Continuum Fluid Mechanics Research Articles

Experimental and Theoretical Insights into Interfacial Properties of 2D Materials for Selective Water Transport Membranes: A Critical Review.

Interfacial properties, such as wettability and friction, play critical roles in nanofluidics and desalination. Understanding the interfacial properties of two-dimensional (2D) materials is crucial in these applications due to the close interaction between liquids and the solid surface. The most important interfacial properties of a solid surface include the water contact angle, which quantifies the extent of interactions between the surface and water, and the water slip length, which determines how much faster water can flow on the surface beyond the predictions of continuum fluid mechanics. This Review seeks to elucidate the mechanism that governs the interfacial properties of diverse 2D materials, including transition metal dichalcogenides (e.g., MoS2), graphene, and hexagonal boron nitride (hBN). Our work consolidates existing experimental and computational insights into 2D material synthesis and modeling and explores their interfacial properties for desalination. We investigated the capabilities of density functional theory and molecular dynamics simulations in analyzing the interfacial properties of 2D materials. Specifically, we highlight how MD simulations have revolutionized our understanding of these properties, paving the way for their effective application in desalination. This Review of the synthesis and interfacial properties of 2D materials unlocks opportunities for further advancement and optimization in desalination.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Estimating water transport in carbon nanotubes: a critical review and inclusion of scale effects.

The quasi-frictionless water flow across graphitic surfaces offers vast opportunities for a wide range of applications from biomedical science to energy. However, the conflicting experimental results impede a clear understanding of the transport mechanism and desired flow control. Existing literature proposes numerous modifications and updated boundary conditions to extend classical hydrodynamic theories for nanoflows, yet a consensus or definitive conclusion remains elusive. This study presents a critical review of the proposed modifications of the pressure driven flow or the Hagen-Poiseuille (HP) equations to estimate the flow enhancement through carbon nanotubes (CNTs). For such a case, we performed (semi-)classical molecular dynamics simulations of water flow in various sizes of CNTs, applied the different forms of boundary definitions from the literature, and derived HP equation models by implementing these modifications. By aggregating seven distinct experimental datasets, we tested various flow enhancement models against our measurements. Our findings indicate that including the interfacial layering-based dynamic slip-definition in the proposed HP equations yields accurate estimations. While considering interfacial viscosity predicts the individual CNT experiments well, using the experimental viscosity yields better estimations of measurements for the water flow enhancement through membranes of CNTs. This critical review testing existing literature demonstrates how to refine continuum fluid mechanics to predict water flow enhancement at the nanoscale providing holistic multiscale modeling.

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

The aim of this paper is twofold: the first aim is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second aim is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, for bulk flow, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics; (ii) the construction of an appropriate discrete equilibrium distribution function recovering all the desired kinetic moments; (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ( $f-f^{(eq)}$). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid–vapour density ratio, curbing spurious currents, and ensuring mass/momentum/energy conservation. Compared with the DBM with only first-order THNE (Ganet al.,Soft Matt., vol. 11 (26), 2015, pp. 5336–5345), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate and strong THNE cases even when the local Knudsen number exceeds$1/3$. Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension suppresses the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

Modeling the colloidal physics of translation elongation in E. coli

An exciting frontier in the study of biological cells resides at the interface between biology and colloid physics: cellular processes that operate over colloidal length scales, where continuum fluid mechanics and Brownian motion underlie whole-cell scale behavior. It is at this scale that much of cell machinery operates and is where reconstitution and manipulation of cells is most challenging. This operational regime is centered between the two well-studied limits of structural and systems biology: the former focuses on atomistic-scale spatial resolution with little time evolution, and the latter on kinetic models that abstract space away.

A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes

A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first-order hyperbolic formulation of continuum fluid and solid mechanics, namely the Godunov-Peshkov-Romenski (GPR) model. The scheme provably respects the stiff relaxation limits of the continuous model at the fully discrete level, thus it is asymptotic preserving. Furthermore, the GCL is satisfied by a compatible discretization that makes use of a nodal solver to compute vertex-based fluxes that are used both for the motion of the computational mesh as well as for the time evolution of the governing PDEs. Second order of accuracy in space is achieved using a TVD piecewise linear reconstruction, while an implicit-explicit (IMEX) Runge-Kutta time discretization allows the scheme to obtain higher accuracy also in time. Particular care is devoted to the design of a stiff ODE solver, based on approximate analytical solutions of the governing equations, that plays a crucial role when the visco-plastic limit of the model is approached. We demonstrate the accuracy and robustness of the scheme on a wide spectrum of material responses covered by the unified continuum model that includes inviscid hydrodynamics, viscous heat conducting fluids, elastic and elasto-plastic solids in multidimensional settings.

