Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Rheology of dilute polyelectrolyte solutions in narrow channels

The shear flow of dilute polyelectrolyte solutions bounded by either neutral or repulsive walls is modeled using a nonlinear dumbbell with conformation-dependent friction. Assuming that the configurational probability density function depends on the internal coordinates (r) and the distance of the center of mass of the molecule to the walls, coupled differential equations for the tensor moments <rr> are obtained. Coulombic repulsion between beads is considered to simulate the charge repulsion between ionized sites distributed along the backbone of a real polyelectrolyte. The repulsive interaction between the polyelectrolyte molecule and the charged walls is that of the DLVO model and the molecule is considered to be a charged sphere. Numerical solutions for the components of the tensor <rr> are worked out with the preaverage approach, and only when neutral walls considered are exact solutions obtained. Viscosity results show that in the limit of very wide channels, the corresponding viscosity in the bulk is obtained. The wall repulsion on the charged molecules produces migration of molecules towards the center of the channel resulting in a depleted layer with lower viscosity next to the walls. The calculated slip phenomenon using the method employed by Grisafi and Brunn is dependent on the beads repulsion and the shear rate. The slip velocity obtained with the Mooney method shows similarities with available experimental results for polyelectrolyte solutions. Birefringence calculations are performed in narrow and wide channels for different bead repulsions, with interesting results for both flexible and rigid molecules. Received: 26 September 1998 Accepted in revised form: 11 March 1999     

On the wall slip of polymer blends

The slip flow of the polypropylene (PP)/poly[ethylene‐co‐(vinyl acetate)] (EVA) system was studied in a capillary rheometer for shear rates of 40–1000 s^?1 at four temperatures. Three dies made of aluminum with a length/diameter (L/D) ratio of 15 and diameters of 1.59, 1.19, and 0.79 mm provided the flow data. Calculations of the slip velocity by the Mooney method showed power‐law behavior with the stress. Blends were prepared at various proportions of PP and EVA for observation of the variation of the slip velocity for different compositions and temperatures. Direct microscopic observations of the slip layer on extruded samples showed domains of the dispersed phase unevenly distributed between the slip layer and the core and provided estimates of the thickness of the layer adjacent to the capillary wall. Results showed that the viscosity in the slip layer was 10–100 times lower than that in the bulk for the same value of the shear stress. In terms of the extrapolation length, the development of the slip layer was the result of different disentanglement dynamics of the molecules in the slip layer in comparison with those in the bulk. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 303–316, 2002     

Permeative flows in cholesterics: shear and Poiseuille flows

By using a lattice Boltzmann scheme that solves the Beris-Edwards equations of motion describing liquid-crystal hydrodynamics, we study the response of cholesterics to shear and Poiseuille flows. The geometry we focus on is a flow along the direction of the helical axis, which is known to give rise to permeation. For both shear and Poiseuille flow we find that the boundary conditions on the director field are crucial in determining the rheological properties of the liquid crystal. For helices pinned at the boundaries, a small forcing leads to a large viscosity increase whereas a stronger forcing induces a sharp decrease towards the Newtonian value. This shear thinning behavior is in agreement with experiments and previous analytic results. If, on the other hand, the director is free to rotate at the walls, different behaviors are found depending on the symmetry of the steady-state primary flow. Some of the cases considered are compared to a similar imposed flow but with the helix lying perpendicular to the plates, for which no viscosity increase is observed.     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009     

Schmidt number effects in dissipative particle dynamics simulation of polymers

Simulation studies for dilute polymeric systems are presented using the dissipative particle dynamics method. By employing two different thermostats, the velocity-Verlet and Lowe's scheme, we show that the Schmidt number (S(c)) of the solvent strongly affects nonequilibrium polymeric quantities. The fractional extension of wormlike chains subjected to steady shear is obtained as a function of S(c). Poiseuille flow in microchannels for fixed polymer concentration and varying number of repeated units within a chain is simulated. The nonuniform concentration profiles and their dependence on S(c) are computed. We show the effect of the bounce-forward wall boundary condition on the depletion layer thickness. A power law fit of the velocity profile in stratified Poiseuille flow in a microchannel yields wall viscosities different from bulk values derived from uniform, steady plane Couette flow. The form of the velocity profiles indicates that the slip flow model is not useful for the conditions of these calculations.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.     

Capillary osmosis through porous partitions and properties of boundary layers of solutions

According to the theory of one of the authors, when the adsorption layer on a solid surface in contact with a solution is mobile, the gradient of concentration of the solution along the solid surface causes capillary-osmotic slip in addition to diffusional flow of the liquid. In the case of porous partitions separating solutions of different concentrations, slip along the pore walls causes convective transfer of the solution, i.e., capillary osmosis. A special unit has been constructed to study this phenomenon and the velocity of capillary-osmotic flow is measured with the aid of radioactive indicators. Formulas are derived for the arising capillary-osmotic flow of substance, making it possible, by introducing a correction for the diffusional flow, to calculate the velocity of capillary-osmotic slip.

