Dynamics of liquid nanojets

Nanowire melting modes during the solid-liquid phase transition: theory and molecular dynamics simulations

Molecular dynamics simulations have shown that after initial surface melting, nanowires can melt via two mechanisms: an interface front moves towards the wire centre; the growth of instabilities at the interface can cause the solid to pinch-off and breakup. By perturbing a capillary fluctuation model describing the interface kinetics, we show when each mechanism is preferred and compare the results to molecular dynamics simulation. A Plateau-Rayleigh-type of instability is found and suggests longer nanowires will melt via an instability mechanism, whereas in shorter nanowires the melting front will move closer to the centre before the solid pinch-off can initiate. Simulations support this theory; preferred modes that destabilise the interface are proportional to the wire length, with longer nanowires preferring to pinch-off and melt; shorter wires have a more stable interface close to their melting temperature, and prefer to melt via an interface front that moves towards the wire centre.

Studying the Influences of Temperature to the Liquid Ejection and Nanodroplet Formation

The influences of temperature parameter for various values of 310[Formula: see text]K, 315[Formula: see text]K and 333[Formula: see text]K (Kelvin (K)) to liquid ejection through nozzle under the same magnitudes of nozzle diameter of 27.5 Angstrom (Å) and pressing force of [Formula: see text] Newton (N) were performed in this study by adopting the molecular dynamics simulation method. For the temperature values, almost all molecules were ejected out of the container through the nozzle and built up the liquid nanojets on the nozzle plate’s surface. Only the liquid jets separate out from the nozzle to form the nanodroplets for the temperature values of greater than or equal to 315[Formula: see text]K. Otherwise, the liquid nanodroplets were not formed for the case of temperature magnitude of 310[Formula: see text]K. Moreover, the witnesses are also provided in this research to explain for the separation of the nanojets from the nozzle plate’s surface to form the liquid nanodroplet.

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ^{*} depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ^{*} scales weakly with system size, i.e., the dependence of ℓ^{*} on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim_{L→∞}(ℓ^{*}/L)=0. In particular, for (2+1)-dimensional interfaces ℓ^{*} is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. This weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

Nanoscale thin-film flows with thermal fluctuations and slip

The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long-wave approximation to fluctuating hydrodynamics. Analytically derived capillary spectra, which evolve in time, are found from the new SLEs and compared to molecular dynamics simulations. It is shown that thermal fluctuations lead to the generation and growth of surface waves, and slip accelerates this growth. SLEs developed here provide useful tools to study nanoscale film dewetting, nanofiber coating, and liquid transport using nanofibers.

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Dripping, jetting and tip streaming

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

Rupture process of liquid bridges: The effects of thermal fluctuations

Rupture of a liquid bridge is a complex dynamic process, which has attracted much attention over several decades. We numerically investigated the effects of the thermal fluctuations on the rupture process of liquid bridges by using a particle-based method know as many-body dissipative particle dynamics. After providing a comparison of growth rate with the classical linear stability theory, the complete process of thinning liquid bridges is captured. The transitions among the inertial regime (I), the viscous regime (V), and the viscous-inertial regime (VI) with different liquid properties are found in agreement with previous work. A detailed description of the thermal fluctuation regime (TF) and another regime, named the breakup regime, are proposed in the present study. The full trajectories of thinning liquid bridges are summarized as I→V→VI→TF→ breakup for low-Oh liquids and V→I→ Intermediate →V→VI→TF→ breakup for high-Oh liquids, respectively. Moreover, the effects of the thermal fluctuations on the formation of satellite drops are also investigated. The distance between the peaks of axial velocity is believed to play an important role in forming satellite drops. The strong thermal fluctuations smooth the distribution of axial velocity and change the liquid bridge shape into a double cone without generating satellite drops for low-Oh liquids, while for high-Oh liquids, this distance is extended and a large satellite drop is formed after the breakup of the liquid filament occurs on both ends, which might be due to strong thermal fluctuations. This work can provide insights on the rupture mechanism of liquid bridges and be helpful for designing superfine nanoprinting.

Diffusion-Dominated Pinch-Off of Ultralow Surface Tension Fluids

We study the breakup of a liquid thread inside another liquid at different surface tensions. In general, the pinch-off of a liquid thread is governed by the dynamics of fluid flow. However, when the interfacial tension is ultralow (2-3 orders lower than normal liquids), we find that the pinch-off dynamics can be governed by bulk diffusion. By studying the velocity and the profile of the pinch-off, we explain why the diffusion-dominated pinch-off takes over the conventional breakup at ultralow surface tensions.

Molecular simulation of thin liquid films: Thermal fluctuations and instability

The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the dynamics of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) can massively amplify the instability, (b) cause the fluctuation wavelength that is dominant to evolve in time (a single fastest-growing mode does not exist), and (c) decrease the critical wavelength so that classically stable films can be ruptured.

