Continuum Hydrodynamic Theory Research Articles

Wall friction should be decoupled from fluid viscosity for the prediction of nanoscale flow.

The accurate determination of fluid viscosity based on the microscopic information of molecules is very crucial for the prediction of nanoscale flow. Despite the challenge of this problem, researchers have done a lot of meaningful work and developed several distinctive methods. However, one of the common approaches to calculate the fluid viscosity is using the Green-Kubo formula by considering all the fluid molecules in nanospace, inevitably causing the involvement of the frictional interaction between fluid and the wall into the fluid viscosity. This practice is certainly not appropriate because viscosity is essentially related only to the interactions among fluid molecules. Here, we clarify that the wall friction should be decoupled from fluid viscosity by distinguishing the frictional region and the viscous region for the accurate prediction of nanoscale flow. By comparing the fluid viscosities calculated from the Green-Kubo formula in the whole region and viscous region and the viscosity obtained from the velocity profile through the Hagen-Poiseuille equation, it is found that only the calculated viscosity in the viscous region agrees well with the viscosity from the velocity profile. To demonstrate the applicability of this clarification, the Lennard-Jones fluid and water confined between Lennard-Jones, graphene, and silica walls, even with different fluid-wall interactions, are extensively tested. This work clearly defines the viscosity of fluids at nanoscales from the inherent nature of physics, aiming at the accurate prediction of nanoscale flow from the classical continuum hydrodynamic theory.

Molecular Dynamics Simulation of Fast Water Transport though Aquaporin-Mimic Nanpores

The aquaporin water channel allows efficiently fast water transport while rejecting ions and protons. We perform molecular dynamics simulations with flexible hourglass-shaped pores by mimicking aquaporin water channels. The simulation model includes a uniform applied external force field to mimic osmotic gradient environment and an added harmonic constraint to achieve nanopore flexibility. We estimated the osmotic permeability from simulation and it is consistent with experimental results to confirm the validity of our model. We performed non-equilibrium molecular dynamics simulation with Nose-Hoover thermostat, the SPC/E water model, and carbon pore atoms. The occupancy (number of water molecules inside the pore) is maintained as a fixed value as long as the pore geometry is the same. The simplified model also successfully captures the important physics of real aquaporin, e.g. a single-file arrangement of water molecules, the reorientation of water dipoles. We found that the model pore has the capacity to house more water molecules. We also found that water flow is up to 5 times than predicted by continuum hydrodynamic theory. This finding suggests that deforming straight nanopores into the hourglass shape (if possible) enhances the ability of water transport in thin membranes. The future work includes the simulations with a longer hourglass-shaped nanopore (maybe up to 1 μm) and changing the chemical characteristics (e.g. surface charge, hydrophobicity) of a membrane surface.

Hydrodynamic theory of liquid slippage on a solid substrate near a moving contact line.

In this Letter a hydrodynamic theory of liquid slippage on a solid substrate near a moving contact line is proposed. A family of spatially varying slip lengths in the Navier slip law recovers the results of past formulations for slip in continuum theories and molecular dynamics simulations and is consistent with well-established experimental observations of complete wetting. This formulation gives a general approach for continuum hydrodynamic theories. New fluid flow behaviors are also predicted yet to be seen in experiment.

Interplay between Hydrodynamics and the Free Energy Surface in the Assembly of Nanoscale Hydrophobes

Solvent plays an important role in the relative motion of nanoscopic bodies, and the study of such phenomena can help elucidate the mechanism of hydrophobic assembly, as well as the influence of solvent-mediated effects on in vivo motion in crowded cellular environments. Here we study important aspects of this problem within the framework of Brownian dynamics. We compute the free energy surface that the Brownian particles experience and their hydrodynamic interactions from molecular dynamics simulations in explicit solvent. We find that molecular scale effects dominate at short distances, thus giving rise to deviations from the predictions of continuum hydrodynamic theory. Drying phenomena, solvent layering, and fluctuations engender distinct signatures of the molecular scale. The rate of assembly in the diffusion-controlled limit is found to decrease from molecular scale hydrodynamic interactions, in opposition to the free energy driving force for hydrophobic assembly, and act to reinforce the influence of the free energy surface on the association of more hydrophilic bodies.

