Surface charge-dependent transport of water in graphene nano-channels

Deionized water flow through positively charged graphene nano-channels is investigated using molecular dynamics simulations as a function of the surface charge density. Due to the net electric charge, Ewald summation algorithm cannot be used for modeling long-range Coulomb interactions. Instead, the cutoff distance used for Coulomb forces is systematically increased until the density distribution and orientation of water atoms converged to a unified profile. Liquid density near the walls increases with increased surface charge density, and the water molecules reorient their dipoles with oxygen atoms facing the positively charged surfaces. This effect weakens away from the charged surfaces. Force-driven water flows in graphene nano-channels exhibit slip lengths over 60 nm, which result in plug-like velocity profiles in sufficiently small nano-channels. With increased surface charge density, the slip length decreases and the apparent viscosity of water increases, leading to parabolic velocity profiles and decreased flow rates. Results of this study are relevant for water desalination applications, where optimization of the surface charge for ion removal with maximum flow rate is desired.     

Surface–gas interaction effects on nanoscale gas flows

Molecular dynamics (MD) method is used to simulate shear driven argon gas flows in the early transition and free molecular flow regimes to investigate surface effects as a function of the surface–gas potential strength ratio (ε_wf/ε_ff). Results show a bulk flow region and a near wall region that extends three molecular diameters away from the surfaces. Within the near wall region the velocity, density, and shear stress distributions exhibit deviations from the kinetic theory predictions. Increased ε_wf/ε_ff results in increased gas density, leading toward monolayer adsorption on surfaces. The near wall velocity profile shows reduced gas slip, and eventually velocity stick with increased ε_wf/ε_ff. Using MD predicted shear stress values and kinetic theory, tangential momentum accommodation coefficients (TMAC) are calculated as a function of ε_wf/ε_ff, and TMAC values are shown to be independent of the Knudsen number. Presence of this near wall region breaks down the dynamic similarity between rarefied and nanoscale gas flows.     

A slip model for micro/nano gas flows induced by body forces

A slip model for gas flows in micro/nano-channels induced by external body forces is derived based on Maxwell’s collision theory between gas molecules and the wall. The model modifies the relationship between slip velocity and velocity gradient at the walls by introducing a new parameter in addition to the classic Tangential Momentum Accommodation Coefficient. Three-dimensional Molecular Dynamics simulations of helium gas flows under uniform body force field between copper flat walls with different channel height are used to validate the model and to determine this new parameter.     

Drag reduction in transitional linearized channel flow using distributed control

This work focuses on feedback control of incompressible transitional Newtonian channel flow described by the twodimensional linearized Navier-Stokes equations. The control objective is to use distributed feedback to achieve stabilization of the parabolic velocity profile, for values of the Reynolds number for which this profile is unstable, and therefore to reduce the frictional drag exerted on the lower channel wall compared to the open-loop values. The control system uses measurements of shear stresses on the lower channel wall and the control actuation is assumed to be in the form of electromagnetic Lorentz forces applied to the flow near the bottom wall. Galerkin's method is initially used to derive a high-order discretization of the linearized flow field that captures the flow instability and accounts for the effect of control actuation on all the modes. Then, a low-order approximation of the linearized flow field is derived and used for the synthesis of a linear output feedback controller that enforces stability in the high-order closed-loop system. The controller is applied to a simulated transitional linearized channel flow and is shown to stabilize the flow field at the parabolic profile and significantly reduce the drag on the lower channel wall.     

Molecular dynamics simulation of nanofluid’s flow behaviors in the near-wall model and main flow model

The flow behaviors of nanofluids were studied in this paper using molecular dynamics (MD) simulation. Two MD simulation systems that are the near-wall model and main flow model were built. The nanofluid model consisted of one copper nanoparticle and liquid argon as base liquid. For the near-wall model, the nanoparticle that was very close to the wall would not move with the main flowing due to the overlap between the solid-like layer near the wall and the adsorbed layer around the nanoparticle, but it still had rotational motion. When the nanoparticle is far away from the wall (d > 11 Å), the nanoparticle not only had rotational motion, but also had translation. In the main flow model, the nanoparticle would rotate and translate besides main flowing. There was slip velocity between nanoparticles and liquid argon in both of the two simulation models. The flow behaviors of nanofluids exhibited obviously characteristics of two-phase flow. Because of the irregular motions of nanoparticles and the slip velocity between the two phases, the velocity fluctuation in nanofluids was enhanced.     

