arXiv subjects

Tomas Fullana

Publications and source records attributed to Tomas Fullana.

9 recordsLinked to original sources

arXiv2026

The rapidly advancing contact line Part-1: Navier slip and microscale inertial effects

Curtain coating, in which a moving plate is coated by a falling liquid sheet, sustains advancing contact lines at large capillary numbers Ca ~ O(1), based on plate speed. Steady states exist up to a critical capillary number, beyond which wetting failure occurs through air-bubble entrainment. In the steady regime, experiments report that velocity along the fluid-fluid interface accelerates as the contact line is approached, down to tens of micrometres; this has been interpreted as evidence against the Navier slip model. We ask whether this acceleration is compatible with slip models, and show that it is. Although Navier slip implies a vanishing velocity at the contact line, the experimentally accessible microscale region lies outside the slip region. The curtain-coating setup is revealing because the local Reynolds number, based on distance from the contact line r ~ 10 microns, is order unity, so the observable flow is governed by local inertia. Our two-phase Navier-Stokes Volume-of-Fluid simulations with quadtree adaptive mesh refinement resolve the smallest scales and study the flow with a Navier slip boundary condition and fixed contact angle. The simulations reproduce the non-monotonic dependence of the critical capillary number on global Reynolds number, based on feed-flow velocity, and the variation of the macroscopic contact angle at the inflection point, in agreement with Liu et al (2016). The interfacial velocity in the microscale region is well described by an inertially corrected wedge flow solution whose wedge angle is set by the inflection-point value, with agreement improving as slip length is reduced; at larger scales, interface bending follows the Benney solution. These inertial effects, absent from pure Stokes flow, are essential in the experimental region. Thus qualitative microscale observations do not decisively invalidate slip models for advancing contact lines.

physics.flu-dyn↗

arXiv2025

Drops can Perpetually Bounce over a Vibrating Wettable Solid

On the surface of a vibrating liquid bath, instead of coalescing, a drop will continually bounce on a thin film of air between the drop and the free surface, giving rise to rich chaotic dynamics and quantum analog behavior. However, perpetual bouncing is yet to be demonstrated on a vibrating rigid solid, where the control of the drop's motion is not limited by the bath dynamics. Here we show that vibration of an atomically smooth mica surface prolongs a drop's hovering state by several orders of magnitude, increasing the time to wet from less than a second to several minutes. The excitation of the second spherical harmonic mode determines a transition between a bouncing state with high-amplitude rebounds, and a bound state, where the drop's motion is locked onto the vibrating solid above a thin air layer. We further develop a coupled linear spring model, accounting for the drop's deformation, that predicts bouncing trajectories without fitting parameters. Our results extend the scope of bouncing drop studies beyond the liquid bath and highlight the potential for precision manipulation of small liquid quantities in air.

physics.flu-dyn↗

arXiv2025

Adjoint-based optimization of the Rayleigh-B\'enard instability with melting boundary

In this work, we propose an adjoint-based optimization procedure to control the onset of the Rayleigh-B\'enard instability with a melting front. A novel cut cell method is used to solve the Navier-Stokes equations in the Boussinesq approximation and the convection-diffusion equation in the fluid layer, as well as the heat equation in the solid phase. To track the interface we use the level set method where its evolution is simply governed by an advection equation. An incomplete continuous adjoint problem is then derived by treating the velocity field obtained from the forward problem as a known variable in the adjoint convection-diffusion equation, thereby avoiding the need to solve a Navier-Stokes adjoint in the fluid phase. To the best of our knowledge, this provides the first adjoint-based optimization framework for Rayleigh-B\'enard instability with a melting boundary. Two optimization problems, together with a comparison against a derivative-free particle-swarm method, demonstrate that the proposed incomplete adjoint yields gradients accurate enough to control the front shape while reducing the number of expensive function evaluations by about an order of magnitude.

math-ph↗

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 $\delta$ and the apparent angle. In the sharp-interface model, we then introduce a fictitious boundary, displaced by a distance $\delta$ 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↗

arXiv2024

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, K\"ohne 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 $\dot{\theta}_d=0$) 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↗

arXiv2022

A Conservative Cartesian Cut Cell Method for the Solution of the Incompressible Navier-Stokes Equations on Staggered Meshes

The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods however introduce new challenges, as the formulation of accurate and well-posed discrete operators becomes nontrivial. Here, a conservative cartesian cut cell method is proposed for the solution of the incompressible Navier--Stokes equation on staggered Cartesian grids. Emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, a divergence is proposed and shown to also be skew-symmetric as long as the divergence-free condition is satisfied, ensuring mass, momentum and kinetic energy conservation (the latter in the inviscid limit). For viscous transport, conservative and symmetric operators are proposed for Dirichlet boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The cut-cell discretization possesses the much desired summation-by-parts (SBP) properties. In addition, it is fully conservative, mathematically provably stable and supports arbitrary geometries. The accuracy and robustness of the method are then demonstrated with flows past a circular cylinder and an airfoil.

physics.comp-ph↗

arXiv2022

Adjoint-based optimization of two-dimensional Stefan problems

A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary (cut cell) method coupled with an implicit time-advancement scheme is employed to solve the heat equation. A conservative implicit-explicit scheme is then used for solving the level set transport equation. The resulting numerical framework is validated with respect to existing analytical solutions of the forward Stefan problem. An adjoint-based algorithm is then employed to efficiently compute the gradient used in the optimisation algorithm (L-BFGS). The algorithm follows a continuous adjoint framework, where adjoint equations are formally derived using shape calculus and transport theorems. A wide range of control objectives are presented, and the results show that using parameterised boundary actuation leads to effective control strategies in order to suppress interfacial instabilities or to maintain a desired crystal shape.

math-ph↗

arXiv2020

Dynamic wetting failure in curtain coating by the Volume-of-Fluid method

In this paper we investigate dynamic wetting in the curtain coating configuration. The two-phase Navier-Stokes equations are solved by a Volume-of-Fluid method on an adaptive Cartesian mesh. We introduce the Navier boundary condition to regularize the solution at the triple point and remove the implicit numerical slip induced by the cell-centered interface advection. We use a constant contact angle to describe the dynamic contact line. The resolution of the governing equations allows us to predict the substrate velocity at which wetting failure occurs. The model predictions are compared with prior computations and experimental observations.

physics.flu-dyn↗

arXiv2020

Steady moving contact line of water over a no-slip substrate

The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn-Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models can reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase field mobility parameter and the local slip length in accurately modelling the moving contact line.

physics.flu-dyn↗