Homo- and hetero-interactions between air bubbles and oil droplets measured by atomic force microscopy

The atomic force microscope was used to analyse the interactions between bubbles and oil droplets in surfactant-free aqueous solutions. Both homo- (bubble-bubble and drop-drop) and hetero- (bubble-drop) interactions were examined to elucidate the role of colloidal and hydrodynamic forces which, together with interfacial deformations dictate the stability in these systems. It is shown that electrical double-layer forces can be rendered attractive within a small pH range, and that the Van der Waals force can be switched from attractive to repulsive by material choice and ionic strength through salt effects on the so-called ‘zero-frequency’ term of the Lifshitz theory. By measuring interaction events between bubbles and drops at higher velocities, it is seen that deformation of the bodies and lubrication in the film generated between them can be predicted with a continuum hydrodynamic theory. These results suggest that solution pH and droplet material choice can be used to enhance or inhibit coalescence in such multi-component and multi-phase systems, and this may prove useful in controlling the behaviour of systems in microfluidics, as well as dispersion and formulation science.

Diffusion−Viscosity Decoupling in Supercooled Aqueous Trehalose Solutions

The diffusional mobility of disodium fluorescein has been measured in supercooled aqueous solutions of trehalose, a widely used cryoprotectant disaccharide. The results were analyzed on the basis of the classical continuum hydrodynamic theory (Stokes-Einstein relationship) and compared with results for the diffusion and electrical conductivity of other ionic and nonionic solutes in trehalose and sucrose aqueous solutions. Disodium fluorescein obeys the classical model over a restricted range of inverse reduced temperatures, T g/ T, scaled by the glass transition temperature. Decoupling in neutral solutes takes place at higher values of T g/ T, while in ionic solutes it occurs all over the range of T g/ T studied, as observed for the water mobility in supercooled sugar solutions.

Molecular Dynamics Study on the Dependence of Contact Angle on the Speed of Contact Line

The flow in the vicinity of a moving contact line is characterized by a steep increase in the fluid slipping relative to the solid surface owing to fluid stress concentration at the contact line. In this study, molecular dynamics (MD) simulations are made to investigate the dependence of microscopic configuration of the fluid-fluid interface, in particular the contact angle, on the speed of contact line relative to the solid surface ΔV. While ΔV increases when the solid surface velocity relative to the bulk fluid, V, is increased from zero, ΔV starts decreasing when V exceeds a certain upper limit for the given material combinations. The contact angle dependence on ΔV (and V) was predicted from the microscopic stress balance near the contact line using the fluid distribution obtained from the continuum hydrodynamic theory. It is also shown that the stress balance prediction agrees with the MD results when appropriate slip velocities are assumed in the hydrodynamic calculation.

Mechanism of Ion Exclusion by Sub-2nm Carbon Nanotube Membranes

AbstractCarbon nanotubes offer an outstanding platform for studying molecular transport at nanoscale, and have become promising materials for nanofluidics and membrane technology due to their unique combination of physical, chemical, mechanical, and electronic properties. In particular, both simulations and experiments have proved that fluid flow through carbon nanotubes of nanometer size diameter is exceptionally fast compared to what continuum hydrodynamic theories would predict when applied on this length scale, and also, compared to conventional membranes with pores of similar size, such as zeolites. For a variety of applications such as separation technology, molecular sensing, drug delivery, and biomimetics, selectivity is required together with fast flow. In particular, for water desalination, coupling the enhancement of the water flux with selective ion transport could drastically reduce the cost of brackish and seawater desalting. In this work, we study the ion selectivity of membranes made of aligned double-walled carbon nanotubes with sub-2 nm diameter. Negatively charged groups are introduced at the opening of the carbon nanotubes by oxygen plasma treatment. Reverse osmosis experiments coupled with capillary electrophoresis analysis of permeate and feed show significant anion and cation rejection. Ion exclusion declines by increasing ionic strength (concentration) of the feed and by lowering solution pH; also, the highest rejection is observed for the salts (A=anion, C=cation, z= valence) with the greatest zA/zC ratio. Our results strongly support a Donnan-type rejection mechanism, dominated by electrostatic interactions between fixed membrane charges and mobile ions, while steric and hydrodynamic effects appear to be less important. Comparison with commercial nanofiltration membranes for water softening reveals that our carbon nanotube membranes provides far superior water fluxes for similar ion rejection capabilities.