There is usually on the surface of glass both a double layer due to the dissociated part of the solution, and an adsorption layer of the undissociated part of the solution. Thus, under real conditions there are flows due both to the double layer on the glass surface and to the mobile part of the adsorption layer of the undissociated part of the solution. Knowing the values of the capillary-osmotic slip and the zeta-potential, one can calculate which of these processes predominates. For this purpose capillary-osmotic flows through Shott filters of certain aqueous solutions and nonaqueous mixtures are measured simultaneously with their zeta-potentials, on the surface of Shott glass. It is shown that for these solutions the flows caused by the double layer at the glass surface are small compared to those due to the mobile part of the adsorption layer of the undissociated part of the solution.

Expressions are obtained for positive and negative adsorption of the undissociated part of the solution, relating the capillary-osmotic velocity to the constant of effective molecular attraction between the dissolved molecules and the glass.

Hence, the constants of molecular attraction between the molecules and the glass, and the average distance between the solute molecules and the plane of slip are calculated from experimental results for the solutions studied.

Thus, the experimental method and calculations proposed may be used for analyzing the structure of adsorption layers at solid-solution interfaces.     

Structural and dynamical properties for confined polymers undergoing planar Poiseuille flow

The authors present the results from nonequilibrium molecular dynamics simulations for the structural and dynamical properties of highly confined linear polymer fluids undergoing planar Poiseuille flow. They study systems confined within pores of several atomic diameters in width and investigate the dependence of the density profiles, the mean squared radius of gyration, the mean squared end-to-end distance, streaming velocity, strain rate, shear stress, and streaming angular velocity as functions of average fluid density and chain length. Their simulation results show that, sufficiently far from the walls, the radius of gyration for molecules under shear in the middle of the pore follows the power law Rg=ANbnu, where Nb is the number of bonds and the exponent has a value of 0.5 which resembles the value for a homogeneous equilibrium fluid. Under the conditions simulated, the authors find the onset of flat velocity profiles but with very little wall slippage. These flat profiles are most likely due to the restricted layering of the fluid into just one or two molecular layers for narrow pore widths compared to chain length, rather than typical plug-flow conditions. The angular velocity is shown to be proportional to half the strain rate in the pore interior when the chain length is sufficiently small compared to the pore width, consistent with the behavior for homogeneous fluids in the linear regime.     

Simulation of tethered oligomers in nanochannels using multi-particle collision dynamics

The effect of a high Reynold's number, pressure-driven flow of a compressible gas on the conformation of an oligomer tethered to the wall of a square channel is studied under both ideal solvent and poor solvent conditions using a hybrid multiparticle collision dynamics and molecular dynamics algorithm. Unlike previous studies, the flow field contains an elongational component in addition to a shear component as well as fluid slip near the walls and results in a Schmidt number for the polymer beads that is less than unity. In both solvent regimes the oligomer is found to extend in the direction of flow. Under the ideal solvent conditions, torsional twisting of the chain and aperiodic cyclical dynamics are observed for the end of the oligomer. Under poor solvent conditions, a metastable helix forms in the end of the chain despite the lack of any attractive potential between beads in the oligomeric chain. The formation of the helix is postulated to be the result of a solvent induced chain collapse that has been confined to a single dimension by a strong flow field.     

Boundary slip and wetting properties of interfaces: correlation of the contact angle with the slip length

Correlations between contact angle, a measure of the wetting of surfaces, and slip length are developed using nonequilibrium molecular dynamics for a Lennard-Jones fluid in Couette flow between graphitelike hexagonal-lattice walls. The fluid-wall interaction is varied by modulating the interfacial energy parameter epsilonr=epsilonsfepsilonff and the size parameter sigmar=sigmasfsigmaff, (s=solid, f=fluid) to achieve hydrophobicity (solvophobicity) or hydrophilicity (solvophilicity). The effects of surface chemistry, as well as the effects of temperature and shear rate on the slip length are determined. The contact angle increases from 25 degrees to 147 degrees on highly hydrophobic surfaces (as epsilonr decreases from 0.5 to 0.1), as expected. The slip length is functionally dependent on the affinity strength parameters epsilonr and sigmar: increasing logarithmically with decreasing surface energy epsilonr (i.e., more hydrophobic), while decreasing with power law with decreasing size sigmar. The mechanism for the latter is different from the energetic case. While weak wall forces (small epsilonr) produce hydrophobicity, larger sigmar smoothes out the surface roughness. Both tend to increase the slip. The slip length grows rapidly with a high shear rate, as wall velocity increases three decades from 100 to 10(5) ms. We demonstrate that fluid-solid interfaces with low epsilonr and high sigmar should be chosen to increase slip and are prime candidates for drag reduction.     

