Vincent Bertin


Brief resume

I am a theoretical Soft-Matter physicist, currently as a PhD student working under the supervision of Thomas Salez and Elie Raphaël. I'm located both at the Université de Bordeaux in the LOMA laboratory and at ESPCI Paris in the Gulliver laboratory.

My research focuses on the behavior of complex materials in confinement. I'm working in close collaboration with experimental physicists with whom I develop theoretical models. I'm using tools in applied mathematics (analytical and numerical) to solve problems in hydrodynamics and mechanics. Recently, I've been working on thin-film dynamics (see [1], [4] and [5]) and in elastohydrodynamic lubrication (see [3]).

Besides, I'm very much interested in climate change and energy transition issues. I joined the french association La Fresque du Climat, which aims at raise awareness about climate change and I organize vulgarization workshop on the subject.

My CV can be download here: English, French.


Publications and Preprints

  • [9] Soft-lubrication interactions between a rigid sphere and an elastic wall .
    V. Bertin, Y. Amarouchene, E. Raphaël and T. Salez
    arXiv 2104.00900. PDF. [Show Abstract]

    Abstract: The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamicstress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohy-drodynamic (EHD) interactions experienced by the particle. Here, we derive a soft-lubrication model, in orderto compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elasticwall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, andperform a perturbation analysis at leading order in dimensionless compliance. The response is computed in thelimiting cases of thick and thin elastic materials. The normal force is also obtained analytically using the Lorentzreciprocal theorem and agrees with the numerical results.

  • [8] Swimming droplet in 1D geometries, an active Bretherton problem.
    C. de Blois, V. Bertin, S. Suda, M. Ichikawa, M. Reyssat and O. Dauchot
    arXiv 2103.09513. PDF. [Show Abstract]

    Abstract: We investigate experimentally the behavior of self-propelled water-in-oil droplets, confined in cap- illaries of different square and circular cross-sections. The droplet’s activity comes from the forma- tion of swollen micelles at its interface. In straight capillaries the velocity of the droplet decreases with increasing confinement. However at very high confinement, the velocity converges toward a non-zero value, so that even very long droplets swim. Stretched circular capillaries are then used to explore even higher confinement. The lubrication layer around the droplet then takes a non-uniform thickness which constitutes a significant difference with usual flow-driven passive droplets. A neck forms at the rear of the droplet, deepens with increasing confinement, and even- tually undergoes successive spontaneous splitting events for large enough confinement. Such observations stress the critical role of the activity of the droplet interface on the droplet’s behavior under confinement. We then propose an analytical formulation by integrating the interface activity and the swollen micelles transport problem into the classical Bretherton approach. The model accounts for the convergence of the droplet’s velocity to a finite value for large confinement, and for the non-classical shape of the lubrication layer. Further including the saturation of the mi- celles concentration along the interface length, it predicts the divergence of the lubrication layer thickness when the length of the droplet increases, eventually leading to the spontaneous droplet division.

  • [7] Non-contact rheology of finite-size air-water interfaces.
    V. Bertin, Z. Zhang, R. Boisgard, C. Grauby-Heywang, E. Raphael, T. Salez, and A. Maali
    arXiv 2009.14531. PDF, Supp. [Show Abstract]

    Abstract: We present non-contact atomic-force-microscopy measurements of the hydrodynamic interactionsbetween a rigid sphere and an air bubble in water at the microscale. The size of the bubble is foundto have a significant effect on the mechanical response due to the long-range capillary deformationof the air-water interface. We develop a viscocapillary lubrication model accounting for the finite-size effect that allows to rationalize the experimental data. This comparison allows us to measurethe air-water surface tension, without contact and thus wetting, paving the way towards robustnon-contact tensiometry of polluted air-water interfaces.

  • [6] Time dependence of advection-di ffusion coupling for nanoparticle ensembles.
    A. Vilquin V. Bertin, P. Soulard, G. Guyard, E. Raphael, F. Restagno, T. Salez, and J. D. McGraw
    arXiv 2007.08261. PDF. [Show Abstract]

    Abstract: Particle transport in fluids at micro- and nano-scales is important in many domains. As compared to the quiescent case, the time evolution of particle dispersion is enhanced by coupling: i) advection along the flow; and ii) diffusion along the associated velocity gradients. While there is a well-known, long-time limit for this advection-diffusion enhancement, understanding the short-time limit and corresponding crossover between these two asymptotic limits is less mature. We use evanescent-wave video microscopy for its spatio-temporal resolution. Specifically, we observe a near-surface zone of where the velocity gradients, and thus dispersion, are the largest within a simple microfluidic channel. Supported by a theoretical model and simulations based on overdamped Langevin dynamics, our experiments reveal the crossover of this so-called Taylor dispersion from short to long time scales. Studying a range of particle size, viscosity and applied pressure, we show that the initial spatial distribution of particles can strongly modify observed master curves for short-time dispersion and its crossover into the long-time regime.

  • [5] Capillary Levelling of Immiscible Bilayer Films.
    V. Bertin, C. L. Lee, T. Salez, E. Raphael, and K. Dalnoki-Veress
    Journal of Fluid Mechanics 911 (2021) A13 PDF. [Show Abstract]

    Abstract: Flow in thin films is highly dependent on the boundary conditions. Here, we study the capillary levelling of thin bilayer films composed of two immiscible liquids. Specifically, a stepped polymer layer is placed atop another, flat polymer layer. The Laplace pressure gradient resulting from the curvature of the step induces flow in both layers, which dissipates the excess capillary energy stored in the stepped interface. The effect of different viscosity ratios between the bottom and top layers is investigated. We invoke a long-wave expansion of low-Reynolds-number hydrodynamics to model the energy dissipation due to the coupled viscous flows in the two layers. Good agreement is found between the experiments and the model. Analysis of the latter further reveals an interesting double crossover in time, from Poiseuille flow, to plug flow, and finally to Couette flow. The crossover time scales depend on the viscosity ratio between the two liquids, allowing for the dissipation mechanisms to be selected and finely tuned by varying this ratio.