Droplet Coalescence is Initiated by Thermal Motion

The classical notion of the coalescence of two droplets of the same radius R is that surface tension drives an initially singular flow. In this Letter we show, using molecular dynamics simulations of coalescing water nanodroplets, that after single or multiple bridges form due to the presence of thermal capillary waves, the bridge growth commences in a thermal regime. Here, the bridges expand linearly in time much faster than the viscous-capillary speed due to collective molecular jumps near the bridge fronts. Transition to the classical hydrodynamic regime only occurs once the bridge radius exceeds a thermal length scale l_{T}∼sqrt[R].

Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261-1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.

Effects of thermal fluctuations in the fragmentation of a nanoligament

We study the effects of thermally induced capillary waves in the fragmentation of a liquid ligament into multiple nanodroplets. Our numerical implementation is based on a fluctuating lattice Boltzmann (LB) model for nonideal multicomponent fluids, including nonequilibrium stochastic fluxes mimicking the effects of molecular forces at the nanoscales. We quantitatively analyze the statistical distribution of the breakup times and the droplet volumes after the fragmentation process at changing the two relevant length scales of the problem, i.e., the thermal length scale and the ligament size. The robustness of the observed findings is also corroborated by quantitative comparisons with the predictions of sharp interface hydrodynamics. Beyond the practical importance of our findings for nanofluidic engineering devices, our study also explores a novel application of LB in the realm of nanofluidic phenomena.

Effect of axial electric field on the Rayleigh instability at small length scales

The effect of an electric field along the longitudinal axis of a nanoscale liquid thread is studied to understand the mechanism of breakup. The Rayleigh instability (commonly known as the Plateau-Rayleigh instability) of a nanosized liquid water thread is investigated by using molecular dynamics simulations. The breakup mechanism of the liquid nanothread is studied by analyzing the temporal evolution of the thread radius. The influence of the temperature of the liquid nanothread and the electric-field strength on the stability and breakup is the major focus of the study. The results show that the axial electric field has a stabilizing effect even at nanoscale. The results from the simulations are in good agreement with the solutions obtained from the dispersion relation developed by Hohman et al. for the liquid thread. The critical electric-field strength necessary to avoid the breakup of the liquid thread is calculated and other effects such as the splaying and whipping instability are also discussed.

Application of the dissipative particle dynamics method to the instability problem of a liquid thread

We investigate the application of the dissipative particle dynamics method to the instability problem of a long liquid thread surrounded by another fluid. The dispersion curves obtained from simulations are compared with classic theoretical predictions. The results from standard dissipative particle dynamics (DPD) simulations at first have a tendency of gradually approaching to Tomotika's Stokes flow prediction when the Reynolds number is decreased. But they then abnormally deviate again when the viscosity is very large. The same phenomenon is also confirmed in droplet retraction simulations when also compared with theoretical Stokes flow results. On the other hand, when a hard-core DPD model is used, with the decrease of the Reynolds number the simulation results did finally approach Tomotika's predictions when Re≈0.1. A combined presentation of the hard-core DPD results and the standard DPD results, excluding the abnormal ones, demonstrates that they are approximately on a continuum when labeled with Reynolds number. These results suggest that the standard DPD method is a suitable method for investigation of the instability problem of immersed liquid thread in the inertioviscous regime (0.1<Re<10), which is relevant for microfluidics applications but there is currently no theory. It cannot reach the Re≈0.1 regime because of some irregular properties of highly viscous DPD fluid, while the hard-core DPD is suitable to overcome this inferiority with standard DPD.

Pinch-off of microfluidic droplets with oscillatory velocity of inner phase flow

When one liquid is introduced into another immiscible one, it ultimately fragments due to hydrodynamic instability. In contrast to neck pinch-off without external actuation, the viscous two-fluid system subjected to an oscillatory flow demonstrates higher efficiency in breaking fluid threads. However, the underlying dynamics of this process is less well understood. Here we show that the neck-thinning rate is accelerated by the amplitude of oscillation. By simply evaluating the momentum transfer from external actuation, we derive a dimensionless pre-factor to quantify the accelerated pinch-off. Our data ascribes the acceleration to the non-negligible inner fluid inertia, which neutralizes the inner phase viscous stress that retards the pinch-off. Moreover, we characterize an equivalent neck-thinning behavior between an actuated system and its unactuated counterpart with decreased viscosity ratio. Finally, we demonstrate that oscillation is capable of modulating satellite droplet formation by shifting the pinch-off location. Our study would be useful for manipulating fluids at microscale by external forcing.

Fully nonlinear dynamics of stochastic thin-film dewetting

The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.