Molecular dynamics simulation of fluid containing gas in hydrophilic rough wall nanochannels

This study performed the molecular dynamic simulations to investigate the boundary behavior of liquid water with entrapped gas bubbles over various hydrophilic roughened substrates. A “liquid–gas–vapor coexistence setup” was employed to maintain a constant thermodynamic state during individual equilibrium simulations and corresponding non-equilibrium Poiseuille flow cases. The two roughened substrates (Si(100) and graphite) adopted in this study present similar contact angles and slip length with gas-free fluid. By considering the effects of argon molecules at the interface, we demonstrated that the boundary slip behavior differed dramatically between these two rough wall channels. This divergence can be attributed to differences in the morphology of argon bubble at the interface due to discrepancies in the atomic arrangement and wall–fluid interaction energy. Furthermore, the density of gas at the interface had a significant impact on the effective slip length of the roughened graphite substrate, whereas shear rate \(\dot{\gamma }\) presented no noticeable influence. On the roughened Si(100) surface, the morphology of the argon bubbles exhibited far higher meniscus curvature and unstable properties under hydrodynamic effects. Thus, this substrate exhibited no slip to slight negative slip and no remarkable influence from either the density of gas at the interface or shear rate. In the present study, we demonstrate that the morphology and behavior of interfacial gas bubbles are influenced by the parameters of wall–fluid interaction as well as the atomic arrangement of the substrate. Our results related to nanochannel flow reveal that different surfaces, such as Si(100) and graphite, may possess similar intrinsic wettability; however, properties of the interfacial gas bubbles can lead to noticeable changes in interfacial characteristics resulting in various degrees of boundary slippage.     

Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions

The effect of interfacial slip on steady-state and time-periodic flows of monatomic liquids is investigated using non-equilibrium molecular dynamics simulations. The fluid phase is confined between atomically smooth rigid walls, and the fluid flows are induced by moving one of the walls. In steady shear flows, the slip length increases almost linearly with shear rate. We found that the velocity profiles in oscillatory flows are well described by the Stokes flow solution with the slip length that depends on the local shear rate. Interestingly, the rate dependence of the slip length obtained in steady shear flows is recovered when the slip length in oscillatory flows is plotted as a function of the local shear rate magnitude. For both types of flows, the friction coefficient at the liquid–solid interface correlates well with the structure of the first fluid layer near the solid wall.     

Multi-scale study of liquid flow in micro/nanochannels: effects of surface wettability and topology

The paper reports parametric study, using a molecular dynamics–continuum hybrid simulation method, of liquid flow in micro/nanochannels with surface nanostructures. The effects of channel height, shape of roughening element, ratio of pitch to length of roughening element and liquid–solid bonding strengths (representing surface wettability) on the velocity and temperature boundary conditions are investigated. The velocity boundary condition is found to shift from significant slip to locking due to the blocking of the surface nanostructure. The blocking appears weak for small pitch ratio and weak liquid–solid bonding. Distorted streamlines, small random eddies and appreciable density oscillations are seen in the vicinity of the wall for small pitch ratio and strong liquid–solid bonding. On the other hand, smooth streamlines and weak density oscillations are seen for large pitch ratio and weak liquid–solid bonding. Results also reveals that: relative slip length, relative Kapitza length and minus pressure gradient vary with channel height and pitch ratio in functions of power law and approximately linear, respectively; relative slip and Kapitza lengths vary with liquid–solid bonding strength as approximately decreasing power functions (except for the strongest case), whereas minus pressure gradient varies with liquid–solid bonding strength as approximately a logarithm-like function. The effect of shape of roughening element is found to be much less significant compared with the other factors studied.     

Near-wall effects in micro scale Couette flow and heat transfer in the Maxwell-slip regimes

The effects of modified transport characteristics within an extremely thin layer adjacent to the fluid–solid interfaces are investigated for fully developed laminar micro-scale Couette flows with slip boundary conditions. The wall-adjacent layer effects are incorporated into the continuum-based mathematical model by imposing variable viscosity and thermal conductivity values close to the channel walls, for solving the momentum and energy conservation equations. Analytical expressions for the velocity profiles are derived and are subsequently utilized to obtain the temperature variations within the parallel plate channel, as a function of the significant system parameters. It is revealed that the variations in effective viscosity and thermal conductivity values within the wall-adjacent layer have profound influences on the fluid flow and the heat transfer characteristics within the channel, with an interesting interplay with the wall slip boundary conditions. These effects cannot otherwise be accurately captured by employing classical continuum based models for microscale Couette flows that do not take into account the alterations in effective transport properties within the wall adjacent layers.     

