Water flow in graphene nanochannels driven by imposed thermal gradients: the role of flexural phonons.

Accurate control of fluid transport in nanoscale structures is key to enable the design of foreseeable nanofluidic devices with applications in many fields such as chip cooling, energy conversion, drug delivery and medical diagnosis. Here, inspired by the experimental observation of intrinsic thermal ripples in graphene and by recent advances in the manipulation of 2D nanomaterials, we introduce a graphene-based thermal nanopump which produces controlled and continuous liquid flow in nanoslit channels. We investigate the performance of this thermal nanopump employing large scale molecular dynamics simulations. Upon systematically imposing thermal gradients, a net water flow towards the low-temperature zone is observed, achieving flow velocities up to 4 m s-1. We observe that water flow rates increase monotonically due to larger ripple fluctuations on the graphene layers as higher thermal gradients are applied. Moreover, we find that the out-of-plane flexural phonons in graphene are responsible for flow generation wherein lower frequency phonon branches are activated with higher imposed thermal gradients. Furthermore, by modifying the wettability of the channel walls, an increase of 50% in the water flow rates is observed, showing that the efficiency of the proposed thermal pump can be enhanced by tuning the channel wall hydrophobicity. Our results indicate that thermal gradients can be employed to drive continuous water flow in graphene nanoslit channels with potential applications in nanofluidic devices.

Effect of charge inversion on nanoconfined flow of multivalent ionic solutions.

A comprehensive understanding of fluid dynamics of dilute electrolyte solutions in nanoconfinement is essential to develop more efficient nanofluidic devices. In nanoconduits, the electrical double layer can occupy a considerable part of the channel cross-section, therefore the transport properties of a nanoconfined electrolyte solution can be altered by interfacial phenomena such as the charge inversion (CI). CI is an electrokinetic effect that has been associated with the presence of hydrated multivalent cations in nanoconfinement. Here, all-atom molecular dynamics simulations are employed to study the structure and dynamics of aqueous multivalent electrolyte solutions within slit-shaped silica channels. All simulations are conducted for more than 100 ns to capture the equilibrium ion distribution, the interfacial hydrodynamic properties, and to reveal the influence of CI on nanoconfined fluid transport. The electrolyte solutions consist of water as solvent, chloride as co-ion and different counter-ions, i.e., sodium, magnesium and aluminum. We find that the interfacial viscosity is related to the concentration and valence of the counter-ions in the solution. Our results suggest that higher CI is correlated to the presence of a layer of fluid with augmented viscosity adjacent to the channel wall. As the thickness of this interfacial high-viscosity fluid increases, lower flow rates are measured whereas higher interfacial viscosities and friction coefficients are computed.

Nanopumps without Pressure Gradients: Ultrafast Transport of Water in Patterned Nanotubes.

The extreme liquid transport properties of carbon nanotubes present new opportunities for surpassing conventional technologies in water filtration and purification. We demonstrate that carbon nanotubes with wettability surface patterns act as nanopumps for the ultrafast transport of picoliter water droplets without requiring externally imposed pressure gradients. Large-scale molecular dynamics simulations evidence unprecedented speeds and accelerations on the order of 1010 g of droplet propulsion caused by interfacial energy gradients. This phenomenon is persistent for nanotubes of varying sizes, stepwise pattern configurations, and initial conditions. We present a scaling law for water transport as a function of wettability gradients through simple models for the droplet dynamic contact angle and friction coefficient. Our results show that patterned nanotubes are energy-efficient nanopumps offering a realistic path toward ultrafast water nanofiltration and precision drug delivery.

Hydrodynamics of sponge pumps and evolution of the sponge body plan.

Sponges are suspension feeders that filter vast amounts of water. Pumping is carried out by flagellated chambers that are connected to an inhalant and exhalant canal system. In 'leucon' sponges with relatively high-pressure resistance due to a complex and narrow canal system, pumping and filtering are only possible owing to the presence of a gasket-like structure (forming a canopy above the collar filters). Here, we combine numerical and experimental work and demonstrate how sponges that lack such sealing elements are able to efficiently pump and force the flagella-driven flow through their collar filter, thanks to the formation of a 'hydrodynamic gasket' above the collar. Our findings link the architecture of flagellated chambers to that of the canal system, and lend support to the current view that the sponge aquiferous system evolved from an open-type filtration system, and that the first metazoans were filter feeders.

Ultrafast Propulsion of Water Nanodroplets on Patterned Graphene.

