Vincent Bertin

Brief resume I am a theoretical Soft-Matter physicist, currently as a postdoc in the Physics of Fluids group at the University of Twente and under the supervision of Jacco Snoeijer. Before I did my PhD at the University of Bordeaux under the supervision of Thomas Salez and Elie Raphaël. 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], [5] and [11]) and in elastohydrodynamic lubrication (see [3], [7], [9] and [10]). 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. Contact E-mail: v [dot] l [dot] bertin [at] utwente [dot] nl Physical address: University of Twente, Faculty Science and Technology, Physics of Fluids, Building MEANDER (27), Office ME212, P.O. Box 217, 7500AE Enschede.

News

• Our recent work with Alexandre Vilquin and Joshua McGraw on Taylor dispersion near interfaces has been published in Phys. Rev. Lett. I will present it at the European Fluid Mechanics Conference in September 2022.

• I received the PhD Prize Science et Technologie 2022 of the University of Bordeaux.

• Starting in October 2021, I will do a post-doc in the University of Twente in the Physics of Fluids group with Jacco Snoeijer.

• I defend my PhD on September 9th 2021 in Bordeaux. You can find the manuscript here.

• I will present my work at the ICTAM 2020+1 conference at 22nd-27th of August 2021.

• I receive the prize of the Jean Langlois foundation for broadcasting research in 2020.

Publications and Preprints

• [19] Interfacial dripping faucet: generating monodisperse liquid lenses.
  L. Champougny, V. Bertin, J. H. Snoeijer and J. Rodriguez-Rogriguez
  arXiv:2401.00459 PDF. [Show Abstract]

  Abstract: We present a surface analog to a dripping faucet, where a viscous liquid slides down an immiscible meniscus. Periodic pinch-off of the dripping filament is observed, generating a succession of monodisperse floating lenses. We show that this interfacial dripping faucet can be described analogously to its single-phase counterpart, replacing surface tension by the spreading coefficient, and even undergoes a transition to a jetting regime. This liquid/liquid/gas system opens perspectives for the study of the dynamics of emulsions at interfaces.

• [18] Frozen Cheerios effect: Particle-particle interaction induced by an advancing solidification front.
  J. G. Meijer, V. Bertin and D. Lohse
  arXiv2311.09477 PDF. [Show Abstract]

  Abstract: Particles at liquid interfaces have the tendency to cluster due to long-range capillary interactions. This is known as the Cheerios effect. Here we experimentally and theoretically study the interaction between two submerged particles near an advancing water-ice interface during the freezing process. Particles that are more thermally conductive than water are observed to attract each other and form clusters once frozen. We call this feature the frozen Cheerios effect. On the other hand, particles less conductive than water separate, highlighting the importance of thermal conduction during freezing. Based on existing models for single particle trapping in ice, we develop an understanding of multiple particle interaction. We find that the overall strength of the particle-particle interaction critically depends on the solidification front velocity. Our theory explains why the thermal conductivity mismatch between the particles and water dictates the attractive/repulsive nature of the particle-particle interaction.

• [17] Viscoelastic wetting: Cox-Voinov theory with normal stress effects.
  M. Kansal, V. Bertin, C. Datt, J. Eggers and J. H. Snoeijer
  Accepted in Journal of Fluid Mechanics (2024) PDF. [Show Abstract]

  Abstract: The classical Cox-Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact line velocity. Here we investigate how viscoelasticity, specifically the normal stress effect, modifies wetting dynamics. Using the thin film equation for the second-order fluid, it is found that the normal stress effect is dominant at small scales. We show that the effect can be incorporated in the Cox-Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory is applied to the classical problems of drop spreading and dip-coating, which shows how normal stress facilitates (inhibits) the motion of advancing (receding) contact lines. For rapid advancing motion, the apparent microscopic angle can tend to zero in which case the dynamics is described by a new regime that was already anticipated in Boudaoud (2007).