  • [4] Symmetrization of Thin Free-Standing Liquid Films via Capillary-Driven Flow.
    V. Bertin, J. Niven, H. A. Stone, T. Salez, E. Raphael, and K. Dalnoki-Veress
    Physical Review Letters, 124 (2020) 184502 PDF. [LOMA][Show Abstract]

    Abstract: We present experiments to study the relaxation of a nano-scale cylindrical perturbation at one of the two interfaces of a thin viscous free-standing polymeric film. Driven by capillarity, the film flows and evolves towards equilibrium by first symmetrizing the perturbation between the two interfaces, and eventually broadening the perturbation. A full-Stokes hydrodynamic model is presented which accounts for both the vertical and lateral flows, and which highlights the symmetry in the system. The symmetrization time is found to depend on the membrane thickness, surface tension, and viscosity.

  • [3] Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale.
    Z. Zhang, V. Bertin, M. Arshad, E. Raphaël, T. Salez, and A. Maali
    Physical Review Letters, 124 (2020) 1054502-(1-5) PDF, Supp. [LOMA] [GULLIVER] [Show Abstract]

    Abstract: We present the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The force increases as the gap is reduced and shows a saturation at small gap. The results are in excellent agreement with scaling arguments and a quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, an empirical scaling law for the observed saturation of the lift force is given and discussed.

  • [2] Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns.
    J. Aurnou, V. Bertin, A. Grannan, S. Horn, and T. Vogt
    Journal of Fluid Mechanics 846 (2018) 846 PDF. [Show Abstract]

    Abstract: Earth’s magnetic field is generated by convective motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum, and thus the Prandtl number Pr is well below unity. The thermally driven convective flow dynamics of liquid metals are very different from moderate-Pr fluids, such as water and those used in current dynamo simulations. In order to characterise rapidly rotating thermal convection in low-Pr number fluids, we have performed laboratory experiments in a cylinder of aspect ratio 𝛤 = 1.94using liquid gallium (Pr ~ 0.025) as the working fluid. The Ekman number varies from E ~ 5 x 10^-6 to 5 x 10^-6 and the Rayleigh number varies from Ra ~ 2 x 10^5 to 1.5 x 10^7. Using spectral analysis stemming from point-wise temperature measurements within the fluid and measurements of the Nusselt number Nu, we characterise the different styles of low-Pr rotating convective flow. The convection threshold is first overcome in the form of container-scale inertial oscillatory modes. At stronger forcing, sidewall-attached modes are identified for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk oscillatory modes. At well below the values where steady rotating columnar convection occurs, the bulk flow becomes turbulent. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasisteady columns, as in moderate-Pr fluids, but in the form of oscillatory convective motions. Thus, thermally driven flows in low-Pr geophysical and astrophysical fluids can differ substantively from those occurring in Pr ~ 1 models. Furthermore, our experimental results show that relatively low-frequency wall modes are an essential dynamical component of rapidly rotating convection in liquid metals.

  • [1] Elastocapillary levelling of thin viscous films on soft substrates.
    M. Rivetti, V. Bertin, T. Salez, C.-Y. Hui, C. Linne, M. Arutkin, H. Wu, E. Raphaël, and O. Bäumchen
    Physical Review Fluids, 2 (2017) 094001-(1-13) PDF, Supp. [Show Abstract]

    Abstract: A thin liquid film with nonzero curvature at its free surface spontaneously flows to reach a flat configuration, a process driven by Laplace pressure gradients and resisted by the liquid's viscosity. Inspired by recent progresses on the dynamics of liquid droplets on soft substrates, we here study the relaxation of a viscous film supported by an elastic foundation. Experiments involve thin polymer films on elastomeric substrates, where the dynamics of the liquid-air interface is monitored using atomic force microscopy. A theoretical model that describes the coupled evolution of the solid-liquid and the liquid-air interfaces is also provided. In this soft-levelling configuration, Laplace pressure gradients not only drive the flow, but they also induce elastic deformations on the substrate that affect the flow and the shape of the liquid-air interface itself. This process represents an original example of elastocapillarity that is not mediated by the presence of a contact line. We discuss the impact of the elastic contribution on the levelling dynamics and show the departure from the classical self-similarities and power laws observed for capillary levelling on rigid substrates.

Present Collaborators

Teaching activities

  • Applied Mathematics - 1st year ESPCI Paris. Tutoring (12h per year)
    Content: Complex Analysis, Fourier and Laplace Transforms, Distributions.

  • Applied Mathematics - 2nd year ESPCI Paris. Tutoring (12h per year), Tutorials (14h per year)
    Content: Partial Differential Equations, Variationnal calculus, Probability

  • Experimental projects - Bachelor of fundamental physics ENS Paris, (32h per year)
    Content: Turbulent flows, fluctuations, intermittency

  • Linear systems, Signals and Noise. - 1st year ESPCI Paris. Exercice session (2h per year)
    Content: Transfer functions, Shannon Nquist theorem