The directed transport of liquids at the nanoscale is of great importance for nanotechnology applications ranging from water filtration to the cooling of electronics and precision medicine. Here we demonstrate such unidirectional, pumpless transport of water nanodroplets on graphene sheets patterned with hydrophilic/phobic areas inspired by natural systems. We find that spatially varying patterning of the graphene surfaces can lead to water transport at ultrafast velocities, far exceeding macroscale estimates. We perform extensive molecular dynamics simulations to show that such high transport velocities ( O(102 m/s)) are due to differences of the advancing and receding contact angles of the moving droplet. This contact angle hysteresis and the ensuing transport depend on the surface pattern and the droplet size. We present a scaling law for the driving capillary and resisting friction forces on the water droplet and use it to predict nanodroplet trajectories on a wedge-patterned graphene sheet. The present results demonstrate that graphene with spatially variable wettability is a potent material for fast and precise transport of nanodroplets with significant potential for directed nanoscale liquid transport and precision drug delivery.

Hydrodynamics of the leucon sponge pump.

Leuconoid sponges are filter-feeders with a complex system of branching inhalant and exhalant canals leading to and from the close-packed choanocyte chambers. Each of these choanocyte chambers holds many choanocytes that act as pumping units delivering the relatively high pressure rise needed to overcome the system pressure losses in canals and constrictions. Here, we test the hypothesis that, in order to deliver the high pressures observed, each choanocyte operates as a leaky, positive displacement-type pump owing to the interaction between its beating flagellar vane and the collar, open at the base for inflow but sealed above. The leaking backflow is caused by small gaps between the vaned flagellum and the collar. The choanocyte pumps act in parallel, each delivering the same high pressure, because low-pressure and high-pressure zones in the choanocyte chamber are separated by a seal (secondary reticulum). A simple analytical model is derived for the pump characteristic, and by imposing an estimated system characteristic we obtain the back-pressure characteristic that shows good agreement with available experimental data. Computational fluid dynamics is used to verify a simple model for the dependence of leak flow through gaps in a conceptual collar-vane-flagellum system and then applied to models of a choanocyte tailored to the parameters of the freshwater demosponge Spongilla lacustris to study its flows in detail. It is found that both the impermeable glycocalyx mesh covering the upper part of the collar and the secondary reticulum are indispensable features for the choanocyte pump to deliver the observed high pressures. Finally, the mechanical pump power expended by the beating flagellum is compared with the useful (reversible) pumping power received by the water flow to arrive at a typical mechanical pump efficiency of about 70%.

Hydrodynamic functionality of the lorica in choanoflagellates.

Choanoflagellates are unicellular eukaryotes that are ubiquitous in aquatic habitats. They have a single flagellum that creates a flow toward a collar filter composed of filter strands that extend from the cell. In one common group, the loricate choanoflagellates, the cell is suspended in an elaborate basket-like structure, the lorica, the function of which remains unknown. Here, we use Computational Fluid Dynamics to explore the possible hydrodynamic function of the lorica. We use the choanoflagellate Diaphaoneca grandis as a model organism. It has been hypothesized that the function of the lorica is to prevent refiltration (flow recirculation) and to increase the drag and, hence, increase the feeding rate and reduce the swimming speed. We find no support for these hypotheses. On the contrary, motile prey are encountered at a much lower rate by the loricate organism. The presence of the lorica does not affect the average swimming speed, but it suppresses the lateral motion and rotation of the cell. Without the lorica, the cell jiggles from side to side while swimming. The unsteady flow generated by the beating flagellum causes reversed flow through the collar filter that may wash away captured prey while it is being transported to the cell body for engulfment. The lorica substantially decreases such flow, hence it potentially increases the capture efficiency. This may be the main adaptive value of the lorica.

Effect of an external electric field on capillary filling of water in hydrophilic silica nanochannels.

Development of functional nanofluidic devices requires understanding the fundamentals of capillary driven flow in nanochannels. In this context, we conduct molecular dynamics simulations of water capillary imbibition in silica nanoslits under externally applied electric (E) fields with strengths between 0 and 1 V nm-1. For increasing E-fields, we observe a systematic lowering in the meniscus contact angle and a decrease in the corresponding water filling rates. These results contrast markedly the classical Washburn-Bosanquet's equation which predicts an increase in filling rates for lower water contact angles. Our study provides evidence that the observed decrease in water filling rates can be attributed to the interplay between two underlying mechanisms, a reduced fluidity of interfacial water and a systematic alignment of the water molecules in the bulk as a response to the particular strength of the applied E-field. Therefore, during water capillary filling a constant E-field applied in the direction parallel to the water imbibition leads to a lower than expected filling rate caused by a viscosity increase in the bulk and an altered solid-liquid friction on the channel walls. These coupled mechanisms governing capillarity under the action of applied E-fields could be manipulated for controlling imbibition of polar liquid solutions in nanofluidic devices.

Water thermophoresis in carbon nanotubes: the interplay between thermophoretic and friction forces.

