Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics and condensed matter physics. This review is intended as a toolbox for fluids at the nanometre scale. After presenting the basic equations that govern fluid behaviour in the continuum limit, we will show how these equations break down and new properties emerge in molecular scale confinement.
We propose a nonlocal model for surface tension. This model, in combination with the Landau-Lifshitz-Navier-Stokes equations, describes mesoscale features of the multiphase flow, including the static (pressure) tensor and curvature dependence of surface tension. The nonlocal model is obtained in the form of an integral of a molecular-force-like function added into the momentum conservation equation. We present an analytical steady-state solution for fluid pressure at the fluid-fluid interface and numerical Smoothed Particle Hydrodynamics solutions that reveal the mesoscopic features of the pro…
We investigate the flow of a nano-scale incompressible ridge of low-volatility liquid along a "chemical channel": a long, straight, and completely wetting stripe embedded in a planar substrate, and sandwiched between two extended less wetting solid regions. Molecular dynamics simulations, a simple long-wavelength approximation, and a full stability analysis based on the Stokes equations are used, and give qualitatively consistent results. While thin liquid ridges are stable both statically and during flow, a (linear) pearling instability develops if the thickness of the ridge exceeds half of t…
We study the time evolution and driven motion of thin liquid films lying on top of chemical patterns on a substrate. Lattice-Boltzmann and molecular dynamics methods are used for simulations of the flow of microscopic and nanoscopic films, respectively. Minimization of fluid surface area is used to examine the corresponding equilibrium free energy landscapes. The focus is on motion across patterns containing diverging and converging flow junctions, with an eye towards applications to lab-on-a-chip devices. Both open liquid-vapor systems driven by body forces and confined liquid-liquid systems …
We study the nanoscale behaviour of the density of a simple fluid in the vicinity of an equilibrium contact line for a wide range of Young contact angles between 40 and 135 degrees. Cuts of the density profile at various positions along the contact line are presented, unravelling the apparent step-wise increase of the film height profile observed in contour plots of the density. The density profile is employed to compute the normal pressure acting on the substrate along the contact line. We observe that for the full range of contact angles, the maximal normal pressure cannot solely be predicte…
A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales (De Fabritiis {\it et. al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as…
We explore the dynamics of a nanoscale doubly-clamped beam that is under high tension, immersed in a viscous fluid, and driven externally by a spatially varying drive force. We develop a theoretical description that is valid for all possible values of tension, includes the motion of the higher modes of the beam, and accounts for a harmonic force that is applied over a limited spatial region of the beam near its ends. We compare our theoretical predictions with experimental measurements for a nanoscale beam that is driven electrothermally and immersed in air and water. The theoretical predictio…
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 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 ang…
Experiments on fluid systems in micro-/nano-scale solid conveyors have shown a violation of the no-slip assumption that have been adopted by the classical fluid mechanics. To correct this mechanics for the fluid slip, various approaches have been proposed to determine the slip boundary conditions. However, these approaches have revealed contradictory results for a variety of systems, and a debate on the mechanisms and the conditions of the fluid slip/no-slip past solid surfaces is sustained for a long time. In this paper, we establish the hybrid continuum-molecular modeling (HCMM) as a general…
We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far-field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are d…
Molecular dynamics simulation is applied to Poiseuille flow of liquid methane in planar graphite channels, covering channel diameters between 3 and 135 nm. On this length scale, a transition is found between the regime where local ordering induced by the wall dominates the entire system and larger channel diameters where the influence of boundary slip is still present, but of a more limited extent. The validity of Darcy's law for pressure-driven flow through porous media is not affected by the transition between these regimes.
The present article reports the governing influence of substituting the M2 site in nanoscale MFe2O4 spinel ferrites by different magnetic metals Fe,Mn,Co,Ni on magnetorheological and magneto elastoviscous behaviors of the corresponding magnetorheological fluids MRFs. Different doped MFe2O4 nanoparticles have been synthesized using the polyol assisted hydrothermal method. Detailed steady and oscillatory shear rheology have been performed on the MRFs to determine the magneto-viscoelastic responses. The MRFs exhibit shear thinning behavior and augmented yield characteristics under influence of ma…
The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular phenomena close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics (MD) simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and co…
Controlling the motion of nano and microscale objects in a fluid environment is a key factor in designing optimized tiny machines that perform mechanical tasks such as transport of drugs or genetic material in cells, fluid mixing to accelerate chemical reactions, and cargo transport in microfluidic chips. Directed motion is made possible by the coupled translational and rotational motion of asymmetric particles. A current challenge in achieving directed and controlled motion at the nanoscale lies in overcoming random Brownian motion due to thermal fluctuations in the fluid. We use a hybrid lat…
A description of thermodynamics for continuum mechanical systems is presented in the coordinate-free language of exterior calculus. First, a careful description of the mathematical tools that are needed to formulate the relevant conservation laws is given. Second, following an axiomatic approach, the two thermodynamic principles will be described, leading to a consistent description of entropy creation mechanisms on manifolds. Third, a specialisation to Fourier-Navier-Stokes fluids will be carried through.
We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring domain described by the Navier-Stokes equations for unsteady flow. The effect of fluctuations from the particle system in the scheme accuracy is also studied.
