Session D2: Nanofluids I

Investigation of Flow Boundary Conditions and Diffusion in Nanochannels using Molecular Dynamics Simulations

The influence of nano-confinement and slip boundary conditions on the thermal motion of fluid molecules is investigated using the LAMMPS molecular dynamics program. We consider a neutral Lennard-Jones fluid confined by crystalline walls with weak surface energy. Particular attention was paid to the implementation of a wall model that allows fine adjustment of the slip length without changing the interfacial fluid structure. We used the original Steele's surface energy decomposition, i.e., that the interaction potential between a fluid molecule and a solid substrate can be expressed as a Fourier expansion in the reciprocal-lattice vectors of the substrate surface. The local diffusion coefficients in the directions parallel and perpendicular to confining walls were estimated as a function of a distance from the walls and then correlated with the slip length. The results of this numerical study are important for interpretation of nano-PIV (Particle Image Velocimetry) measurements of interfacial shear flows and boundary slippage. Financial support from the National Science Foundation (CBET-1033662) is gratefully acknowledged.   

Studying nanoscale slip mechanisms of simple fluids at low and high shearing velocities by molecular dynamics

Understanding slip is of great importance, especially in the emerging research topics and applications of nanofluidics. In this study, we reveal the nanoscale slip mechanisms in different flow regimes that are characterized by shearing velocities. They are modeled using direct molecular dynamics simulation of a nanoscale Couette flow system. An isothermal fluid system is built by the Dissipative Particle Dynamics thermostat, with either rigid or thermal walls. The purpose of using isothermal simulation is to simplify the discussion by excluding the significant influence on the slip from dramatic viscous heating at high shear rates. Our results show an abrupt jump of slip length when the shearing velocity is increased to a critical value, implying a transition in the slip mechanisms. The transition is followed by a linear increase in slip length, with a slope that is dependent on the characteristic of the walls and wall models. Increasing the rigidity of the thermal walls results in slip behaviors that asymptotically approach the one of a rigid wall. The slip behavior supports the two mechanism hypothesis shown in Martini et al.,\footnote{A. Martini, H.-Y. Hsu, N. A. Patankar, and S. Lichter, Phys. Rev. Lett. 100, 206001 (2008).} but with a different interpretation for the slip mechanism at high shearing velocities.   

A High-Order Accurate Numerical Solution of Incompressible Microchannel Flows in Slip and Transition Flow Regimes

In this study, a high-order accurate numerical solution of steady incompressible flows in 2D microchannels is presented. The numerical method used is a fourth-order compact implicit operator scheme which is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. The present methodology considers the solution of the Navier-Stokes equations with employing different slip boundary conditions on the wall to model the slip flow in microchannels. Since the slip boundary conditions contain the derivatives of the $u$ velocity, using the compact method the slip boundary conditions can be easily and accurately implemented. Herein, different slip boundary conditions are used and the results for fully developed velocity profiles in the slip flow regime $(Kn < 0.1)$ and in the transition flow regime $(Kn > 0.1)$ are compared with the available numerical and analytical results which show good agreement.   

Gas Flow near a Smooth Plate

We examine gas flow adjacent to a molecularly smooth solid, muscovite mica. The fluctuations in force acting on a glass sphere as a function of proximity to a mica plate were measured in air, and were used to obtain the damping. The damping was interpreted as a lubrication force. The measured damping as a function of separation in the slip-flow regime corresponds to a slip length of 480 $\pm $ 70 nm, which is equivalent to highly specular gas molecule collisions. The slip flow model also fits the data for separations as small as one mean free path.   

Molecular diffusion and tensorial slip at surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. This study is motivated by the possibility to generate transverse flows in microfluidics devices to enhance mixing and separation processes. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In case of anisotropic textures, the interfacial diffusion coefficient of fluid molecules near heterogeneous surfaces correlates well with the effective slip length as a function of the shear flow direction with respect to the texture orientation. In addition, it was found that the angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the pattern size is larger than several molecular diameters. These findings lend support for the microscopic justification of recently introduced tensor formulation of the effective slip boundary conditions in the case of noninertial flows of Newtonian fluids over smooth surfaces with nanoscale anisotropic textures. Funding from NSF (CBET-1033662) is gratefully acknowledged.   

