Exact solutions for viscous Marangoni spreading.

When surface-active molecules are released at a liquid interface, their spreading dynamics is controlled by Marangoni flows. Though such Marangoni spreading was investigated in different limits, exact solutions remain very few. Here we consider the spreading of an insoluble surfactant along the interface of a deep fluid layer. For two-dimensional Stokes flows, it was recently shown that the nonlinear transport problem can be exactly mapped to a complex Burgers equation [D. Crowdy, SIAM J. Appl. Math. 81, 2526 (2021)]SMJMAP0036-139910.1137/21M1400316. We first present a very simple derivation of this equation. We then provide fully explicit solutions and find that varying the initial surfactant distribution-pulse, hole, or periodic-results in distinct spreading behaviors. By obtaining the fundamental solution, we also discuss the influence of surface diffusion. We identify situations where spreading can be described as an effective diffusion process but observe that this approximation is not generally valid. Finally, the case of a three-dimensional flow with axial symmetry is briefly considered. Our findings should provide reference solutions for Marangoni spreading that may be tested experimentally with fluorescent or photoswitchable surfactants.

Self-propulsion of symmetric chemically active particles: Point-source model and experiments on camphor disks.

Solid undeformable particles surrounded by a liquid medium or interface may propel themselves by altering their local environment. Such nonmechanical swimming is at work in autophoretic swimmers, whose self-generated field gradient induces a slip velocity on their surface, and in interfacial swimmers, which exploit unbalance in surface tension. In both classes of systems, swimmers with intrinsic asymmetry have received the most attention but self-propulsion is also possible for particles that are perfectly isotropic. The underlying symmetry-breaking instability has been established theoretically for autophoretic systems but has yet to be observed experimentally for solid particles. For interfacial swimmers, several experimental works point to such a mechanism, but its understanding has remained incomplete. The goal of this work is to fill this gap. Building on an earlier proposal, we first develop a point-source model that may be applied generically to interfacial or phoretic swimmers. Using this approximate but unifying picture, we show that they operate in very different regimes and obtain analytical predictions for the propulsion velocity and its dependence on swimmer size and asymmetry. Next, we present experiments on interfacial camphor disks showing that they indeed self-propel in an advection-dominated regime where intrinsic asymmetry is irrelevant and that the swimming velocity increases sublinearly with size. Finally, we discuss the merits and limitations of the point-source model in light of the experiments and point out its broader relevance.

Generalized run-and-turn motions: From bacteria to Lévy walks.

Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.

[Optimal permeability of aquaporins: a question of shape?]. / Perméabilité optimale des aquaporines - Une histoire de forme ?

Aquaporins are transmembrane proteins, ubiquitous in the human body. Inserted into the cell membranes, they play an important role in filtration, absorption and secretion of fluids. However, the excellent compromise between selectivity and permeability of aquaporins remains elusive. In this review, we focus on the hourglass shape of aquaporins, and we investigate its influence on water permeability, using numerical calculations and a simple theoretical model. We show that there is an optimum opening angle that maximizes the hydrodynamic permeability, and whose value is close to the angles observed in aquaporins.

Anomalous ζ potential in foam films.

Electrokinetic effects offer a method of choice to control flows in micro- and nanofluidic systems. While a rather clear picture of these phenomena exists now for the liquid-solid interfaces, the case of liquid-air interfaces remains largely unexplored. Here, we investigate at the molecular level electrokinetic transport in a liquid film covered with ionic surfactants. We find that the ζ potential, quantifying the amplitude of electrokinetic effects, depends on the surfactant coverage in an unexpected way. First, it increases upon lowering surfactant coverage from saturation. Second, it does not vanish in the limit of low coverage but instead approaches a finite value. This behavior is rationalized by taking into account the key role of interfacial hydrodynamics, together with an ion-binding mechanism. We point out implications of these results for the strongly debated measurements of the ζ potential at free interfaces and for electrokinetic transport in liquid foams.

Optimizing water permeability through the hourglass shape of aquaporins.

The ubiquitous aquaporin channels are able to conduct water across cell membranes, combining the seemingly antagonist functions of a very high selectivity with a remarkable permeability. Whereas molecular details are obvious keys to perform these tasks, the overall efficiency of transport in such nanopores is also strongly limited by viscous dissipation arising at the connection between the nanoconstriction and the nearby bulk reservoirs. In this contribution, we focus on these so-called entrance effects and specifically examine whether the characteristic hourglass shape of aquaporins may arise from a geometrical optimum for such hydrodynamic dissipation. Using a combination of finite-element calculations and analytical modeling, we show that conical entrances with suitable opening angle can indeed provide a large increase of the overall channel permeability. Moreover, the optimal opening angles that maximize the permeability are found to compare well with the angles measured in a large variety of aquaporins. This suggests that the hourglass shape of aquaporins could be the result of a natural selection process toward optimal hydrodynamic transport. Finally, in a biomimetic perspective, these results provide guidelines to design artificial nanopores with optimal performances.

Thermal fluctuations of hydrodynamic flows in nanochannels.

