Session EN: Nano Fluids III

Slip: How it Happens

Liquids do not always obey the no-slip condition: the liquid and the adjacent boundary can be in relative motion. The amount of slip is often presented as a slip length, which is an average over all molecules adjacent to the boundary. Hence, the molecular-level detail of how the liquid molecules traverse over the solid surface is lost. For example, the same slip length can arise due to the fast motion of a few molecules as well as from the slow drift of many molecules. We present data from molecular dynamics simulations which shows how liquids slip. At low shear rates, only a small percentage of the molecules at the liquid-solid interface participate in slip: the creation of a vacancy at the liquid-solid interface precipitates a sequence of molecular hops which can be described in terms of the propagation of a local nonlinear mode along the interface. At high shear rates, there is a global motion in which all molecules at the interface contribute. There is a well-defined bifurcation from defect slip to global slip. This transition can be controlled through choice of channel geometry, lattice orientation and liquid properties.   

A continuum approach to reproduce molecular scale slip behavior

In this work we ask the question: Is it possible to reproduce molecular scale slip behavior by using continuum equations? To that end we note that: i) near the wall, the fluid experiences a potential, ii) the fluid density responds to the wall potential, hence, fluid compressibility is relevant, and iii) the fluid can loose momentum to the wall. To incorporate these features we simulate shear flow of a \textit{compressible} fluid between two walls \textit{in the presence of a wall potential}. Compressibility is important only in the near wall region. The slip length is calculated from the mean velocity profile. The slip length vs. shear rate trend is similar to that in molecular dynamic calculations. First, there is a constant value of slip length at low shear rates. Then, the slip length increases beyond a critical shear rate. Lastly, the slip length reaches another constant value if the wall momentum loss parameter is non-zero. The scaling for the critical shear rate emerges from our results. The value of the slip length increases if the wall potential is less corrugated and if the momentum loss to the wall is low. An understanding of the overall force balance during various slip modes, suggested previously, emerges from the governing equations. This work could be useful to develop continuum simulation tools for nanoscale problems without the need for expensive hybrid computations.   

Non-equilibrium Molecular Dynamics Simulations of Channel Flows.

We present non-equilibrium molecular dynamics simulations of liquid argon flow through nano-channels formed by two infinite krypton plates. Density, velocity and temperature distributions across the channel are studied for channels widths in the range 2.65$\sigma $-18.58$\sigma $ ($\sigma $ is the argon atom diameter). For small channels (2.65$\sigma $-7.9$\sigma )$ the fluid is ordered in layers and this ordering persists close to the walls even for wider channels. Velocity profiles in small channels deviate from the parabolic behavior predicted by continuum theory. The no-slip condition breaks down in small channels for all external forces and system temperatures studied while for large channels it is always satisfied. For channels of intermediate width the validity of the no-slip condition depends on the system temperature and the magnitude of the driving force. Temperature distribution remains uniform across the channel for values of the driving force below a threshold value which depends on channel width. We calculated also the diffusion coefficient, D, along the flow (x-direction) and across the channel (z-direction). The ratio Dz/Dx increases as the channel width increases with diffusion being higher in layers close to the center of the flow. Acknowledgment: The authors acknowledge financial support of the Hellenic Secretariat for Research {\&} Technology under grant pened-03-uth-3337.   

Molecular dynamics simulations of the shear-rate-dependent slip length in thin liquid films

The dynamic behavior of the slip length in the flow of simple and polymeric fluids confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear rate provided that the interface between simple fluid and rigid solid forms incommensurable structures. A gradual transition to approximately linear rate- dependence is observed upon increasing the wall-fluid interaction. A pronounced upward curvature in the shear rate dependence of the slip length is reported for the shear flow of the polymer melt. We found that the slip length can be well described by a function of a single variable, which is a combination of the in-plane structure factor, contact density and temperature of the first fluid layer near the solid wall. Extensive simulations show that this scaling holds in a wide range of shear rates and wall-fluid interactions for both simple fluids and short polymer chains. A relation to recent slip flow experiments is discussed. Reference: N.V. Priezjev, ``Rate-dependent slip boundary conditions for simple fluids,'' Phys. Rev. E 75, 051605 (2007).   