Investigation of Gas and Fluid Flow through a Single Nanopore

Mass flow through ion-track etched nanopores with diameters ranging in size from 100 to 300 nm was measured using mass spectrometry. The thickness of the membrane was 12 micron, so our system was modeled after flow through a long pipe. The mass flow was caused by a pressure difference across the membrane of order 1 atm, with the low pressure side at vacuum. At room temperature diffusive transport through the membrane was comparable to mass flow through the hole so the temperature was lowered to -50 C which stopped the diffusive transport. The flow rates for gaseous Helium, Argon, and Nitrogen were studied and agreed with theory at a variety of Knudsen numbers. In contrast, with liquid water or Nitrogen on the high pressure side of the membrane, preliminary results show higher flow rates than can be accounted for by classical viscous flow theory.   

Surface-Gas Interaction Effects on Nanoscale Flows

Three-dimensional molecular dynamics (MD) simulations of linear Couette flow of argon gas confined within nano-scale channels are investigated as a function of the surface-gas interaction strength ratio (ISR). Simulations are performed in the slip, transition and free molecular flow regimes by keeping the base pressure constant for different ISR cases. Near-wall gas density increases with increased ISR and eventually results in adsorption of argon on the surfaces. Although the velocity profiles agree with the kinetic theory predictions in the bulk of the channel, they show sudden increase in the near wall region, resulting in decreased velocity slip at the interface. High ISR values are shown to induce velocity stick. Increase in the ISR results in stronger surface--particle interactions. Hence, the surface virial becomes more dominant in the near wall region, resulting in increasingly anisotropic normal stresses. Utilizing the kinetic theory and MD predicted shear stress values, the tangential momentum accommodation coefficient for argon gas, interacting with FCC structured walls (100) plane facing the fluid, is shown to increase with increased ISR.   

Confinement Effects in Oscillating Nanoscale Flows

We present an experimental study of confinement in oscillating nanoscale flows. In the experiment, we measure the resonant parameters of a microcantilever with a sphere attached at the tip. As the sphere is brought towards a flat plate in a dry nitrogen environment, the flow becomes confined in the gap between the sphere and the plate, affecting the resonant frequency and dissipation of the cantilever. We tune the gap, the nitrogen pressure, and the oscillation frequency in order to study the flow over a broad range of dimensionless parameters. We observe deviations from continuum fluid dynamics at small gaps, low pressures, and high frequencies. Using these measurements, we provide an in-depth characterization of confinement effects in oscillating nanoflows.   

Small Scale Effect on Flow-Induced Instability of Double-Walled Carbon Nanotubes

Small scale effect on flow-induced instability of double-walled carbon nanotubes (DWCNTs) is investigated using an elastic shell model based on Donnell's shell theory. The dynamic governing equations of DWCNTs are derived on the basis of nonlocal elasticity theory, in addition, the van der Waals (vdW) interaction between the inner and outer walls is considered in the shell modeling. The instability of DWCNTs that is induced by a pressure-driven steady flow is studied. The numerical computations indicate that as the flow velocity increases, DWNCTs have a way to get through multi-bifurcations of the first and second bifurcations in turn. It can be concluded that the critical flow velocity is closely correlated to the ratio of the length to the radius of DWCNTs, the pressure of the fluid and the small scale effects. Furthermore, it is interesting to notice that as the small scale effects are considered, the first critical flow velocities of DWCNTs decrease as compared to the results with the classical (local) continuum mechanics, therefore, the small scale effects play an important role on performing the instability analysis in the fluid-conveying DWCNTs.   

Fast Water Transport in CNTs: length dependence and entrane/exit effects

Superfast water transport in carbon nanotube (CNT) membranes has been reported in experimental studies. We use Molecular Dynamics simulations to elucidate the mechanisms of water entry, exit and transport in $2\,nm$-diameter hydrophobic CNTs embedded in a hydrophilic membrane matrix. We demonstrate, for the first time, that under imposed pressures of the order of 1 bar, water entry into the CNT cavity and exit from the CNT end, can occur only on pre-wetted membranes. We conduct large scale simulations for up to $500\,nm$ long CNTs and observe a previously unseen dependence of the flow enhancement rates on the CNT length. We relate the present findings to past computational and experimental studies, we discuss previous continuum assessments for this flow and propose underlying physical mechanisms.