arXiv subjects

Bastien Di Pierro

Publications and source records attributed to Bastien Di Pierro.

4 recordsLinked to original sources

arXiv2026

A conservation-consistent boundary condition for nonlinear models of soluble-surfactant-laden falling films

A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced models, Pascal et al. (PRF, 2019), D'Alessio et al. (JFM, 2020), which exhibit a gradual drift of mass during nonlinear evolution in a closed periodic domain. We show that this originates from an inconsistency in the surface transport reduction and derive a corrected boundary condition that removes this defect. As the discrepancy appears only at the nonlinear order, linear stability results remain unaffected, explaining why the issue has remained unnoticed.

math.AP↗

arXiv2026

Solutocapillary instability in slipping falling films

We present a comprehensive framework for gravity-driven, surfactant-laden thin films flowing over slippery substrates, elucidating how wall slip modifies the coupled hydrodynamics and interfacial transport. A long-wave model is formulated with a conservative bulk-surface mass balance and a Navier slip condition. The Orr-Sommerfeld eigenvalue problem governs the linear regime, while a weighted-residual model captures the nonlinear evolution over a range of equilibrium surfactant coverages, Marangoni strengths, and adsorption kinetics. The analysis predicts a non-monotonic variation of the critical Reynolds number with equilibrium coverage, exhibiting a maximum at intermediate $Γ_e$, and a slip-induced transition from single- to double-hump solitary structures with increasing Marangoni number, accompanied by attenuated capillary ripples. Under fast adsorption kinetics, the surface field homogenizes, preserving the mean film shape and flux while flattening both the surface concentration $Γ$ and the bulk inventory $χ+ hϕ$. A spurious interfacial mass growth reported by Pascal et al.(PRF, 2019) and D'Alessio et al.(JFM, 2020) is resolved through a revised surface balance ensuring strict conservation. Wall slip thus emerges as a key control parameter, reducing viscous resistance and mitigating Marangoni back-stress. The slip parameter $β$ is a useful control knob for surfactant-laden films. Slip prevents fragile multi-hump bound states, promoting a single broad crest or an almost flat, uniform sheet by carefully bonding $β$ to wave selection, ripple damping, and the bulk-surface surfactant balance.

physics.flu-dyn↗

arXiv2024

A preconditioning for the spectral solution of incompressible variable-density flows

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy in space is investigated. The method, in which the inverse operator for the constant-density flow system acts as preconditioner, is implemented for three iterative solvers: the General Minimal Residual, the Conjugate Gradient and the Richardson Minimal Residual. We discuss the method, first, in the context of the one-dimensional flow case where a top-hat like profile for the density is used. Numerical evidence shows that the convergence is significantly improved due to the notable decrease in the condition number of the operators. Most importantly, we then validate the robustness and convergence properties of the method on two more realistic problems: the two-dimensional Rayleigh-Taylor instability problem and the three-dimensional variable-density swirling jet.

physics.flu-dyn↗

arXiv2018

A note on Stokes' problem in dense granular media using the $μ(I)$--rheology

The classical Stokes' problem describing the fluid motion due to a steadily moving infinite wall is revisited in the context of dense granular flows of mono-dispersed beads using the recently proposed $μ(I)$--rheology. In Newtonian fluids, molecular diffusion brings about a self-similar velocity profile and the boundary layer in which the fluid motion takes place increases indefinitely with time $t$ as $\sqrt{νt}$, where $ν$ is the kinematic viscosity. For a dense granular visco-plastic liquid, it is shown that the local shear stress, when properly rescaled, exhibits self-similar behaviour at short-time scales and it then rapidly evolves towards a steady-state solution. The resulting shear layer increases in thickness as $\sqrt{ν_g t}$ analogous to a Newtonian fluid where $ν_g$ is an equivalent granular kinematic viscosity depending not only on the intrinsic properties of the granular media such as grain diameter $d$, density $ρ$ and friction coefficients but also on the applied pressure $p_w$ at the moving wall and the solid fraction $ϕ$ (constant). In addition, the $μ(I)$--rheology indicates that this growth continues until reaching the steady-state boundary layer thickness $δ_s = β_w (p_w/ϕρg )$, independent of the grain size, at about a finite time proportional to $β_w^2 (p_w/ρg d)^{3/2} \sqrt{d/g}$, where $g$ is the acceleration due to gravity and $β_w = (τ_w - τ_s)/τ_s$ is the relative surplus of the steady-state wall shear-stress $τ_w$ over the critical wall shear stress $τ_s$ (yield stress) that is needed to bring the granular media into motion... (see article for a complete abstract).

physics.flu-dyn↗