Study of liquid flows over solid surfaces by particle nanovelocimetry

In nanometric flows, interactions of the liquid with the surface become important. However, only indirect measurements of the slip length or the Debye length have been yet performed. Here we used near-field imaging of nanoparticles to observe water flows over solid surfaces. Water containing fluorescent nanoparticles was driven in microchannels and illuminated by an evanescent wave. Three-dimensional positioning of tracers allows the reconstruction of particle concentration and diffusion coefficient and of flow speed with 30 nm accuracy from 20 to 300~nm over the surface. We probed energy landscape over the surface which allows the first local \textit{in situ} determination of surface potential and Debye length. We moreover directly measured slip length L$_{s}$. On hydrophilic surfaces, slippage is negligible but on smooth hydrophobic surface L$_{s}$=29+/-10~nm. This constitutes the first direct observation of slippage in a water flow. Altogether our results provide a novel insight into the behavior of fluids close of solid surfaces. The application of the tools we developed could be extended to study of composite surfaces and electro-osmotic flows.   

A Theoretical Study of Magnetic Pressure Driven Flow in a Narrow Channel

Shape and height of a ferrofluid meniscus in a narrow channel composed of two vertical flat plates in response to a vertical, spatially oscillatory, magnetic field are theoretically studied. The formulation is based on an extension of the Young-Laplace equation combined with the mean curvature equation for a two-dimensional free surface. The formulation results in a hydrodynamic-magnetic problem governed by a nonlinear second order differential equation. According to this formulation, there are two relevant physical parameters in the equation: the gravitational Bond number and a new parameter: the magnetic Bond number. To solve the equation, an adaptive integration step, fourth order Runge-Kutta coupled with a Secant method is used. This procedure accelerates the convergence of a solution by checking if the boundary condition associated with the contact angle is satisfied. Influence of the magnetic Bond number on the height and shape of the ferrofluid column is evaluated for different oscillation regimes of the magnetic field. Results indicate that it is possible to make the fluid column rise even in the absence of common surface tension capillary effects.   

The fluid-coupled motion of micro and nanoscale elastic objects

We consider two closely spaced elastic objects immersed in a viscous fluid subject to thermal (Brownian) driving and external driving. For Brownian driving the objects exhibit cross-correlations in equilibrium fluctuations in displacement through the long-range effects of fluid motion. For external driving, one object is driven to oscillate while the adjacent object is passive. We model the system as two simple harmonic oscillators whose motion is coupled through the fluid. For external driving we demonstrate the feasibility of shaker-based actuation for nanoscale systems. For Brownian driving the cross-correlations are determined using a thermodynamic approach based upon the fluctuation-dissipation theorem. We perform full numerical simulations of the fluid-solid interactions that include the precise geometries of interest. We then develop analytical expressions using simplified geometries and the unsteady Stokes equations. The analytics are compared with the numerics to develop insight into the fluid-coupled dynamics over a range of experimentally relevant parameters including object separations and frequency based Reynolds numbers.   

Experimental Verification of Diffusion-Induced Bias in Mean Velocity Using Near-Wall Velocimetry with Quantum Dots

Results from recent simulations of the Brownian motion of nanoparticles next to a wall have shown that the mean velocity measured from their displacement would tend to overestimate the actual mean fluid velocity depending on the separation time between the two successive realizations of particles. This effect is most serious for highly diffusive nanoparticles. We report experimental verification of this phenomenon by measuring the motion of quantum dots (QDs) within a 100 nm evanescent layer above the surface of a 200 micron microchannel carrying an aqueous solution of QDs in pressure-driven flow. Experimental results are compared with Brownian simulations based on Langevin equations and conditions adopted from the experiment. It is shown that the simulation results agree with the experimental data once the diffusion coefficient in the simulation is matched to the one observed in the experiment.