Universal Scaling Law for the Collapse of Viscous Nanopores

Below a threshold size, a small pore nucleated in a fluid sheet will contract to minimize the surface energy. Such behavior plays a key role in nature and technology, from nanopores in biological membranes to nanopores in sensors for rapid DNA and RNA sequencing. Here we show that nanopores nucleated in viscous fluid sheets collapse following a universal scaling law for the pore radius. High-fidelity numerical simulations reveal that the scaling is largely independent of the initial conditions, including the size, shape, and thickness of the original nanopore. Results further show that the scaling law yields a constant speed of collapse as observed in recent experiments. Nanopores in fluid sheets of moderate viscosity also attain this constant terminal speed provided that they are sufficiently close to the singularity.

Mesoscopic simulation of a thinning liquid bridge using the dissipative particle dynamics method

In this research, the dissipative particle dynamics method was used to investigate the problem of thinning and breakup in a liquid bridge. It was found that both the inertial-force-dominated thinning process and the thermal-fluctuation-dominated thinning process can be reproduced with the dissipative particle dynamics (DPD) method by varying the simulation parameters. A highly suspect viscous thinning regime was also found, but the conclusion is not irrefutable because of the complication of the shear viscosity of DPD fluid. We show in this article that the DPD method can serve as a good candidate to elucidate crossover problem in liquid bridge thinning from being hydrodynamics dominated to being thermal fluctuation dominated.

Superconfinement tailors fluid flow at microscales

Understanding fluid dynamics under extreme confinement, where device and intrinsic fluid length scales become comparable, is essential to successfully develop the coming generations of fluidic devices. Here we report measurements of advancing fluid fronts in such a regime, which we dub superconfinement. We find that the strong coupling between contact-line friction and geometric confinement gives rise to a new stability regime where the maximum speed for a stable moving front exhibits a distinctive response to changes in the bounding geometry. Unstable fronts develop into drop-emitting jets controlled by thermal fluctuations. Numerical simulations reveal that the dynamics in superconfined systems is dominated by interfacial forces. Henceforth, we present a theory that quantifies our experiments in terms of the relevant interfacial length scale, which in our system is the intrinsic contact-line slip length. Our findings show that length-scale overlap can be used as a new fluid-control mechanism in strongly confined systems.

An understanding of how fluid–solid interactions affect flow dynamics is essential for microfluidics design. Here the authors show how fluids in linear channels can be controlled by the degree of confinement when the contact-line slip length is comparable to the channel size.

Inkjet print microchannels based on a liquid template

A simple method to fabricate microchannels is demonstrated based on an inkjet printing liquid template. The morphology of the liquid template can be well controlled by using ink with viscosity sensitive to temperature. The as-prepared Y-shape microchannel is used as a microfluidic reactor for an acylation fluorigenic reaction in a matrix of polydimethylsiloxane (PDMS). Arbitrary modification of the microchannels could be easily realized synchronously with the formation of the microchannels. By grafting polyethylene glycol (PEG) onto the internal surface, an anti-biosorption microchannel is obtained. The facile method will be significant for the fabrication of a microfluidic chip with functional modifications.

Rayleigh instability at small length scales

The Rayleigh instability (also called the Plateau-Rayleigh instability) of a nanosized liquid propane thread is investigated using molecular dynamics (MD). The validity of classical predictions at small length scales is verified by comparing the temporal evolution of liquid thread simulated by MD against classical predictions. Previous works have shown that thermal fluctuations become dominant at small length scales. The role and influence of the stochastic nature of thermal fluctuations in determining the instability at small length scale is also investigated. Thermal fluctuations are seen to dominate and accelerate the breakup process only during the last stages of breakup. The simulations also reveal that the breakup profile of nanoscale threads undergo modification due to reorganization of molecules by the evaporation-condensation process.

Modeling multiphase flow using fluctuating hydrodynamics

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single-component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several nonequilibrium examples to illustrate the capability of the algorithm to model multiphase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.

Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit

We analyze both theoretically and experimentally the dynamical behavior of an isothermal axisymmetric liquid bridge close to the minimum-volume stability limit. First, the nature of this stability limit is investigated experimentally by determining the liquid bridge response to a mass force pulse for volumes just above that limit. In our experiments, the liquid bridge breakup takes place only when the critical volume is surpassed and is never triggered by the mass force pulse. Second, the growth of the small-amplitude perturbation mode initiating the liquid bridge breakage is measured experimentally and calculated from the linearized Navier-Stokes equations. The results of the linear stability analysis allow one to explain why liquid bridges with volumes just above the stability limit are so robust. Finally, the nonlinear process leading to the liquid bridge breakup is described from both experimental data and the solution of the full Navier-Stokes equations. Special attention is paid to the free-surface pinchoff. The results show that the flow becomes universal (independent of both the initial and boundary conditions) sufficiently close to that singularity and suggest that the transition from the inviscid to the viscous regime is about to take place in the final stage of both the experiments and numerical simulations.

