field ones on two cases: the steady state profiles of a liquid bridge between two plates moving in opposite directions and the transient behaviors of a drop spreading on a solid with a prescribed equilibrium angle. This offers a practical and efficient alternative to solve contact line problems at lower cost in a sharp-interface framework with input parameters from phase-field models.

physics.flu-dyn↗

arXiv2025

An Unsplit Scheme for Interface Advection in the Edge-based Interface Tracking (EBIT) Method

We propose an unsplit scheme for interface advection in a novel Front-Tracking method, called the Edge-Based Interface Tracking (EBIT) method. In the EBIT method, the markers are placed on the grid edges, and their connectivity is implicitly represented using a color vertex field. In our previous publications, a split scheme was used to advect the interface in the EBIT method. Although the split scheme facilitates the extension of the EBIT method to three dimensions, it also imposes some limitations. First, implementing high-order time integration methods for interface advection becomes challenging. Second, in multiscale simulations using Front-Tracking methods with a boundary layer model applied to the interface, the redistribution of physical quantities inside the boundary layer, such as a scalar concentration, along the interface becomes difficult due to the loss of correspondence between interface segments before and after each advection step, caused by the operator split. Here, we present an unsplit scheme for interface advection to enhance the capability of the EBIT method. In the unsplit scheme, a reconstruction step based on a circle fit, similar to that used in the split scheme, is performed to reposition markers on the cell edges. Furthermore, the algorithm used to update the color vertex field, which implicitly represents marker connectivity and distinguishes among ambiguous topology configurations, is modified to achieve consistent connectivity results. An EBIT method based on an unsplit scheme has been implemented in the free Basilisk platform, and validated with four kinematic test cases: translation with uniform velocity, solid body rotation, Zalesak's disk rotation, and single vortex test. The results are compared with those obtained using the original EBIT method based on a split scheme.

physics.flu-dyn↗

arXiv2025

Viscoelasticity reduces the droplet size in mucosalivary film fragmentation during intense respiratory events

We examine the fundamental fluid dynamical mechanisms dictating the generation of bioaerosols in the human trachea during intense respiratory events such as coughing and sneezing, with an emphasis on the role played by the mucosalivary fluid viscoelasticity. An experimental investigation of the shear-induced fragmentation of a mucosalivary-mimetic fluid in a confined geometry reveals that viscoelastic liquids undergo atomization in a manner akin to Newtonian liquids -- via the formation of bag-like structures -- which ultimately rupture through the appearance of retracting holes on the bag surface. Droplets are produced via the unstable retraction of liquid rims bounding these holes. However, in comparison to Newtonian liquids, viscoelastic bags inflate to larger sizes -- implying thinner sheets and, consequently smaller droplets upon rupture. Numerical simulations support that the smaller droplets can be attributed to the thinner sheets, with a more uniform thickness, for viscoelastic bags prior to rupture. Hence, we highlight the role of the viscoelasticity in determining the thickness of the intermediate bag-like structures, which, in turn, govern the droplet size distribution of the expelled aerosol.

physics.flu-dyn↗

arXiv2025

Direct numerical simulation of nucleate boiling with a resolved microlayer and conjugate heat transfer

In this paper, a phase-change model based on a geometric Volume-of-Fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with Interfacial Heat-Transfer Resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared to previous literature studies, the computational cost is reduced by three orders of magnitude. The influence of contact angle is further investigated, revealing consistent thermodynamic effects across different contact angles. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.

physics.flu-dyn↗

arXiv2025

The atomizing pulsed jet

Direct Numerical Simulations of the injection of a pulsed round liquid jet in a stagnant gas are performed in a series of runs of geometrically progressing resolution. The Reynolds and Weber numbers and the density ratio are sufficiently large for reaching a complex high-speed atomization regime but not so large so that the small length scales of the flow are impossible to resolve, except for very small liquid-sheet thickness. The Weber number based on grid size is then small, an indication that the simulations are very well resolved. Computations are performed using octree adaptive mesh refinement with a finite volume method and height-function computation of curvature, down to a specified minimum grid size $Δ$. Qualitative analysis of the flow and its topology reveals a complex structure of ligaments, sheets, droplets and bubbles that evolve and interact through impacts, ligament breakup, sheet rupture and engulfment of air bubbles in the liquid. A rich gallery of images of entangled structures is produced. Most processes occurring in this type of atomization are reproduced in detail, except at the instant of thin sheet perforation or breakup. We analyze droplet statistics, showing that as the grid resolution is increased, the small-scale part of the distribution does not converge, and contains a large number of droplets close in order of magnitude to the minimum grid size with a significant peak at $d = 3Δ$. This non-convergence arises from the numerical sheet breakup effect, in which the interface becomes rough just before it breaks. The rough appearance of the interface is associated to a high-wavenumber oscillation of the curvature. To recover convergence, we apply the controlled "manifold death" numerical procedure, in which thin sheets are detected, and then pierced by fiat before they reach a set critical thickness $h_c$.

physics.flu-dyn↗

arXiv2025

Exact computation of the color function for triangular element interfaces

The calculation of the volume enclosed by curved surfaces discretized into triangular elements, and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust algorithm, the Front2VOF (F2V) algorithm, to address this problem. The F2V algorithm consists of two main steps. First, it identifies the polygons within the cube by segmenting the triangular elements on the surface, retaining only the portions inside the cube boundaries. Second, it computes the volume enclosed by these polygons in combination with the cube faces. To validate the algorithm's accuracy and robustness, we tested it using a range of synthetic configurations with known analytical solutions.

cs.GR↗

arXiv2024

Statistics of drops generated from ensembles of randomly corrugated ligaments

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent non-linearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios.

physics.flu-dyn↗

arXiv2024

Dynamic hysteresis of an oscillatory contact line

During oscillatory wetting, a phase retardation emerges between contact angle variation and contact line velocity, presenting as a hysteresis loop in their correlation -- an effect we term dynamic hysteresis. This phenomenon is found to be tunable by modifying the surface with different molecular layers. A comparative analysis of dynamic hysteresis, static hysteresis, and contact line friction coefficients across diverse substrates reveals that dynamic hysteresis is not a result of dissipative effects but is instead proportionally linked to the flexibility of the grafted layer on the surface. In the quest for appropriate conditions to model oscillatory contact line motion, we identify the generalized Hocking's linear law and modified Generalized Navier Boundary Condition (GNBC) as alternative options for predicting realistic dynamic hysteresis.

physics.flu-dyn↗

arXiv2024

An Edge-based Interface Tracking (EBIT) Method for Multiphase Flows with Phase Change

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

physics.flu-dyn↗

arXiv2024

An Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

physics.flu-dyn↗