Computational synthesis of 2D materials grown by chemical vapor deposition

The exotic properties of 2D materials made them ideal candidates for applications in quantum computing, flexible electronics, and energy technologies. A major barrier to their adaptation for industrial applications is their controllable and reproducible growth at a large scale. A significant effort has been devoted to the chemical vapor deposition (CVD) growth of wafer-scale highly crystalline monolayer materials through exhaustive trial-and-error experimentations. However, major challenges remain as the final morphology and growth quality of the 2D materials may significantly change upon subtle variation in growth conditions. Here, we introduced a multiscale/multiphysics model based on coupling continuum fluid mechanics and phase-field models for CVD growth of 2D materials. It connects the macroscale experimentally controllable parameters, such as inlet velocity and temperature, and mesoscale growth parameters such as surface diffusion and deposition rates, to morphology of the as-grown 2D materials. We considered WSe2 as our model material and established a relationship between the macroscale growth parameters and the growth coverage. Our model can guide the CVD growth of monolayer materials and paves the way to their synthesis-by-design.Graphic abstract

Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosity concept of the Navier-Stokes theory and representation of the solid state as an infinitely rigid non-deformable solid, the solid state in our theory is deformable and the fluid state is considered rather as a “melted” solid via a certain procedure of relaxation of tangential stresses similar to Maxwell’s visco-elasticity theory. The model is formulated as a system of first-order hyperbolic partial differential equations with possibly stiff non-linear relaxation source terms. The computational strategy is based on a staggered semi-implicit scheme which can be applied in particular to low-Mach number flows as usually required for flows of non-Newtonian fluids. The applicability of the model and numerical scheme is demonstrated on a few standard benchmark test cases such as Couette, Hagen-Poiseuille, and lid-driven cavity flows. The numerical solution is compared with analytical or numerical solutions of the Navier-Stokes theory with the Herschel-Bulkley constitutive model for nonlinear viscosity.

Thermo-osmosis in hydrophilic nanochannels: mechanism and size effect.

Understanding thermo-osmosis in nanoscale channels and pores is essential for both theoretical advances of thermally induced mass flow and a wide range of emerging industrial applications. We present a new mechanistic understanding and quantification of thermo-osmosis at nanometric/sub-nanometric length scales and link the outcomes with the non-equilibrium thermodynamics of the phenomenon. The work is focused on thermo-osmosis of water in quartz slit nanochannels, which is analysed by molecular dynamics (MD) simulations of mechano-caloric and thermo-osmotic systems. We investigate the applicability of Onsager reciprocal relation, irreversible thermodynamics, and continuum fluid mechanics at the nanoscale. Further, we analyse the effects of channel size on the thermo-osmosis coefficient, and show, for the first time, that these arise from specific liquid structures dictated by the channel size. The mechanical conditions of the interfacial water under different temperatures are quantified using a continuum approach (pressure tensor distribution) and a discrete approach (body force per molecule) to elucidate the underlying mechanism of thermo-osmosis. The results show that the fluid molecules located in the boundary layers adjacent to the solid surfaces experience a driving force which generates the thermo-osmotic flow. While the findings provide a fundamental understanding of thermo-osmosis, the methods developed provide a route for analysis of the entire class of coupled heat and mass transport phenomena in nanoscale structures.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles.

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

Dissipative Solutions and Semiflow Selection for the Complete Euler System

To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at the selection of physically relevant solutions. Even under the presence of infinitely many solutions to the full Euler system describing the motion of a compressible inviscid fluid, our approach permits to select a system of solutions (one trajectory for every initial condition) satisfying the classical semiflow property. Moreover, the selection respects the well accepted admissibility criteria for physical solutions, namely, maximization of the entropy production rate and the weak–strong uniqueness principle. Consequently, strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well. To this end, we introduce a notion of dissipative solution, which is given by a triple of density, momentum and total entropy defined as expectations of a suitable measure-valued solution.