• [16] Similarity solutions in elastohydrodynamic bouncing.
  V. Bertin
  Accepted in Journal of Fluid Mechanics (2024) PDF. [Show Abstract]

  Abstract: We investigate theoretically and numerically the impact of an elastic sphere on a rigid wall in a viscous fluid. Our focus is on the dynamics of the contact, employing the soft lubrication model in which the sphere is separated from the wall by a thin liquid film. In the limit of large sphere inertia, the sphere bounces and the dynamics is close to the Hertz theory. Remarkably, the film thickness separating the sphere from the wall exhibits non-trivial self-similar properties that vary during the spreading and retraction phases. Leveraging these self-similar properties, we establish the energy budget and predict the coefficient of restitution for the sphere. The general framework derived here opens many perspectives to study the lubrication film in impact problems.

• [15] Unsteady drag force on an immersed sphere oscillating near a wall.
  Z. Zhang, V. Bertin, M. H. Essink, H. Zhang, N. Fares, Z. Shen, T. Bickel, T. Salez, and A. Maali
  Journal of Fluid Mechanics 977 A21 (2023) PDF. [Show Abstract]

  Abstract: The unsteady hydrodynamic drag exerted on an oscillating sphere near a planar wall is addressed experimentally, theoretically, and numerically. The experiments are performed by using colloidal-probe Atomic Force Microscopy (AFM) in thermal noise mode. The natural resonance frequencies and quality factors are extracted from the measurement of the power spectrum density of the probe oscillation for a broad range of gap distances and Womersley numbers. The shift in the natural resonance frequency of the colloidal probe as the probe goes close to a solid wall infers the wall-induced variations of the effective mass of the probe. Interestingly, a crossover from a positive to a negative shift is observed as the Womersley number increases. In order to rationalize the results, the confined unsteady Stokes equation is solved numerically using a finite-element method, as well as asymptotic calculations. The in-phase and out-of-phase terms of the hydrodynamic drag acting on the sphere are obtained and agree well to the experimental results. All together, the experimental, theoretical, and numerical results show that the hydrodynamic force felt by an immersed sphere oscillating near a wall is highly dependent on the Womersley number.

• [14] Coalescence of bubbles in a viscoelastic liquid.
  A. Oratis, V. Bertin and J. H. Snoeijer
  Physical Review Fluids, 8, 083603 (2023) PDF. [Show Abstract]

  Abstract: When two bubbles submerged in a liquid are brought closely together, the intermediate liquid film separating the bubbles begins to drain. Once the film ruptures, the bubbles coalesce and form a neck that expands with time. The dynamics of the neck growth are well understood in the context of pure, Newtonian liquids. Yet, much less is known about the dynamics of this singularity when the surrounding liquid contains long flexible polymers, which provide viscoelastic characteristics to the liquid’s properties. Here, we experimentally study the coalescence of bubbles surrounded by polymer solutions. In contrast to drop coalescence, and in spite of the singular stretching of polymers, we find that the presence of the dissolved polymers does not at all affect the coalescence dynamics at early times. The polymer elasticity is found to slow down the flow only during the later stages of coalescence. These observations are interpreted using an asymptotic solution of the Oldroyd-B model, which predicts a strong stress singularity near the extremity of the neck. However, the polymer stress turns out to diverge only in the azimuthal direction, which can explain why elastic effects remain subdominant during the initial stages of coalescence.

• [13] Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology.
  C. Kopecz-Muller, V. Bertin, E. Raphael, J. D. McGraw, and T. Salez
  Proceedings of the Royal Society A 479 (2271), 20220832 (2023) PDF. [Show Abstract]

  Abstract: When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which complexifies further the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.

• [12] Nanoparticle Taylor dispersion near charged surfaces with an open boundary.
  A. Vilquin, V. Bertin, E. Raphael, D. S. Dean, T. Salez, and J. D. McGraw
  Physical Review Letters, 130 (3), 038201 (2023) PDF. [Show Abstract]

  Abstract: The dispersion of microscopic particles in shear flows is influenced both by advection and thermal motion. At the nanoscale, the interactions between such particles and their confining boundaries, along with their size, cannot be neglected. Here, using evanescent-wave microscopy with sub-micrometric observation zones, we study the transport of charged nanoparticles in linear shear flows, near a charged, planar wall on one side, and an open, particle-consuming boundary on the other side where the particle leaves the observation zone. By varying the concentration of electrolytes, we show how electrostatic interactions between particles and surface affect dispersion. In addition, an absorption-like condition at the open boundary induces an exponential decay of the particle number, which alters the transport efficiency. The combination of these two effects reduces the overall dispersion by an order of magnitude, as captured by our theoretical model. Our findings might have implications in biological contexts as well as in technological devices based on the transport of confined diffusive objects at small scales.