Molecular diffusion and slip boundary conditions at smooth 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. 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 the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.     

Pressure dependence of confined liquid behavior subjected to boundary-driven shear

Non-equilibrium molecular dynamics simulations of boundary-driven sheared Lennard-Jones liquids at variable pressure up to 5 GPa (for argon) reveal a rich out-of-equilibrium phase behavior with a strong degree of shear localization. At the lowest apparent shear rate considered (wall speed ~1 m s(-1)) the confined region is an homogeneously sheared solid (S) with no slip at the walls. This transforms at higher shear rates to a non-flowing plug with slip at the walls, referred to as the plug slip (PS) state. At higher shear rate a central localized (CL) state formed in which the shear gradient was localized in the center of the film, with the rest of the confined sample in a crystalline state commensurate with the wall lattice. The central zone liquidlike region increased in width with shear rate. A continuous rounded temperature profile across the whole system reflects strong dynamical coupling between the wall and confined region. The temperature rise in the confined film is consistent with the Brinkman number. The transition from the PS to CL states typically occurred at a wall speed near where the shear stress approached a critical value of ~3% of the shear modulus, and also near the peak in the traction coefficient, μ. The peak traction coefficient values computed, ~0.12-0.14 at 1000 MPa agree with those found for traction fluids and occur when the confined liquid is in the PS and CL states. At low wall speeds slip can occur at one wall and stick at the other. Poorly wetting liquids manifest long-lived asymmetries in the confined liquid properties across the system, and a shift in solid-liquid phase co-existence to higher shear rates. A non-equilibrium phase diagram based on these results is proposed. The good agreement of the tribological response of the Lennard-Jones fluid with that of more complicated molecular systems suggests that a corresponding states scaling of the tribological behavior could apply.     

纳米通道内混合气体流动的分子动力学模拟

采用非平衡分子动力学方法, 模拟了混合气体在纳米通道中的Poiseuille流动. 结果显示气体混合物的化学成分与物理结构不再均匀一致, 随着亲水性气体粒子的减少, 亲水性粒子逐渐被吸附于壁面, 而疏水性粒子主要分布于通道中间. 当亲水性粒子为10%时, 混合气体在壁面处形成有序的“类固体”. 在本文的模拟条件下, 流体速度分布显示混合气体流动速度随着疏水性粒子比例的增加而升高; 同时, 混合气体滑移速度也从负滑移速度逐渐转变为正滑移速度.     

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.     

Effect of liquid slip in electrokinetic parallel-plate microchannel flow

Liquid slip at hydrophobic surfaces in microchannels has frequently been observed. We present here an analytical solution for oscillating flow in parallel-plate microchannels by combining the electrokinetic transport phenomena with Navier's slip condition. Our parametric results suggest that electrokinetic transport phenomena and liquid slip at channel walls are both important and should be considered simultaneously. Their significance depends on channel wall material, electrolyte concentration, and pH. For pressure-driven-flow, liquid slip counteracts the effect by the electrical double layer and induces a larger flow rate. A higher apparent viscosity would be predicted if slip is neglected. For electroosmotic flow, liquid slip alters the flow rate by about 20% for a thick electrical double layer. Our results provide design guidelines to precisely control time-dependent microflow in hydrophobic microfluidic microelectromechanical system devices.     

Effect of surface roughness on rate-dependent slip in simple fluids

Molecular dynamics simulations are used to investigate the influence of molecular-scale surface roughness on the slip behavior in thin liquid films. The slip length increases almost linearly with the shear rate for atomically smooth rigid walls and incommensurate structures of the liquid/solid interface. The thermal fluctuations of the wall atoms lead to an effective surface roughness, which makes the slip length weakly dependent on the shear rate. With increasing the elastic stiffness of the wall, the surface roughness smoothes out and the strong rate dependence is restored again. Both periodically and randomly corrugated rigid surfaces reduce the slip length and its shear rate dependence.     

Effects of overlapping electric double layer on mass transport of a macro‐solute across porous wall of a micro/nanochannel for power law fluid

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye–Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential −73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant.     

Near-wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5 µm in a dilute (volume fractions φ_∞ < 4 × 10⁻³) suspension assemble into highly elongated structures called “bands” under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Re_p < < 1. The particles are first concentrated near, then form “bands” within ∼6 µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual “tracer” particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%–50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.