Thermophoresis is the phenomenon wherein particles experience a net drift induced by a thermal gradient. In this work, molecular dynamics simulations are conducted to study with atomistic detail the thermophoresis of water nanodroplets inside carbon nanotubes (CNTs) and its interplay with the retarding liquid-solid friction. Different applied temperatures, thermal gradients, and droplet sizes are used to reveal the dynamics of the two kinetic regimes of the thermophoretic motion in CNTs. The results indicate that during the droplet motion, the thermophoretic force is independent of the velocity of the droplet, whereas the magnitude of the retarding friction force exhibits a linear dependence. In fact, in the initial regime the magnitude of the friction force increases linearly with the droplet velocity, until the thermophoretic force is balanced by the friction force as the droplet reaches its terminal velocity in the final regime. In addition, an increase in the magnitude of the thermophoretic force is found for longer water droplets. These findings provide a deeper understanding of liquid transport driven by temperature gradients in nanoconfined geometries where liquid-solid interfaces govern fluidics.

Suspended particle transport through constriction channel with Brownian motion.

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

Hydrodynamics of microbial filter feeding.

Microbial filter feeders are an important group of grazers, significant to the microbial loop, aquatic food webs, and biogeochemical cycling. Our understanding of microbial filter feeding is poor, and, importantly, it is unknown what force microbial filter feeders must generate to process adequate amounts of water. Also, the trade-off in the filter spacing remains unexplored, despite its simple formulation: A filter too coarse will allow suitably sized prey to pass unintercepted, whereas a filter too fine will cause strong flow resistance. We quantify the feeding flow of the filter-feeding choanoflagellate Diaphanoeca grandis using particle tracking, and demonstrate that the current understanding of microbial filter feeding is inconsistent with computational fluid dynamics (CFD) and analytical estimates. Both approaches underestimate observed filtration rates by more than an order of magnitude; the beating flagellum is simply unable to draw enough water through the fine filter. We find similar discrepancies for other choanoflagellate species, highlighting an apparent paradox. Our observations motivate us to suggest a radically different filtration mechanism that requires a flagellar vane (sheet), something notoriously difficult to visualize but sporadically observed in the related choanocytes (sponges). A CFD model with a flagellar vane correctly predicts the filtration rate of D. grandis, and using a simple model we can account for the filtration rates of other microbial filter feeders. We finally predict how optimum filter mesh size increases with cell size in microbial filter feeders, a prediction that accords very well with observations. We expect our results to be of significance for small-scale biophysics and trait-based ecological modeling.

Slip divergence of water flow in graphene nanochannels: the role of chirality.

Graphene has attracted considerable attention due to its characteristics as a 2D material and its fascinating properties, providing a potential building block for nanofabrication. In nanochannels the solid-liquid interface plays a non-negligible role in determining the fluid dynamics. Therefore, for an optimal design of nanofluidic devices, a comprehensive understanding of the slippage in a water flow confined between graphene walls is important. In nanoconfinement, experimental and computational studies have found the slip length to increase nonlinearly when the shear rate is larger than a critical value. Here, by conducting molecular dynamics simulations, we study the influence of the graphene crystallographic orientation on the slip boundary conditions inside a nanoslit channel. The flow in channels with heights of 2.0, 2.4 and 2.8 nm is driven parallel to the zig-zag and arm-chair crystallographic directions. We extract flow rates, velocity profiles, slip velocities and slip lengths. The slip velocity displays a linear relationship to the shear stress up to a critical value, which is not size dependent. Moreover, the slip length is found to be shear stress dependent above a critical shear stress value of 0.4 MPa. Furthermore, our results indicate that after this critical shear stress is reached, the flow rates are significantly influenced (up to 10%) by the particular orientation of the graphene topology.

Effect of the meniscus contact angle during early regimes of spontaneous imbibition in nanochannels.

Nanoscale capillarity has been extensively investigated; nevertheless, many fundamental questions remain open. In spontaneous imbibition, the classical Lucas-Washburn equation predicts a singularity as the fluid enters the channel consisting of an anomalous infinite velocity of the capillary meniscus. Bosanquet's equation overcomes this problem by taking into account fluid inertia predicting an initial imbibition regime with constant velocity. Nevertheless, the initial constant velocity as predicted by Bosanquet's equation is much greater than those observed experimentally. In the present study, large scale atomistic simulations are conducted to investigate capillary imbibition of water in slit silica nanochannels with heights between 4 and 18 nm. We find that the meniscus contact angle remains constant during the inertial regime and its value depends on the height of the channel. We also find that the meniscus velocity computed at the channel entrance is related to the particular value of the meniscus contact angle. Moreover, during the subsequent visco-inertial regime, as the influence of viscosity increases, the meniscus contact angle is found to be time dependent for all the channels under study. Furthermore, we propose an expression for the time evolution of the dynamic contact angle in nanochannels which, when incorporated into Bosanquet's equation, satisfactorily explains the initial capillary rise.

