Osmotic and diffusio-osmotic flow generation at high solute concentration. II. Molecular dynamics simulations

Non-equilibrium molecular dynamics of steady-state fluid transport through a 2D membrane driven by a concentration gradient

We use a novel non-equilibrium algorithm to simulate steady-state fluid transport through a two-dimensional (2D) membrane due to a concentration gradient by molecular dynamics (MD) for the first time. We confirm that, as required by the Onsager reciprocal relations in the linear-response regime, the solution flux obtained using this algorithm agrees with the excess solute flux obtained from an established non-equilibrium MD algorithm for pressure-driven flow. In addition, we show that the concentration-gradient-driven solution flux in this regime is quantified far more efficiently by explicitly applying a transmembrane concentration difference using our algorithm than by applying Onsager reciprocity to pressure-driven flow. The simulated fluid fluxes are captured with reasonable quantitative accuracy by our previously derived continuum theory of concentration-gradient-driven fluid transport through a 2D membrane [D. J. Rankin, L. Bocquet, and D. M. Huang, J. Chem. Phys. 151, 044705 (2019)] for a wide range of solution and membrane parameters, even though the simulated pore sizes are only several times the size of the fluid particles. The simulations deviate from the theory for strong solute-membrane interactions relative to thermal energy, for which the theoretical approximations breakdown. Our findings will be beneficial for a molecular-level understanding of fluid transport driven by concentration gradients through membranes made from 2D materials, which have diverse applications in energy harvesting, molecular separations, and biosensing.

Non-equilibrium ordering of liquid crystalline (LC) films driven by external gradients in surfactant concentration

HYPOTHESIS

Gradients in the concentration of amphiphiles play an important role in many non-equilibrium processes involving complex fluids. Here we explore if non-equilibrium interfacial behaviors of thermotropic (oily) liquid crystals (LCs) can amplify microscopic gradients in surfactant concentration into macroscopic optical signals.

EXPERIMENTS

We use a milli-fluidic system to generate gradients in aqueous sodium dodecyl sulfate (SDS) concentration and optically quantify the dynamic ordering of micrometer-thick nematic LC films that contact the gradients.

FINDINGS

We find that the reordering of the LCs is dominated by interfacial shearing by Marangoni flows, thus providing simple methods for rapid mapping of interfacial velocities from a single optical image and investigating the effects of confinement of surfactant-driven interfacial flows. Additionally, we establish that surface advection and surfactant desorption are the two key processes that regulate the interfacial flows, revealing that the dynamic response of the LC can provide rapid and potentially high throughput approaches to measurement of non-equilibrium interfacial properties of amphiphiles. We also observe flow-induced assemblies of microparticles to form at the LC interface, hinting at new non-equilibrium approaches to microparticle assembly. We conclude that dynamic states adopted by LCs in the presence of surfactant concentration gradients provide new opportunities for engineering complex fluids beyond equilibrium.

Non-Equilibrium Modeling of Concentration-Driven processes with Constant Chemical Potential Molecular Dynamics Simulations

ConspectusConcentration-driven processes in solution, i.e., phenomena that are sustained by persistent concentration gradients, such as crystallization and surface adsorption, are fundamental chemical processes. Understanding such phenomena is crucial for countless applications, from pharmaceuticals to biotechnology. Molecular dynamics (MD), both in- and out-of-equilibrium, plays an essential role in the current understanding of concentration-driven processes. Computational costs, however, impose drastic limitations on the accessible scale of simulated systems, hampering the effective study of such phenomena. In particular, due to these size limitations, closed system MD of concentration-driven processes is affected by solution depletion/enrichment that unavoidably impacts the dynamics of the chemical phenomena under study. As a notable example, in simulations of crystallization from solution, the transfer of monomers between the liquid and crystal phases results in a gradual depletion/enrichment of solution concentration, altering the driving force for phase transition. In contrast, this effect is negligible in experiments, given the macroscopic size of the solution volume. Because of these limitations, accurate MD characterization of concentration-driven phenomena has proven to be a long-standing simulation challenge. While disparate equilibrium and nonequilibrium simulation strategies have been proposed to address the study of such processes, the methodologies are in continuous development.In this context, a novel simulation technique named constant chemical potential molecular dynamics (CμMD) was recently proposed. CμMD employs properly designed, concentration-dependent external forces that regulate the flux of solute species between selected subregions of the simulation volume. This enables simulations of systems under a constant chemical drive in an efficient and straightforward way. The CμMD scheme was originally applied to the case of crystal growth from solution and then extended to the simulation of various physicochemical processes, resulting in new variants of the method. This Account illustrates the CμMD method and the key advances enabled by it in the framework of in silico chemistry. We review results obtained in crystallization studies, where CμMD allows growth rate calculations and equilibrium shape predictions, and in adsorption studies, where adsorption thermodynamics on porous or solid surfaces was correctly characterized via CμMD. Furthermore, we will discuss the application of CμMD variants to simulate permeation through porous materials, solution separation, and nucleation upon fixed concentration gradients. While presenting the numerous applications of the method, we provide an original and comprehensive assessment of concentration-driven simulations using CμMD. To this end, we also shed light on the theoretical and technical foundations of CμMD, underlining the novelty and specificity of the method with respect to existing techniques while stressing its current limitations. Overall, the application of CμMD to a diverse range of fields provides new insight into many physicochemical processes, the in silico study of which has been hitherto limited by finite-size effects. In this context, CμMD stands out as a general-purpose method that promises to be an invaluable simulation tool for studying molecular-scale concentration-driven phenomena.