Boundary conditions for shear flow past a permeable interface modeled as an array of cylinders

The boundary condition relating the macroscopic jump in the tangential velocity across a permeable interface consisting of a particulate lattice to the shear rate prevailing on either side of the interface is discussed. The computation of the velocity jump hinges on the realization that shear flow on one side of the interface induces a slip velocity on that side and a streaming drift velocity on the other side. The direction and magnitude of the slip and drift velocities depend on the interface constitution, solid fraction, and Reynolds number. Numerical computations are performed for a model two-dimensional interface consisting of a periodic array of cylinders. In the case of longitudinal unidirectional flow, the boundary conditions are defined in terms of previously computed drift and slip velocity coefficients for any ratio of the shear rates above and below the interface and any Reynolds number. To study the behavior in the complementary case of transverse flow, the Navier-Stokes equation is solved numerically using a finite-difference method on an orthogonal grid generated by conformal mapping, using the stream function/vorticity formulation. The results reveal that inertial effects promote the magnitude of the slip and drift velocity, and illustrate the streamline pattern near the interface.     

Nonlocal vibration and instability analysis of carbon nanotubes conveying fluid considering the influences of nanoflow and non-uniform velocity profile

In this article, the influences of non-uniform velocity profile attributable to slip boundary condition and viscosity of fluid on the dynamic instability of carbon nanotubes (CNTs) conveying fluid are investigated. The nonlocal elasticity theory and the Euler–Bernoulli beam theory are employed to derive partial differential equation of nanotubes conveying fluid. Furthermore, a dimensionless momentum correction factor (MCF) is obtained as a function of Knudsen number (Kn) so as to insert the effects of non-uniform velocity profile into the equation of motion. In continuation, complex eigen-frequencies of the system are attained with respect to different boundary conditions, the momentum correction factor, slip boundary condition and nonlocal parameter. The results delineate that considering the effects of non-uniform velocity profile could diminish predicted critical velocity of flow. Therefore, the divergence instability occurs in the lower values of flow velocity. In addition, the MCF decreases through enhancement of Kn; hence, the effects of non-uniform velocity profile are more noticeable for liquid fluid than gas fluid.     

Molecular dynamics simulations of shear-driven gas flows in nano-channels

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.     

A multiplicative decomposition of Poiseuille number on rarefaction and roughness by lattice Boltzmann simulation

Poiseuille number of rarefied gas flow in channels with designed roughness is studied and a multiplicative decomposition of Poiseuille number on the effects of rarefaction and roughness is proposed. The numerical methodology is based on the mesoscopic lattice Boltzmann method. In order to eliminate the effect of compressibility, the incompressible lattice Boltzmann model is used and the periodic boundary is imposed on the inlet and outlet of the channel. The combined bounced condition is applied to simulate the velocity slip on the wall boundary. Numerical results reveal the two opposite effects that velocity gradient and friction factor near the wall increase as roughness effect increases; meanwhile, the increments of the rarefaction effect and velocity slip lead to a corresponding decrement of friction factor. An empirical relation of Poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition, and then is validated by available experimental and numerical results.     

Viscous heating in nanoscale shear driven liquid flows

Three-dimensional Molecular Dynamics (MD) simulations of heat and momentum transport in liquid Argon filled shear-driven nano-channels are performed using 6–12 Lennard–Jones potential interactions. Work done by the viscous stresses heats the fluid, which is dissipated through the channel walls, maintained at isothermal conditions through a recently developed interactive thermal wall model. Shear driven nano-flows for weak wetting surfaces (ε _wf /ε ≤ 0.6) are investigated. Spatial variations in the fluid density, kinematic viscosity, shear- and energy dissipation rates are presented. Temperature profiles in the nano-channel are obtained as a function of the surface wettability, shear rate and the intermolecular stiffness of wall molecules. The energy dissipation rate is almost a constant for ε _wf /ε ≤ 0.6, which results in parabolic temperature profiles in the domain with temperature jumps due to the well known Kapitza resistance at the liquid/solid interfaces. Using the energy dissipation rates predicted by MD simulations and the continuum energy equation subjected to the temperature jump boundary conditions developed in [Kim et al. Journal of Chemical Physics, 129, 174701, 2008b], we obtain analytical solutions for the temperature profiles, which agree well with the MD results.     

Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solid–liquid interfaces

Molecular dynamics (MD) simulations of nano-scale flows typically utilize fixed lattice crystal interactions between the fluid and stationary wall molecules. This approach cannot properly model interactions and thermal exchange at the wall–fluid interface. We present a new interactive thermal wall model that can properly simulate the flow and heat transfer in nano-scale channels. The new model utilizes fluid molecules freely interacting with the thermally oscillating wall molecules, which are connected to the lattice positions with “bonds”. Thermostats are applied separately to each layer of the walls to keep the wall temperature constant, while temperature of the fluid is sustained without the application of a thermostat. Two-dimensional MD simulation results for shear driven nano-channel flow shows parabolic temperature distribution within the domain, induced by viscous heating due to a constant shear rate. As a result of the Kapitza resistance, temperature profiles exhibit jumps at the fluid–wall interface. Time dependent simulation results for freezing of liquid argon in a nano-channel are also presented.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

In this work we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow. A Giesekus model is chosen as constitutive equation of the suspending liquid. In order to study the sole effect of the fluid viscoelasticity, both fluid and particle inertia are neglected.The governing equations are solved through the finite element method with proper stabilization techniques to get convergent solutions at relatively large flow rates. An Arbitrary Lagrangian–Eulerian (ALE) formulation is adopted to manage the particle motion. The mesh grid is moved along the flow so as to limit particle motion only in the gradient direction to substantially reduce mesh distortion and remeshing.Viscoelasticity of the suspending fluid induces particle cross-streamline migration. Both large Deborah number and shear thinning speed up the migration velocity. When the particle is small compared to the gap (small confinement), the particle migrates towards the channel centerline or the wall depending on its initial position. Above a critical confinement (large particles), the channel centerline is no longer attracting, and the particle is predicted to migrate towards the closest wall when its initial position is not on the channel centerline. As the particle approaches the wall, the translational velocity in the flow direction is found to become equal to the linear velocity corresponding to the rolling motion over the wall without slip.     

Effects of shear rate and small periodic corrugation on the slip velocity in microscopic domain

We obtain analytically the slip velocity (up to the second order) of shear-thinning fluids inside the periodically corrugated microtube by using the verified fluid model and boundary perturbation method. Our results show that, even the slip length being zero, there is a slip velocity which is proportional to the small amplitude of periodic corrugation, the (referenced) shear rate, the applied forcing, and the orientation or the angle. Our results could be applied to the flow control in microfluidics as well as biofluidics.     

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.     

New approach to mimic rheological actual shear rate under wall slip condition

Engineering with Computers - The presence of wall slip in concentrated suspensions affect the rheological measurements such as shear stress, shear rate, and viscosity. The measured shear rate will...     

Transient response analysis and modeling of near wall flow conditions in a micro channel: evidence of slip flow

An experimental tool for determination of the near wall transport parameters in a micro channel, supported by flow simulation, is presented. The method is based on the transient flow response due to convective diffusion, in absence of specific adsorption. An approximately step-function type temporal solute concentration variation serves as the input signal. The associated response signal of a surface plasmon resonance sensor, acting as an integral part of a micro channel, has been taken as the output signal. It provides the flow-dependent change of the NaOH solute concentration in the channel within the optical detection and near wall distance interval 0 < d < 0.5 μm. The temporal signal evolution and response time, until an initially plain aqueous solution is replaced by the solute, varies inversely with solute concentration and flow rate. In the asymptotic limits, the near wall forced convective and diffusive channel transit times, along with the associated velocities, can be extracted and separated. A low convective near wall flow speed would account for 100% adsorption efficiency. The validity of the scaling relation for Fickian diffusive transport has been confirmed by experiments. Convective near wall flow reveals a distorted parabolic flow profile. This indicates relaxation of the no-slip condition, and presence of slip flow. Neither boundary layer formation, nor near wall micro turbulences have been observed. Eventually, a compact mathematical transient flow model, outlined in the Laplace domain for the electrical equivalent analogue circuit and applicable to the convective diffusion equation, has been developed for the flow transients.