Microscopic Slip Boundary Conditions in Unsteady Fluid Flows

Demonstrating the Interfacial Polymer Thermal Transition from Coil-to-Globule to Coil-to-Stretch under Shear Flow Using SFG and MD Simulation

Revealing interfacial shear-induced structural responsiveness has long been an important topic in that most fluids in nature and human life are in motion and cause interesting boundary phenomena. It is amazing how the polymer chain conformation or local structural features at a boundary change under the effective shear condition. In this study, microfluidic-assisted sum frequency generation (SFG) vibrational spectroscopy and all-atom molecular dynamics (MD) simulation are combined to reveal that the shear flow can effectively block the so-called thermal coil-to-globule transition of the poly(N-isopropylacrylamide) (PNIPAM) brushes on the solid substrate, and the normal coil-to-globule transition transfers to a coil-to-stretch one under shear flow with increasing ambient temperature. Such findings are attributed to the balance between the shear flow and the molecular interaction with respect to the polymer chains and adjacent water molecules, thus demonstrating the significant effect of the shear flow on the structural and dynamic behaviors of the polymer chains at the boundaries from the molecular level.

A review on slip boundary conditions at the nanoscale: recent development and applications

The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed.

Rheology of water in small nanotubes

The properties of water in confinement are very different from those under bulk conditions. In some cases the melting point of ice may be shifted and one may find either ice, icelike water, or a state in which freezing is completely inhibited. Understanding the dynamics and rheology of water in confined media, such as small nanotubes, is of fundamental importance to the biological properties of micro-organisms at low temperatures, to the development of new devices for preserving DNA samples, and for other biological materials and fluids, lubrication, and development of nanostructured materials. We study rheology and dynamics of water in small nanotubes using extensive equilibrium and nonequilibrium molecular dynamics simulations. The results demonstrate that in strong confinement in nanotubes at temperatures significantly below and above bulk freezing temperature water behaves as a shear-thinning fluid at shear rates smaller than the inverse of the relaxation time in the confined medium. In addition, our results indicate the presence of regions in which the local density of water varies significantly over the same range of temperature in the nanotube. These findings may also have important implications for the design of nanofluidic systems.

Non-local viscosity from the Green-Kubo formula

We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the plateau problem [Español et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.

Equilibrium measurement method of slip length based on fluctuating hydrodynamics

We perform equilibrium molecular dynamics simulations for nanoscale fluids confined between two parallel walls and investigate how the autocorrelation function of force acting on one wall is related to the slip length. We demonstrate that for atomically smooth surfaces, the autocorrelation function is accurately described by linearized fluctuating hydrodynamics (LFH). Excellent agreement between the simulation and the LFH solution is found over a wide range of scales, specifically, from the timescale of fluid relaxation even to that of molecular motion. Fitting the simulation data yields a reasonable estimation of the slip length. We show that LFH provides a starting point for examining the relationship between the slip length and the force fluctuations.

Discrete hydrodynamics near solid walls: Non-Markovian effects and the slip boundary condition

A simple Markovian theory for the prediction of averages and correlations of discrete hydrodynamics near parallel solid walls is presented. The discrete momentum of bins is defined through a finite element basis function. The effect of the walls on the fluid is through irreversible extended friction forces appearing in the very equations of hydrodynamics. The Markovian assumption is critically assessed from the exponential decay of the eigenvalues of the correlation matrix of the discrete transverse momentum. We observe that for bins smaller than molecular dimensions, allowing one to resolve the density layering near the wall, the dynamics near the wall is non-Markovian. Bins larger than the molecular size do behave in a Markovian way. We measure the nonlocal viscosity and frictions kernels that appear in the discrete hydrodynamic equations, which are given in terms of Green-Kubo formulas. They suffer dramatically from the plateau problem. We use a recent procedure for reliably extracting the transport kernels out of the plateau-problematic Green-Kubo formula. With the so-measured transport kernels the nonlocal theory predicts very well the decay of the average of the transverse momentum when the initial velocity profile is a plug flow. The theory allows us to derive the slip boundary condition with microscopic expressions for the slip length and the hydrodynamic position of the wall. The slip boundary condition is not satisfied at the initial stages of the discontinous plug flow, but good agreement is obtained at later stages.