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**PhD thesis manuscript:** __ Fluctuation-induced electro-fluidic couplings at the solid-liquid interface__, under the direction of Lydéric Bocquet and Nikita Kavokine (2024)

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*Show abstract*This thesis explores couplings at the solid-liquid interface, arising from fluctuations in the microscopic degrees of freedom of both the solid and the liquid. We describe in which contexts these couplings dominate solid-liquid friction, then impacting hydrodynamics at the nanoscale, and how they can be used to engineer the friction coefficient. We show that the solid modes are impacted by a flow at their surface, driving them out of equilibrium. This modifies the friction, so that the study of liquid dynamics now requires describing the dynamics of the solid to which it is coupled. In particular, it becomes possible to engineer the friction by changing the electronic properties of the solid. Moreover, it also becomes possible to transfer a flow throughout a solid and thus to make flows forbidden by standard hydrodynamics. Finally, we prove that it is possible to convert the friction force into an electrical power, thus using these couplings to make a promising hydroelectric generator.

[7] Baptiste Coquinot, Lydéric Bocquet, Nikita Kavokine,

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*Hydroelectric energy conversion of waste flows through hydro-electronic drag***Submitted**(2024)

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*Show abstract*Hydraulic energy is a key component of the global energy mix, yet there exists no practical way of harvesting it at small scales, from flows at low Reynolds number. This has triggered the search for alternative hydroelectric conversion methodologies, leading to unconventional proposals based on droplet triboelectricity, water evaporation, osmotic energy or flow-induced ionic Coulomb drag. Yet, these approaches systematically rely on ions as intermediate charge carriers, limiting the achievable power density. Here, we predict that the kinetic energy of small-scale “waste” flows can be directly and efficiently converted into electricity thanks to the hydro-electronic drag effect, by which an ion-free liquid induces an electronic current in the solid wall along which it flows. This effect originates in the fluctuation-induced coupling between fluid motion and electron transport.

We develop a non-equilibrium thermodynamic formalism to assess the efficiency of such hydroelectric energy conversion, dubbed hydronic energy. We find that hydronic energy conversion is analogous to thermoelectricity, with the efficiency being controlled by a dimensionless figure of merit. However, in contrast to its thermoelectric analogue, this figure of merit combines independently tunable parameters of the solid and the liquid, and can thus significantly exceed unity. Our findings suggest new strategies for blue energy harvesting without electrochemistry, and for waste flow mitigation in membrane-based filtration processes.

[6] Mathieu Lizée, Baptiste Coquinot, Guilhem Mariette, Alessandro Siria, Lydéric Bocquet,

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*Anomalous friction of supercooled glycerol on mica***Submitted**(2024)

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*Show abstract*The fundamental understanding of friction of liquids on solid surfaces remains one of the key knowledge gaps in the transport of fluids. While the standard perspective emphasizes the role of wettability and commensurability, recent works have unveiled the crucial role of the solid’s internal excitations, whether electronic or phononic, on liquid-solid dissipation. In this work, we take advantage of the considerable variation of the molecular timescales of supercooled glycerol under mild change of temperature, in order to explore how friction depends on the liquid’s molecular dynamics. Using a dedicated tuning-fork-based AFM to measure the hydrodynamic slippage of glycerol on mica, we report a 2-order of magnitude increase of the slip length with decreasing temperature by only 30°C. However the solid-liquid friction coefficient is found to be a non monotonous function of the fluid molecular relaxation rate, the alpha frequency, at odd with an expected Arrhenius behavior. In particular, the linear increase of friction with the liquid molecular rate measured at high temperature cannot be accounted for by existing modelling. We show that this unconventional and non-arrhenian friction is consistent with a contribution of the solid’s phonons to the liquid-solid friction. This dynamical friction opens new perspectives to control hydrodynamic flows by properly engineering phononic and electronic excitation spectra in channel walls.