Hierarchical nanoparticle ensembles synthesized by liquid phase directed self-assembly

A liquid metal filament supported on a dielectric substrate was directed to fragment into an ordered, mesoscale particle ensemble. Imposing an undulated surface perturbation on the filament forced the development of a single unstable mode from the otherwise disperse, multimodal Rayleigh-Plateau instability. The imposed mode paved the way for a hierarchical spatial fragmentation of the filament into particles, previously seen only at much larger scales. Ultimately, nanoparticle radius control is demonstrated using a micrometer scale switch.

Fluctuating hydrodynamics of multispecies nonreactive mixtures

In this paper we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.

Nonstationary magnetosonic wave dynamics in plasmas exhibiting collapse

In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.

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.

Break-up dynamics of fluctuating liquid threads

The thinning dynamics of a liquid neck before break-up, as may happen when a drop detaches from a faucet or a capillary, follows different rules and dynamic scaling laws depending on the importance of inertia, viscous stresses, or capillary forces. If now the thinning neck reaches dimensions comparable to the thermally excited interfacial fluctuations, as for nanojet break-up or the fragmentation of thermally annealed nanowires, these fluctuations should play a dominant role according to recent theory and observations. Using near-critical interfaces, we here fully characterize the universal dynamics of this thermal fluctuation-dominated regime and demonstrate that the cross-over from the classical two-fluid pinch-off scenario of a liquid thread to the fluctuation-dominated regime occurs at a well-defined neck radius proportional to the thermal length scale. Investigating satellite drop formation, we also show that at the level of the cross-over between these two regimes it is more probable to produce monodisperse droplets because fluctuation-dominated pinch-off may allow the unique situation where satellite drop formation can be inhibited. Nonetheless, the interplay between the evolution of the neck profiles from the classical to the fluctuation-dominated regime and the satellites' production remains to be clarified.

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.

Initial spreading of low-viscosity drops on partially wetting surfaces

Liquid drops start spreading directly after coming into contact with a partially wetting substrate. Although this phenomenon involves a three-phase contact line, the spreading motion is very fast. We study the initial spreading dynamics of low-viscosity drops using two complementary methods: molecular dynamics simulations and high-speed imaging. We access previously unexplored length and time scales and provide a detailed picture on how the initial contact between the liquid drop and the solid is established. Both methods unambiguously point toward a spreading regime that is independent of wettability, with the contact radius growing as the square root of time.

Lattice-Boltzmann-Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

Capillary waves of compressible fluids

The interplay of thermal noise and molecular forces is responsible for surprising features of liquids on sub-micrometer lengths-in particular at interfaces. Not only does the surface tension depend on the size of an applied distortion and nanoscopic thin liquid films dewet faster than would be expected from hydrodynamics, but also the dispersion relation of capillary waves differ at the nanoscale from the familiar macroscopic behavior. Starting with the stochastic Navier-Stokes equation we study the coupling of capillary waves to acoustic surface waves which is possible in compressible fluids. We find propagating 'acoustic-capillary waves' at nanometer wavelengths where in incompressible fluids capillary waves are overdamped.

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Pattern formation and interface pinch-off in rotating Hele-Shaw flows: a phase-field approach

Viscous fingering dynamics driven by centrifugal forcing is studied for arbitrary viscosity contrast. Theoretical methods, including exact solutions, and numerics based on a phase-field approach are used. Both confirm that pinch-off singularities in patterns originated from the centrifugally driven instability may occur spontaneously and be inherent to the two-dimensional Hele-Shaw dynamics. They are systematically more frequent for lower viscosity contrasts consistently with experimental evidence. The analytical insights provide an interpretation of this fact in terms of the asymptotic matching of the different regions of the fingering patterns. The phase-field numerical scheme is shown to be particularly adequate to elucidate the existence of finite-time singularities through the dependence of the singularity time on the interface thickness, in particular for varying viscosity contrast.

Pinch-off singularities in rotating Hele-Shaw flows at high viscosity contrast

We study the evolution of a family of dumbbell-shaped liquid patches surrounded by air inside a rotating Hele-Shaw cell with lubrication methods and numerical simulations. Depending on initial conditions, the dumbbell either stretches to infinity, pinches off at the neck to form a droplet, or collects into a circular drop at the center of rotation. Whether or not pinch-off occurs results from a subtle interplay between centrifugal and capillary forces. In particular, rotation may delay or even prevent pinch-off from occurring owing to stretching and smoothing of the fluid neck. However, frequently rotation may have the opposite effect leading to pinch-off where the relaxation toward a circular drop would be observed in an ordinary Hele-Shaw cell.