Continuum mechanics with torsion

This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irregular dynamics of small scale vortexes, we further generalize our unified first-order hyperbolic formulation of continuum fluid and solid mechanics which treats the flowing medium as a Riemann-Cartan manifold with zero curvature but non-vanishing torsion. We associate the rotational degrees of freedom of the main field of our theory, the distortion field, to the dynamics of microscopic (unresolved) vortexes. The distortion field characterizes the deformation and rotation of the material elements and can be viewed as anholonomic basis triad with non-vanishing torsion. The torsion tensor is then used to characterize distortion's spin and is treated as an independent field with its own time evolution equation. This new governing equation has essentially the structure of the non-linear electrodynamics in a moving medium and can be viewed as a Yang-Mills-type gauge theory. The system is closed by providing an example of the total energy potential. The extended system describes not only irreversible dynamics (which raises the entropy) due to the viscosity or plasticity effect but it also has dispersive features which are due to the reversible energy exchange (which conserves the entropy) between micro and macro scales. Both the irreversible and dispersive processes are represented by relaxation-type algebraic source terms so that the overall system remains first-order hyperbolic. The turbulent state is then treated as an excitation of the equilibrium laminar state due to the non-linear interplay between dissipation and dispersion.

Microkinetic Rate Theory:Formalization, Current Limitations, Prospects As Basis for Continuum Rate Theory

Microkinetic Rate Theory (MRT) has been an important part of chemical kinetics, being taught in undergraduate physics and chemistry courses, and forming the basis of modern descriptor theory used widely in research. In spite of MRT’s ubiquitous importance, it has remain unformalized and ungeneralized. In this talk, MRT is formalized and generalized. MRT is cast as an algebraic expansion and those matrix elements forming the coefficients of the generalization defined in terms of reaction rate constants, which are in turn connect to statistical mechanics. A transport formulation of MRT is given and it shown that Fickian diffusion is a subset of MRT. MRT is shown to deviate from direct kMC simulations in a certain rate regime which is attributed to phenomenologically distinct stochastic and deterministic rate regimes, similar to diffusion and continuum fluid mechanics, but relevant to chemical and complex kinetics.

Absorption and dispersion of low-frequency sound waves in the main cloud layers of Venus

We present predictions for the acoustic wavenumbers at low frequencies in the condensational cloud layers of Venus, occurring between 50 and 70 km, approximately. While the general thermodynamics of Earth clouds is well understood, that of Venusian clouds is still a matter of debate. Venus' clouds are formed primarily of H2O and H2SO4 vapors and aqueous sulfuric acid droplets, the fluxes of which are not fully constrained due to the few insitu observations. This study is based on and adapted from the terrestrial model of Baudoin et al. (J. Acoust. Soc. Am. 130, 1142 (2011)). Inside the clouds, the Navier-Stokes equations of continuum fluid mechanics are used for the gaseous (dry + vapor) and liquid phases of H2O and H2SO4, combined with the equations describing the evaporation/condensation processes; the gaseous phase is treated as an ideal gas. Outside the clouds, in the CO2—dominated atmosphere, the van der Waals equation of state is used. [The work was supported by a Grant from the Louisiana Space Consortium (LaSPACE).]

Translational diffusion of proteins in nanochannels.

Hydrodynamic interactions play an important role in the transport of analytes through nanoscale devices. Of particular note is the role that no-slip boundary conditions have on the drag coefficient of confined particles and molecules. In this work, we use a coarse grained molecular dynamics model to measure the diffusion coefficients of proteins confined within cylindrical nanochannels of similar dimension. Finite-size corrected bulk diffusion coefficients are found to agree with experimental data, while in channels, a good match is found between theoretical expressions based on continuum fluid mechanics and the reduction of the translational diffusion coefficient across a range of protein to channel size ratios. These results demonstrate that it is possible to directly use molecular simulation to make quantitative predictions of the effects of hydrodynamics on diffusion at length scales of order 1 nm.

Temperature profiles and heat fluxes observed in molecular dynamics simulations of force-driven liquid flows.

This paper concentrates on the unconventional temperature profiles and heat fluxes observed in non-equilibrium molecular dynamics (MD) simulations of force-driven liquid flows in nano-channels. Using MD simulations of liquid argon flows in gold nano-channels, we investigate the manifestation of the first law of thermodynamics for the MD system, and compare it with that of the continuum fluid mechanics. While the energy equation for the continuum system results in heat conduction determined by viscous heating, the first law of thermodynamics in the MD system includes an additional slip-heating term. Interaction strength between argon and gold molecules is varied in order to investigate the effects of slip-velocity on the slip-heating term and the resulting temperature profiles. Heat fluxes and temperature profiles from "continuum", "continuum augmented with slip-heating", and "heat conduction due to the power input by the driving force" are modeled and compared with the MD results. The continuum model can neither predict the heat fluxes nor the temperature profiles from MD simulations. While the continuum model augmented with slip-heating matches the MD heat fluxes, the resulting temperature profiles do not agree with the MD predictions. Overall the analytical model based on "heat conduction due to power input by the driving force" matches the heat fluxes from MD simulations, while the temperature profiles match MD predictions using an effective thermal conductivity that is about 70% of the thermodynamic value. Using different liquid-wall pairs affects the slip velocity, temperature jump, and the resulting thermal conductivity of the fluid, but results in similar physical observations. The inability of the MD method in mimicking continuum fluid mechanics in energy transport for force-driven liquid flows is scale independent, and it is more likely a numerical artifact.