Compressing a porous, fluid-filled material will drive the interstitial fluid out of the pore space, as when squeezing water out of a kitchen sponge. Inversely, injecting fluid into a porous material can deform the solid structure, as when fracturing a shale for natural gas recovery. These poromechanical interactions play an important role in geological and biological systems across a wide range of scales, from the propagation of magma through the Earth's mantle to the transport of fluid through living cells and tissues. The theory of poroelasticity has been largely successful in modeling poro…
Porous structures of shales are reconstructed based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analyzes of the nanoscale reconstructed shales are performed, including porosity, pore size distribution, specific surface area and pore connectivity. The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) fluid flow model and single-relaxation-time (SRT) LBM diffusion model are adopted to simulate the fluid flow and Knudsen diffusion process within the reconstructed shales, respectively. Tortuosity, intrinsic permeability and …
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear continuum mechanics. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization.…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier-Stokes for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas the actual mass density is treated as a thermodynamic variable. A new set of balance laws is proposed, including a mass balance equation with a non-convective flux. The basic principles of irreversible thermodynamics are used to obtain linear constitutive equations that are expansions of--not only the usual affinities involving gradients of temperature and ve…
A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect.
We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems with interfacial mass. Since the published work is not fully consistent, we provide a rigorous derivation of the local balance equations and the entropy production rates, including all relevant steps and mathematical tools. Special emphasis is put on an axiomatic form of the entropy principle which, at the same time, allows for an efficient closure process. The latter builds on an appropriate representation of the entropy production rates, which is based on structural information being obtained fr…
The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps more importantly, in the investigation of fluid turbulence phenomena, which involve a broad range of scales. In this paper, we rely on the energy equation, along with some kinematical considerations, to establish a consistent couple-stress theory for polar continua that resolves all indeterminacies. After presenting the general formulation and obtaining con…
In this work, we present a computational fluid-structure interaction (FSI) study for a healthy patient-specific pulmonary arterial tree using the unified continuum and variational multiscale (VMS) formulation we previously developed. The unified framework is particularly well-suited for FSI, as the fluid and solid sub-problems are addressed in essentially the same manner and can thus be uniformly integrated in time with the generalized-$α$ method. In addition, the VMS formulation provides a mechanism for large-eddy simulation in the fluid sub-problem and pressure stabilization in the solid sub…
In this work, we will present a physically consistent theory to derive the governing equations of the Large Eddy Simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable simulations of turbulent flows. Therefore, we assume that a coarse-grained fluid element, subsequently called super fluid element, can be locally defined comprising a large number of smaller elementary fluid elements. Then, similar to non-equilibrium molecular dynamics (NEMD), in which the transport equations of an elementary fluid element can be consistently reconst…
In part I of this paper, I proposed a new set of equations, which I refer to as the M(D,η)-formulation and which differs from the Navier-Stokes-Fourier description of fluid motion. Here, I use these equations to model several classic examples in fluid mechanics, with the intention of providing a general sense of comparison between the two approaches. A few broad facts emerge: (1) it is as simple--or in most cases, much simpler--to find solutions with the M(D,η)-formulation, (2) for some examples, there is not much of a difference in predictions--in fact, for sound propagation and for examples …
Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity and diffusion in conditions of a thermally nonequilibrium and heterogeneous composition continuum. It is rotined that the appearance of a temperature drop in fluid stipulates the appearance of the continuum stratification and formation of the flowing bodies interacting among themselves. It is rotined that the known expressions for a thermal conductivity, visco…
The union of quantum fluids research with nanoscience is rich with opportunities for new physics. The relevant length scales in quantum fluids, 3He in particular, are comparable to those possible using microfluidic and nanofluidic devices. In this article, we will briefly review how the physics of quantum fluids depends strongly on confinement on the microscale and nanoscale. Then we present devices fabricated specifically for quantum fluids research, with cavity sizes ranging from 30 nm to 11 microns deep, and the characterization of these devices for low temperature quantum fluids experiment…
We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic applications. Both dense fluid and dilute gas formulations are considered. The choice of coupling method and its relation to the fluid physics is discussed. The differences in hybrid methods resulting from underlying compressible and incompressible continuum formulations as well as the importance of timescale decoupling are highlighted. We also discuss recently developed compressible and incompressible hybrid methods for dilute gases. The incompressible framework is based on the Schwarz alternating method whereas the com…
In this paper a new monolithic Eulerian formulation in the framework of non-classical continuum is presented for the analysis of fluid-strucuture interaction problems. In this respect, Cosserat continuum theory taking into account the micro-rotational degrees of freedom of the particles is considered. Continuum description of the model and variational formulation of the governing flow dynamics for non-classical -fluid-structure interaction nCFSI is presented. The model is analyzed by computing a well known benchmark problem by Hecht and Pironneau (2017). The algorithmic description is presente…
We propose a computational framework for vascular fluid-structure interaction (FSI), focusing on biomechanical modeling, geometric modeling, and solver technology. The biomechanical model is constructed based on the unified continuum formulation. We highlight that the chosen time integration scheme differs from existing implicit FSI integration methods in that it is indeed second-order accurate, does not suffer from the overshoot phenomenon, and optimally dissipates high-frequency modes in both subproblems. We propose a pipeline for generating subject-specific meshes for FSI analysis for anato…