[5] Baptiste Coquinot, Maximilian Becker, Roland R. Netz, Lydéric Bocquet, Nikita Kavokine,

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*Collective modes and quantum effects in two-dimensional nanofluidic channels***Faraday Discussions**(2023)

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*Show abstract*Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 Å. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter in nanoscale confinement.

[4] Baptiste Coquinot, Lydéric Bocquet, Nikita Kavokine,

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*Quantum feedback at the solid-liquid interface: flow-induced electronic current and its negative contribution to friction***Physical Review X**(2023)

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*Show abstract*An electronic current driven through a conductor can induce a current in another conductor through the famous Coulomb drag effect. Similar phenomena have been reported at the interface between a moving fluid and a conductor, but their interpretation has remained elusive. Here, we develop a quantum-mechanical theory of the intertwined fluid and electronic flows, taking advantage of the non-equilibrium Keldysh framework. We predict that a globally neutral liquid can generate an electronic current in the solid wall along which it flows. This hydrodynamic Coulomb drag originates from both the Coulomb interactions between the liquid’s charge fluctuations and the solid’s charge carriers, and the liquid-electron interaction mediated by the solid’s phonons. We derive explicitly the Coulomb drag current in terms of the solid’s electronic and phononic properties, as well as the liquid’s dielectric response, a result which quantitatively agrees with recent experiments at the liquid-graphene interface. Furthermore, we show that the current generation counteracts momentum transfer from the liquid to the solid, leading to a reduction of the hydrodynamic friction coefficient through a quantum feedback mechanism. Our results provide a roadmap for controlling nanoscale liquid flows at the quantum level, and suggest strategies for designing materials with low hydrodynamic friction.

[3] Mathieu Lizée, Alice Marcotte, Baptiste Coquinot, Nikita Kavokine, Karen Sobnath, Clément Barraud, Ankit Bhardwaj, Boya Radha, Antoine Niguès, Lydéric Bocquet, Alessandro Siria,

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*Strong electronic winds blowing under liquid flows on carbon surfaces***Physical Review X**(2023)

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*Show abstract*The interface between a liquid and a solid is the location of plethora of intrincate mechanisms at the nanoscale, at the root of their specific emerging properties in natural processes or technological applications. However, while the structural properties and chemistry of interfaces have been intensively explored, the effect of the solid-state electronic transport at the fluid interface has been broadly overlooked up to now. It has been reported that water flowing against carbon-based nanomaterials, such as carbon nanotubes or graphene sheets , does induce electronic currents, but the mechanism at stake remains controversial. Here, we unveil the molecular mechanisms underlying the hydro-electronic couplings by investigating the electronic conversion under flow at the nanoscale. We use a tuning fork-Atomic Force Microscope (AFM) to deposit and displace a micrometric droplet of both ionic and non- ionic liquids on a multilayer graphene sample, while recording the electrical current across the carbon flake. We report measurements of an oscillation-induced current which is several orders of magnitude larger than previously reported for water on carbon , and further boosted by the presence of surface wrinkles on the carbon layer. Our results point to a peculiar momentum transfer mechanism between fluid molecules and charge carriers in the carbon walls mediated by phonon excitations in the solid. Our findings pave the way for active control of fluid transfer at the nanoscale by harnessing the complex interplay between collective excitations in the solid and the molecules in the fluid.

[2] Baptiste Coquinot, Pau Mir, Eva Miranda,

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*Singular cotangent models and complexity in fluids with dissipation***Physica D**(2023)

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*Show abstract*In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in b-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The first one models systems on manifolds with boundary and the twisted model represents Hamiltonian systems where the singularity of the system is in the fiber of the bundle. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We relate the complexity of the fluids in terms of the Reynolds number and the (non)-existence of cotangent lift dynamics. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. These models offer a Hamilton- ian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems.

[1] Baptiste Coquinot, Philip J. Morrison,

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*A General Metriplectic Framework With Application To Dissipative Extended Magnetohydrodynamics***Journal of Plasma Physics**(2020)

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*Show abstract*General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.