Flows at the nanoscale are subject to thermal fluctuations. In this work, we explore the consequences for a fluid confined within a channel of nanometric size. First, the phenomenon is illustrated on the basis of molecular dynamics simulations. The center of mass of the confined fluid is shown to perform a stochastic, non-Markovian motion, whose diffusion coefficient satisfies Einstein's relation, and which can be further characterized by the fluctuation relation. Next, we develop an analytical description of the thermally induced fluid motion. We compute the time- and space-dependent velocity correlation function, and characterize its dependence on the nanopore shape, size, and boundary slip at the surface. The experimental implications for mass and charge transports are discussed for two situations. For a particle confined within the nanopore, we show that the fluid fluctuating motion results in an enhanced diffusion. The second situation involves a charged nanopore in which fluid motion within the double layer induces a fluctuating electric current. We compute the corresponding contribution to the current power spectrum.

Thermal fluctuations in nanofluidic transport.

We explore the impact of thermal fluctuations on nanofluidic transport. We develop a generic description of the stochastic motion of a fluid confined in a nanopore, on the basis of the fluctuating hydrodynamics framework. The center of mass of the confined fluid is shown to perform a non-markovian random walk, whose diffusion coefficient depends on the nanopore geometrical characteristics and boundary slip at its surface. We discuss the implications of this brownian-like motion of hydrodynamic degrees of freedom in two different contexts. First, we show that hydrodynamic fluctuations can lead to a strongly enhanced diffusion of particles confined in a nanopore. Second, we extend our results to account for the hydrodynamic contribution to electrical noise in charged nanopores.

Graphoepitaxial assembly of asymmetric ternary blends of block copolymers and homopolymers.

Ternary blends of cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers and polystyrene and poly(methyl methacrylate) homopolymers were assembled in trench features of constant width. Increasing the fraction of homopolymer in the blend increased the spacing and size of block copolymer domains, which were oriented perpendicular to the substrate to form a hexagonal lattice within the trench. The number of rows of cylinders within the trench was controlled by the blend composition. Depending on the domain size and spacing, the hexagonal lattice was stretched or compressed perpendicular to the trench walls but not perturbed parallel to the walls, indicating a decoupling of the perturbation in the perpendicular and parallel directions. The row spacing was uniform across the trench as a function of position from the trench wall. The results are compared with an analytical model and with Monte Carlo simulations.

Simulations of theoretically informed coarse grain models of polymeric systems.

Simulations of theoretically informed coarse grain models, where the interaction energy is given by a functional of the local density, are discussed in the context of polymeric melts. Two different implementations are presented by addressing two examples. The first relies on a grid-based representation of non-bonded interactions and focuses on the concept of density multiplication in block copolymer lithography. Monte Carlo simulations are used in a high-throughput manner to explore the parameter space, and to identify morphologies amenable to lithographic fabrication. In the second example, which focuses on the order-disorder transition of block copolymers, the constraints imposed by a grid are removed, thereby enabling simulations in arbitrary ensembles and direct calculation of local stresses and free energies.

Theoretically informed coarse grain simulations of polymeric systems.

A Monte Carlo formalism for the study of polymeric melts is described. The model is particle-based, but the interaction is derived from a local density functional that appears in the field-based model. The method enables Monte Carlo simulations in the nVT, nPT, semigrandcanonical and Gibbs ensembles, and direct calculation of free energies. The approach is illustrated in the context of two examples. In the first, we consider the phase separation of a binary homopolymer blend and present results for the phase diagram and the critical point. In the second, we address the microphase separation of a symmetric diblock copolymer, examine the distribution of local stresses in lamellae, and determine the order-disorder transition temperature.

Monte carlo simulation of coarse grain polymeric systems.

We introduce a particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models. The method enables Monte Carlo simulations in arbitrary ensembles and direct calculation of free energies. We present results for the phase diagram and the critical point of a binary homopolymer blend. For a symmetric diblock copolymer, we compute the distribution of local stress in lamellae and locate the order-disorder transition.

Density multiplication and improved lithography by directed block copolymer assembly.

Self-assembling materials spontaneously form structures at length scales of interest in nanotechnology. In the particular case of block copolymers, the thermodynamic driving forces for self-assembly are small, and low-energy defects can get easily trapped. We directed the assembly of defect-free arrays of isolated block copolymer domains at densities up to 1 terabit per square inch on chemically patterned surfaces. In comparing the assembled structures to the chemical pattern, the density is increased by a factor of four, the size is reduced by a factor of two, and the dimensional uniformity is vastly improved.

Hierarchical assembly of nanoparticle superstructures from block copolymer-nanoparticle composites.

We investigate the assembly of block copolymer-nanoparticle composite films on chemically nanopatterned substrates and present fully three-dimensional simulations of a coarse grain model for these hybrid systems. The location and distribution of nanoparticles within the ordered block copolymer domains depends on the thermodynamic state of the composite in equilibrium with the surface. Hierarchical assembly of nanoparticles enables applications in which the ability to precisely control their locations within periodic and nonregular geometry patterns and arrays is required.