• [11] Enhanced Dip-Coating on a Soft Substrate.
  V. Bertin, J. H. Snoeijer, E. Raphaël and T. Salez
  Physical Review Fluids, 7(10) L102002 (2022) PDF. [Show Abstract]

  Abstract: A solid, withdrawn from a liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by animals, and is widely used for surface-coating purposes in industry. Motivated by the emerging interest in the mechanics of very soft materials, and in particular the resulting elastocapillary coupling, we develop a dip-coating model that accounts for the additional presence of a soft solid layer atop the rigid plate. The elastic response of this soft layer is described by a Winkler’s foundation. Using a combination of numerical, scaling and asymptotic- matching methods, we find a new softness-dependent power-law regime for the thickness of entrained liquid at small capillary number, which corresponds to a modified physics at play in the dynamic meniscus. The crossover between this regime and the classical dip-coating one occurs when the substrate’s deformation is comparable to the thickness of the entrained liquid film.

• [10] Contactless Rheology of Soft Gels over a Broad Frequency Range.
  Z. Zhang, M. Arshad, V. Bertin, S. Almohamad, E. Raphaël, T. Salez, and A. Maali
  Physical Review Applied, 17, 064045 (2022) PDF. [Show Abstract]

  Abstract: We report contactless measurements of the viscoelastic rheological properties of soft gels. The experiments are performed using a colloidal-probe Atomic Force Microscope (AFM) in a liquid environment and in dynamic mode. The mechanical response is measured as a function of the liquid gap thickness for different oscillation frequencies. Our measurements reveal an elastohydrodynamic (EHD) coupling between the flow induced by the probe oscillation and the viscoelastic deformation of the gels. The data are quantitatively described by a viscoelastic lubrication model. The frequency-dependent storage and loss moduli of the polydimethylsiloxane (PDMS) gels are extracted from fits of the data to the model and are in good agreement with the Chasset–Thirion law. Our results demonstrate that contactless colloidal-probe methods are powerful tools that can be used for probing soft interfaces finely over a wide range of frequencies.

• [9] Soft-lubrication interactions between a rigid sphere and an elastic wall.
  V. Bertin, Y. Amarouchene, E. Raphaël and T. Salez
  Journal of Fluid Mechanics 933 A23 (2022) 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
  Soft Matter 17, (27) 6646-6660 (2021) 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
  Physical Review Research 3, L032007 (2021) 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-diffusion coupling for nanoparticle ensembles.
  A. Vilquin V. Bertin, P. Soulard, G. Guyard, E. Raphael, F. Restagno, T. Salez, and J. D. McGraw
  Physical Review Fluids 6, 064201 (2021) 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 A13 (2021) 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, 184502 (2020) 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 1054502-(1-5) (2020) 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, 846-876 (2018) 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, 094001-(1-13) (2017) 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

• Detlef Lohse (POF, University of Twente)

• Javier Rodriguez Rodriguez (U. Carlos III Madrid)

• Jens Eggers (Bristol University)

• Uwe Thiele (U. Munster)

• Pierre Chantelot (Institut Langevin)

Past Collaborators

• Yacine Amarouchene, David Dean, Abdelhamid Maali (LOMA, University of Bordeaux)

• Olivier Dauchot, Mathilde Reyssat , Joshua McGraw, (Gulliver, ESPCI Paris)

• Herbert Hui (Cornell University)

• Frédéric Restagno (LPS, Paris-Sud University)

• Oliver Bäumchen (Max Planck Institute, Göttingen)

• Kari Dalnoki Veress (McMaster University)

(Past) 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