Ultrafast cooling by covalently bonded graphene-carbon nanotube hybrid immersed in water.

The increasing power density and the decreasing dimensions of transistors present severe thermal challenges to the design of modern microprocessors. Furthermore, new technologies such as three-dimensional chip-stack architectures require novel cooling solutions for their thermal management. Here, we demonstrate, through transient heat-dissipation simulations, that a covalently bonded graphene-carbon nanotube (G-CNT) hybrid immersed in water is a promising solution for the ultrafast cooling of such high-temperature and high heat-flux surfaces. The G-CNT hybrid offers a unique platform to integrate the superior axial heat transfer capability of individual CNTs via their parallel arrangement. The immersion of the G-CNT in water enables an additional heat dissipation path via the solid-liquid interaction, allowing for the sustainable cooling of the hot surface under a constant power input of up to 10 000 W cm-2.

Kapitza Resistance between Few-Layer Graphene and Water: Liquid Layering Effects.

The Kapitza resistance (RK) between few-layer graphene (FLG) and water was studied using molecular dynamics simulations. The RK was found to depend on the number of the layers in the FLG though, surprisingly, not on the water block thickness. This distinct size dependence is attributed to the large difference in the phonon mean free path between the FLG and water. Remarkably, RK is strongly dependent on the layering of water adjacent to the FLG, exhibiting an inverse proportionality relationship to the peak density of the first water layer, which is consistent with better acoustic phonon matching between FLG and water. These findings suggest novel ways to engineer the thermal transport properties of solid-liquid interfaces by controlling and regulating the liquid layering at the interface.

Sustaining dry surfaces under water.

Rough surfaces immersed under water remain practically dry if the liquid-solid contact is on roughness peaks, while the roughness valleys are filled with gas. Mechanisms that prevent water from invading the valleys are well studied. However, to remain practically dry under water, additional mechanisms need consideration. This is because trapped gas (e.g. air) in the roughness valleys can dissolve into the water pool, leading to invasion. Additionally, water vapor can also occupy the roughness valleys of immersed surfaces. If water vapor condenses, that too leads to invasion. These effects have not been investigated, and are critically important to maintain surfaces dry under water. In this work, we identify the critical roughness scale, below which it is possible to sustain the vapor phase of water and/or trapped gases in roughness valleys - thus keeping the immersed surface dry. Theoretical predictions are consistent with molecular dynamics simulations and experiments.

Early regimes of water capillary flow in slit silica nanochannels.

Molecular dynamics simulations are conducted to investigate the initial stages of spontaneous imbibition of water in slit silica nanochannels surrounded by air. An analysis is performed for the effects of nanoscopic confinement, initial conditions of liquid uptake and air pressurization on the dynamics of capillary filling. The results indicate that the nanoscale imbibition process is divided into three main flow regimes: an initial regime where the capillary force is balanced only by the inertial drag and characterized by a constant velocity and a plug flow profile. In this regime, the meniscus formation process plays a central role in the imbibition rate. Thereafter, a transitional regime takes place, in which, the force balance has significant contributions from both inertia and viscous friction. Subsequently, a regime wherein viscous forces dominate the capillary force balance is attained. Flow velocity profiles identify the passage from an inviscid flow to a developing Poiseuille flow. Gas density profiles ahead of the capillary front indicate a transient accumulation of air on the advancing meniscus. Furthermore, slower capillary filling rates computed for higher air pressures reveal a significant retarding effect of the gas displaced by the advancing meniscus.

Strain engineering of Kapitza resistance in few-layer graphene.

We demonstrate through molecular dynamics simulations that the Kapitza resistance in few-layer graphene (FLG) can be controlled by applying mechanical strain. For unstrained FLG, the Kapitza resistance decreases with the increase of thickness and reaches an asymptotic value of 6 × 10(-10) m(2)K/W at a thickness about 16 nm. Uniaxial cross-plane strain is found to increase the Kapitza resistance in FLG monotonically, when the applied strain varies from compressive to tensile. Moreover, uniaxial strain couples the in-plane and out-of-plane strain/stress when the surface of FLG is buckled. We find that with a compressive cross-plane stress of 2 GPa, the Kapitza resistance is reduced by about 50%. On the other hand it is almost tripled with a tensile cross-plane stress of 1 GPa. Remarkably, compressive in-plane strain can either increase or reduce the Kapitza resistance, depending on the specific way it is applied. Our study suggests that graphene can be exploited for both heat dissipation and insulation through strain engineering.