Electroviscous effects on thermal transport of electrolytes in pressure driven flow through nanoslit

Fluid flow through micro/nanofluidics is of utmost importance in analyzing mechanical, biological and medical systems. Biological liquids are often electrolytes that produce spontaneous electrokinetic effects when flowing through pores and channels. The streaming potential which is resultant of this electrokinetic phenomenon drives the ions in the channel to move in the direction opposite to the pressure-driven flow and causes a resistance against fluid flow along the channel. It is simply similar to the case when the viscosity of the fluid is slightly increased. It is expected to have a lower flow rate in the presence of the electroviscous effects; however, understanding of these effects on thermal transport characteristics would be interesting. The present study attempts to present a theoretical investigation of the electroviscous effects on heat transfer in nanofluidics based on continuum fluid mechanics while boundary slip is assumed on the walls. Results show that the presence of electroviscous effects will remarkably enhance the heat transfer rate.

Lattice Boltzmann based simulation of gas flow regimes in low permeability porous media: Klinkenberg’s region and beyond

Tight gas reservoirs are of prominent importance among unconventional petroleum reservoirs. Due to the complicated flow dynamics of gas in tight porous media and compressibility effects, corrections have to be applied to the Darcy equation so that it can properly predict gas flow dynamics. As the mean pore diameter of tight rocks (e.g. shales) decreases, the ratio of the mean free path to the pore diameter, known as the non-dimensional Knudsen number, rises, the gas rarefaction effects becomes important, and the condition of no-slip on the pore surface is violated. Proper treatments of these complexities have been attempted by using classical continuum fluid mechanics and kinetic theory of gases approaches. The most well-known slip condition correction was presented by Klinkenberg in 1941. Many researchers have tried to correct and extend Klinkenberg's model beyond the slip flow regime. In this research the slip condition of the rarefied gas in low permeability simple porous media is studied by the lattice Boltzmann method and new corrections to Klinkenberg's coefficients are investigated. These corrections allow the extension of Klinkenberg model to higher ranges of Knudsen numbers. All the simulations in this work were performed by codes developed by the authors.

Computational fluid dynamics modeling of fluid flow and heat transfer in the central pore of carbon nanopipes

Carbon nanopipes, which can be employed in micro- and nano-fluidic devices, have some extraordinary mechanical, optical, flow and electrical properties. In addition, these devices can manipulate very small amounts of liquid. One of the main aspects of these pipes is an unusual enhancement in the flow rate, and it should be explored whether this enhancement can be justified by continuum fluid mechanics or not. Computational fluid dynamics were employed for exploring this phenomenon. To explore this unusual flow enhancement, different parameters, such as temperature, inlet pressure, tube diameter, tube length and slip length were used. With varying parameters, the slip length can explain this phenomenon. The heat transfer was also numerically investigated and an improvement in the heat transfer coefficient and the convective heat flux magnitude were observed for the carbon nanopipes. Then, based on the numerical investigation, correlations were developed for the friction factor and the Nusselt number, and these correlations were verified by the reported experimental data for nanopipes. Moreover, the effects of this slip length on the velocity profile was investigated and the observed shape of the velocity profile was also completely changed from convex to plug-like by importing the effect of slip length on the walls of the tubes.

Computational study of the propagation of the longitudinal velocity in a polymer melt contained within a cylinder using a scale-bridging method

The "constitutive equation"-free scale-bridging method connecting nonequilibrium molecular dynamics and continuum fluid mechanics, that had hitherto been applied only to a parallel-plates geometry, is extended to study the flow of a polymer melt in a cylindrical pipe subject to a velocity in the direction parallel to the cylinder's axis. The system, initially at rest, is given a velocity at the cylinder's surface, and the evolution of the velocity profile within the fluid is studied, along with the time taken for the velocity to propagate toward the cylinder's axis. The said time of propagation is found to increase with the boundary velocity-a fact in contrast with the case of a Newtonian fluid for which the time of propagation is expected to be independent of the boundary velocity. For a fixed value of the boundary velocity, the propagation time is found to increase with the cylinder radius according to a power law with an exponent that is smaller than the corresponding exponent for a Newtonian fluid. For the lower values of the boundary velocity and the lower values of the radius studied, a velocity overshoot is observed at the cylinder's axis-a manifestation of elastic behavior of the fluid.