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.

Spreading dynamics of reactive surfactants driven by Marangoni convection.

We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport equations is derived in the regime of large Schmidt number, where viscous effects are dominant. We demonstrate that the variance of the surfactant distribution increases linearly with time, providing an unambiguous definition for the enhanced diffusion coefficient observed in the experiments. The model thus presents new insight regarding the actuation of camphor grains at the water-air interface.

Erratum: Polarization of active Janus particles [Phys. Rev. E 89, 050303(R) (2014)].

This corrects the article DOI: 10.1103/PhysRevE.89.050303.

Light-Driven Transport of a Liquid Marble with and against Surface Flows.

Liquid marbles, that is, liquid drops coated by a hydrophobic powder, do not wet any solid or liquid substrate, making their transport and manipulation both highly desirable and challenging. Herein, we describe the light-driven transport of floating liquid marbles and emphasize a surprising motion behavior. Liquid marbles are deposited on a water solution containing photosensitive surfactants. Irradiation of the solution generates photoreversible Marangoni flows that transport the liquid marbles toward UV light and away from blue light when the thickness of the liquid substrate is large enough (Marangoni regime). Below a critical thickness, the liquid marbles move in the opposite direction to that of the surface flow at a speed increasing with decreasing liquid thickness (anti-Marangoni). We demonstrate that the anti-Marangoni motion is driven by the free surface deformation, which propels the non-wetting marble against the surface flow. We call this behavior "slide effect".

Polarization of active Janus particles.

We theoretically study the motion of surface-active Janus particles, driven by an effective slip velocity due to a nonuniform temperature or concentration field ψ. With parameters realized in thermal traps, we find that the torque exerted by the gradient ∇ψ inhibits rotational diffusion and favors alignment of the particle axes. In a swarm of active particles, this polarization adds a novel term to the drift velocity and modifies the collective behavior. Self-polarization in a nonuniform laser beam could be used for guiding hot particles along a given trajectory.

Flow pattern in the vicinity of self-propelling hot Janus particles.

We study the temperature field and the resulting flow pattern in the vicinity of a heated metal-capped Janus particle. If its thickness exceeds about 10 nm, the cap forms an isotherm and the flow pattern comprises a quadrupolar term that decays with the square of the inverse distance ~r(-2). For much thinner caps the velocity varies as ~r(-3). These findings could be relevant for collective effects in dense suspensions and for the circular tracer motion observed recently in the vicinity of a tethered Janus particle.

Nonequilibrium fluctuations of an interface under shear.

The steady-state properties of an interface in a stationary Couette flow are addressed within the framework of fluctuating hydrodynamics. Our study reveals that thermal fluctuations are driven out of equilibrium by an effective shear rate that differs from the applied one. In agreement with experiments, we find that the mean-square displacement of the interface is reduced by the flow. We also show that nonequilibrium fluctuations present a certain degree of universality in the sense that all features of the fluids can be factorized into a single control parameter. Finally, the results are discussed in the light of recent experimental and numerical studies.

Cryo-electron tomography of nanoparticle transmigration into liposome.

Nanoparticle transport across cell membrane plays a crucial role in the development of drug delivery systems as well as in the toxicity response induced by nanoparticles. As hydrophilic nanoparticles interact with lipid membranes and are able to induce membrane perturbations, hypothetic mechanisms based on membrane curvature or hole formation have been proposed for activating their transmigration. We report on the transport of hydrophilic silica nanoparticles into large unilamellar neutral DOPC liposomes via an internalization process. The strong adhesive interactions of lipid membrane onto the silica nanoparticle triggered liposome deformation until the formation of a curved neck. Then the rupture of this membrane neck led to the complete engulfment of the nanoparticle. Using cryo-electron tomography we determined 3D architectures of intermediate steps of this process unveiling internalized silica nanoparticles surrounded by a supported lipid bilayer. This engulfing process was achieved for a large range of particle size (from 30 to 200 nm in diameter). These original data provide interesting highlights for nanoparticle transmigration and could be applied to biotechnology development.

Thermophoresis of charged colloidal particles.

Thermally induced particle flow in a charged colloidal suspension is studied in a fluid-mechanical approach. The force density acting on the charged boundary layer is derived in detail. From Stokes' equation with no-slip boundary conditions at the particle surface, we obtain the particle drift velocity and the thermophoretic transport coefficients. The results are discussed in view of previous work and available experimental data.

Hindered mobility of a particle near a soft interface.

The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled to the instantaneous conformation of the interface. Using a two-dimensional Fourier transform technique, we are able to account for the multiple backflows scattered from the interface. The correction to the mobility tensor is then obtained from the matrix elements of the relevant Green's function. Our perturbative analysis allows us to express the explicit position and frequency dependence of the mobility for small particles. We recover in the steady limit the result for a sphere near a perfectly flat interface. At intermediate time scales, the mobility exhibits an imaginary part which is a signature of the elastic response of the interface. In the short time limit, we find that the perpendicular mobility may, under some circumstances, become lower than the bulk value. All the results can be explained using the definition of the relaxation time of the soft interface.

Thermodiffusion of charged micelles.

We study diffusion of charged nanoparticles in a temperature gradient and derive the corresponding Ludwig-Soret transport coefficient. Charge effects are found to enhance thermodiffusion by up to 2 orders of magnitude. We show that the inverse Soret coefficient 1/S(T) is a linear function of the colloid density n; the proportionality factor, or second virial coefficient, varies algebraically with inverse salinity, n0(-alpha); the precise value of the exponent alpha depends on the ratio of particle size and Debye length. Our findings compare favorably with experimental observations and provide, without adjustable parameters, a good fit to the data on 3-nm sodium dodecylsulfate micelles.

The nuclear pore complex mystery and anomalous diffusion in reversible gels.

The exchange of macromolecules between the cytoplasm and the nucleus of eukaryotic cells takes place through the nuclear pore complex (NPC), which contains a selective permeability barrier. Experiments on the physical properties of this barrier appear to be in conflict with current physical understanding of the rheology of reversible gels. This paper proposes that the NPC gel is anomalous and characterized by connectivity fluctuations. It develops a simplified model to demonstrate the possibility of enhanced diffusion constants of macromolecules trapped in such a gel.