Numerical Test of the Onsager Relations in a Driven System

The Onsager reciprocity relations were formulated in the context of irreversible thermodynamics, but they are based on assumptions that have a wider applicability. Here, we present simulations testing the Onsager relations between surface-coupled diffusive and bulk fluxes in a system prepared in a nonequilibrium steady state. The system consists of a mixture of two identical species maintained at different temperatures inside a channel. In order to tune the friction of the two species with the walls independently, while keeping the particle-wall interaction potentials the same, we allow the kinematics of particle-wall collisions to be different: "bounce-back" (B) or "specular" (S). In the BB case, diffusio-capillary transport can only take place if the two species have different temperatures. We find that the Onsager reciprocity relations are obeyed in the linear regime, even in the BB case where all fluxes are the result of perturbing the system from a nonequilibrium steady state in a way that does not satisfy time-reversal symmetry. Our Letter provides a direct, numerical illustration of the validity of the Onsager relations outside their original range of application, and suggests their relevance for transport in driven or active systems.

Generating Shear Flows without Moving Parts by Thermo-osmosis in Heterogeneous Nanochannels

Shear flows play critical roles in biological systems and technological applications and are achieved experimentally using moving parts. However, when the system size is reduced to micro- and nanoscale, fabrication of moving parts becomes exceedingly challenging. We demonstrate that a heterogeneous nanochannel composed of two parallel walls with different wetting behaviors can generate shear flow without moving parts. Molecular dynamics simulations show that shear flows can be formed inside such a nanochannel under a temperature gradient. The physical origin is that thermo-osmosis velocities with different rates and directions can be tuned by wetting behaviors. Our analysis reveals that thermo-osmosis is governed by surface excess enthalpy and nanoscale interfacial hydrodynamics. This finding provides an efficient method of generating controllable shear flows at micro- and nanoscale confinement. It also demonstrates the feasibility of using fluids to drive micromechanical elements via shear torques generated by harvesting energy from temperature differences.

High Osmotic Power Generation via Nanopore Arrays in Hybrid Hexagonal Boron Nitride/Silicon Nitride Membranes

Nanopores embedded in two-dimensional (2D) nanomaterials are a promising emerging technology for osmotic power generation. Here, coupling our new AFM-based pore fabrication approach, tip-controlled local breakdown (TCLB), with a hybrid membrane formed by coating silicon nitride (SiN) with hexagonal boron nitride (hBN), we show that high osmotic power density can be obtained in systems that do not possess the thinness of atomic monolayers. In our approach, the high osmotic performance arises from charge separation induced by the highly charged hBN surface rather than charge on the inner pore wall. Moreover, exploiting TCLB's capability of producing sub 10 nm pore arrays, we investigate the effects of pore-pore interaction on the overall power density. We find that an optimum pore-to-pore spacing of ∼500 nm is required to maintain an efficient selective transport mechanism.

Studying polymer diffusiophoresis with non-equilibrium molecular dynamics

We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute that has a concentration gradient and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition, we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows.

Effect of the interaction strength and anisotropy on the diffusio-phoresis of spherical colloids

Gradients in temperature, concentration or electrostatic potential cannot exert forces on a bulk fluid; they can, however, exert forces on a fluid in a microscopic boundary layer surrounding a (nano)colloidal solute, resulting in so-called phoretic flow. Here we present a simulation study of phoretic flow around a spherical colloid held fixed in a concentration gradient. We show that the resulting flow velocity depends non-monotonically on the strength of the colloid-fluid interaction. The reason for this non-monotonic dependence is that solute particles are effectively trapped in a shell around the colloid and cannot contribute to diffusio-phoresis. We also observe that the flow depends sensitively on the anisotropy of solute-colloid interaction.

Diffusiophoresis in Cells: A General Nonequilibrium, Nonmotor Mechanism for the Metabolism-Dependent Transport of Particles in Cells

The more we learn about the cytoplasm of cells, the more we realize that the cytoplasm is not uniform but instead is highly inhomogeneous. In any inhomogeneous solution, there are concentration gradients, and particles move either up or down these gradients due to a mechanism called diffusiophoresis. I estimate that inside metabolically active cells, the dynamics of particles can be strongly accelerated by diffusiophoresis, provided that they are at least tens of nanometers across. The dynamics of smaller objects, such as single proteins, are largely unaffected.