Erratum: Capillary wave dynamics on supported viscoelastic films: Single and double layers [Phys. Rev. E.75, 021604 (2007)

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev. E {\bf 74}, 010602 (R) (2006)].

Capillary wave dynamics on supported viscoelastic films: Single and double layers

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].

Studies of Transport of Asphaltenes through Membranes Using Hindered Diffusion Theories for Spheres and Spheroids

The results of ongoing efforts by this group to model the transport of asphaltene molecules through model membranes are presented. A model is described which aims to capture the effect of the polydisperse nature of asphaltene molecules on their transport properties. The asphaltene structure is generated stochastically using Monte Carlo techniques. Individual asphaltene molecules are approximated as spheroids for the purpose of calculating their hindered diffusivities. Continuum hydrodynamic theories and boundary element methods are used to calculate the diffusion coefficients. A number of analytical expressions, scaling relationships, and approximations utilized in the literature are evaluated.

Studies of transport of asphaltenes through porous membranes: statistical structural models and continuum hydrodynamic theories

The results of our ongoing studies of the transport os asphaltene molecules through model membranes are presented. The experimental results are briefly reviewed, and a model is presented which aims to capture the effect on the transport of the polydisperse nature of the asphaltene molecules. The asphaltene molecular structure is first generated stochastically using a Monte Carlo technique. The individual asphaltene molecules are then approximated as spheroids for the purpose of calculating their hindered diffusivities. Continuum hydrodynamic theories of hindered diffusion are then used to calculate the individual transport coefficients.

Vortex oscillations and hydrodynamics of rotating superfluids

This review covers the progress in the study of vortex oscillations in rotating superfluids. The paper deals with the theory as its principal concern, but the experiments that one can compare with the theory considered are also discussed. Attention is focused mainly on the effects of crystalline order in the vortex lattice (the Tkachenko waves especially) and on the boundary problems arising in studies of vortex oscillations in finite containers. The approach is based mostly on the continuum hydrodynamic theory dealing with dense vortex arrays, and considerable attention is devoted to discussion of this theory in order to understand better the principles upon which the obtained results rest. The theory is traced from the simple description of a rotating classical fluid with continuous vorticity, through that of a perfect fluid with quantized vorticity in the form of an array of vortex lines, then the two-fluid theory of an isotropic superfluid, and finally the theory of rotating anisotropic superfluids such as $^{3}\mathrm{He}$-$A$. Applications of the theory to He II, the superfluid phases of $^{3}\mathrm{He}$, and the superfluid neutron matter in pulsars are discussed.

Flame Propagation and Overdense Heating in a Laser Created Plasma

A one-dimensional continuum hydrodynamic theory is used to investigate the structure of the deflagration wave which occurs when a laser light beam impinges on a solid target. It is shown that the nonlinear electron heat conduction is responsible for most of the structure; a region of density higher than the cutoff is strongly heated. Density and temperature profiles are calculated. An approximate solution for the thickness x of the overdense layer gives x = 45[(γ−1) / (5γ−1)](m/k)3/2A(Tc2/ρc) (m is the ion mass, k is the Boltzmann constant, A T5/2 is the nonlinear electron heat conduction coefficient, Tc is the temperature of the plasma at cutoff density ρc. The average density in the layer is about twice the cutoff density. The effects of viscosity and (since electrons are heated by the laser light) of ion-electron relaxation are evaluated.