Osmosis, from molecular insights to large-scale applications

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.

Interfacially driven transport in narrow channels

When colloids flow in a narrow channel, the transport efficiency is controlled by the non-equilibrium interplay between colloid-wall interactions and hydrodynamics. In this paper, a general, unifying description of colloidal dispersion flow in a confined system is proposed. A momentum and mass balance founded framework implementing the colloid-interface interactions is introduced. The framework allows us to depict how interfacial forces drive the particles and the liquid flows. The interfacially driven flow (osmotic or Marangoni flows for repulsive or attractive colloid-wall interactions respectively) can be directly simulated in 2D domains. The ability of the model to describe the physics of transport in a narrow channel is discussed in detail. The hydrodynamic nature of osmosis and the associated counter-pressure are mechanically related to the colloid-interface interactions. The simulation shows an unexpected transition from axial plug to pillar accumulation for colloidal accumulation at a channel bottleneck. This transition has important consequences in transport efficiencies. Existing limiting cases, such as diffusio-osmosis, are recovered from the simulations, showing that the framework is physically well-founded. The model generalizes the existing approaches and proves the hydrodynamic character of osmosis, which cannot be fully described by purely thermodynamic considerations.

Pressure gradients fail to predict diffusio-osmosis

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results.

Theory of diffusioosmosis in a charged nanochannel

We probe the diffusioosmotic transport in a charged nanofluidic channel in the presence of an applied tangential salt concentration gradient. Ionic salt gradient driven diffusioosmosis or ionic diffusioosmosis (IDO) is characterized by the generation of an induced tangential electric field and a diffusioosmotic velocity (DOSV) that is a combination of an electroosmotic velocity (EOSV) triggered by this electric field and a chemiosmotic velocity (COSV) triggered by an induced tangential pressure gradient. We explain that unlike the existing theories on IDO, it is more appropriate to apply the zero net current conditions (formulation F2) and not more restrictive zero net local flux conditions (formulation F1) particularly for the case where one considers a nanochannel connected to two reservoirs. We pinpoint limitations in the existing literature in correctly predicting the diffusioosmotic behavior even for the case where formulation F1 is used. We address these limitations and establish that (a) the induced electric field is an interplay of the differences in ionic diffusivity, the EDL-induced imbalance in ion concentrations, and the advection effects, (b) formulation F1 may overpredict or underpredict the electric field and the EOSV leading to an overprediction/underprediction of the DOSV and (c) formulation F2 demonstrates remarkable fluid physics of localized backflows owing to a dominant local influence of the COSV, which is missed by formulation F1. We anticipate that our theory will provide the first rigorous understanding of nanofluidic IDO with applications in multiple areas of low Reynolds number transport such as biofluidics, microfluidic separation, and colloidal transport.

Diffusiophoresis in nonadsorbing polymer solutions: The Asakura-Oosawa model and stratification in drying films

A colloidal particle placed in an inhomogeneous solution of smaller nonadsorbing polymers will move towards regions of lower polymer concentration in order to reduce the free energy of the interface between the surface of the particle and the solution. This phenomenon is known as diffusiophoresis. Treating the polymer as penetrable hard spheres, as in the Asakura-Oosawa model, a simple analytic expression for the diffusiophoretic drift velocity can be obtained. In the context of drying films we show that diffusiophoresis by this mechanism can lead to stratification under easily accessible experimental conditions. By stratification we mean spontaneous formation of a layer of polymer on top of a layer of the colloid. Transposed to the case of binary colloidal mixtures, this offers an explanation for the stratification observed recently in these systems [A. Fortini et al., Phys. Rev. Lett. 116, 118301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.118301]. Our results emphasize the importance of treating solvent dynamics explicitly in these problems and caution against the neglect of hydrodynamic interactions or the use of implicit solvent models in which the absence of solvent backflow results in an unbalanced osmotic force that gives rise to large but unphysical effects.

What Controls Thermo-osmosis? Molecular Simulations Show the Critical Role of Interfacial Hydrodynamics

Thermo-osmotic and related thermophoretic phenomena can be found in many situations from biology to colloid science, but the underlying molecular mechanisms remain largely unexplored. Using molecular dynamics simulations, we measure the thermo-osmosis coefficient by both mechanocaloric and thermo-osmotic routes, for different solid-liquid interfacial energies. The simulations reveal, in particular, the crucial role of nanoscale interfacial hydrodynamics. For nonwetting surfaces, thermo-osmotic transport is largely amplified by hydrodynamic slip at the interface. For wetting surfaces, the position of the hydrodynamic shear plane plays a key role in determining the amplitude and sign of the thermo-osmosis coefficient. Finally, we measure a giant thermo-osmotic response of the water-graphene interface, which we relate to the very low interfacial friction displayed by this system. These results open new perspectives for the design of efficient functional interfaces for, e.g., waste-heat harvesting.