Hybrid Molecular-continuum Research Articles

COUPLED EFFECT OF VARIABLE WETTABILITY AND BODY FORCE ON FLUID FLOW THROUGH NANOCHANNELS: A MULTISCALE APPROACH

Fluid flow through sub-micron domains has been an area of active research in recent years with immense scientific and technological interests. Such flows can show deviation in behavior from the theories of classical hydrodynamics, thus opening up a new paradigm to exploit these unique effects in applications related to transport and detection. By performing extensive molecular-dynamics (MD) simulations of fluid flow through a parallel plate nanochannel of non-uniform wetting characteristics, we bring out the coupled effect of surface wettability and applied body force on interfacial slip. Our results reveal distinctive slip-stick alteration which can be useful in designing channels with engineered effective slip. Moreover, in this study, we revisit a hybrid molecular-continuum multiscale model which can significantly reduce the computational cost of full-scale MD simulations and further provide a framework to discern the flow behavior for a wide spectrum of length scales. The results obtained from this study may provide useful insights, thus carrying immense implications towards designing of multifaceted nanoscale devices and futuristic smart surfaces.

Upstream events dictate interfacial slip in geometrically converging nanopores.

Continuum computations of fluid flow in conduits approaching molecular scales are often executed with a certain level of abstractions via the imposition of a pre-defined slip condition at the wall. However, in reality, the interfacial slip may not be affixed a priori as a direct one-to-one mapping with the surface wettability and charge but is implicitly interconnected with the concomitant dynamical events that may be effectively captured only under flow conditions. The flow in nanofluidic channels with axially varying cross sections hallmarks such situations in which the effective slip at the wall gets dynamically modulated by upstream flow conditions and cannot be trivially stamped as guided by localized intermolecular interactions over interfacial scales alone. In an effort to capture such flows without resorting to full-domain molecular dynamics simulations, here we bring out advancements on hybrid molecular-continuum simulations and report predictions that closely capture molecular dynamics based predictions of water transport through converging nanopores. Our results turn out to be of significant implications toward designing of emerging nanoscale devices of multifarious applications ranging from miniaturized reactors to highly targeted drug delivery systems.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations.

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

Advances and challenges in computational research of micro- and nanoflows

This paper presents an overview of past and current research in computational modelling of micro- and nanofluidic systems with particular focus on recent advances in multiscale modelling. Different mesoscale and hybrid molecular–continuum methods are presented. The contributions of these methods to a broad range of applications, as well as the physical and computational modelling challenges associated with the development of these methods, are also discussed.

Special issue: Micro and Nano Flows (MNF2014)

microand nanoflows and provided a platform for identifying synergies and exploring cross-over opportunities in biomedicine/biotechnology and thermofluids engineering. Such cross-over was nicely illustrated in the plenary lecture given by Professor Dimitris Drikakis entitled “Advances and Challenges in Computational Research of Micro Nano Flows” whose lecture presented application examples across a range of technology sectors. The lead paper of this issue, which presents recent advances in multiscale modelling with a focus on a variety of mesoscale and hybrid molecular-continuum methods, is based on his plenary lecture. The remaining articles in this issue were selectively invited and successfully passed the journal’s high-standard peer-review process. In the last 20 years, a key goal in the drug discovery field has been the development of reliable in vitro models. The paper by Rasponi et al. presents the development of lab on a chip (LoC) technology that allows for testing myelotoxic effects of drugs and chemicals. The LoC platform consists of 180 bioreactor chambers, designed to host a controlled and limited number of cells in suspension. The probability of each chamber to contain a colony-forming unit was evaluated based on the clonogenicity of the cell population and on a specifically developed statistical model. Kefala et al. presented a labyrinth split and merge (SAM) micromixer for bioanalytical applications. By means of a computational study, they demonstrated the mixing advantages of SAM compared to passive micromixers. Experimental validation based on fluorescence microscopy was conducted for enzymatic digestion of DNA. Ritos et al. introduced flow simulations of water through carbon nanotube membranes of realistic thickness, based on a new hybrid molecular-continuum model. The results of their model for a membrane thickness of 150 nm compared well with computationally more expensive molecular dynamics (MD) simulations. There is an increasing interest in understanding heat and fluid flow on small scales. This interest stems from the need to address design issues associated with small devices such as microand nanofluidics as well as from the need to understand phenomena and interactions occurring on micro-/nanometre scales. Microfluidics and nanofluidics technologies are relevant to many applications in engineering, physics, chemistry, biochemistry, nanotechnology, and biotechnology. Advances have been made in terms of practical application ranging from the design of systems allowing smaller volumes of fluids to be processed, aiming at achieving multiplexing, automation, and high-throughput screening, to on-chip characterisation. This Special Issue was seeded as a result of a Special Session at the 2014 Conference on Micro and Nano Flows (MNF2014), held at University College London, 7–10 September, which was the fourth, successful conference of the series. The Special Session was entitled Biomedical Microfluidics of Lab-on-a-Chip Technology and was organised by the two lead editors. A unique feature of the conference series is that it provides a forum for scientists and engineers working on small scale flows in the areas of both biofluid mechanics and thermofluids engineering to present their recent research findings. This allowed for interdisciplinary exchange of ideas that advanced understanding of

Hybrid molecular-continuum simulations of water flow through carbon nanotube membranes of realistic thickness

We present new hybrid molecular-continuum simulations of water flow through filtration membranes. The membranes consist of aligned carbon nanotubes (CNTs) of high aspect ratio, where the tube diameters are ~1–2 nm and the tube lengths (i.e. the membrane thicknesses) are 2–6 orders of magnitude larger than this. The flow in the CNTs is subcontinuum, meaning standard continuum fluid equations cannot adequately model the flow; also, full molecular dynamics (MD) simulations are too computationally expensive for modelling these membrane thicknesses. However, various degrees of scale separation in both time and space in this problem can be exploited by a multiscale method: we use the serial-network internal-flow multiscale method (SeN-IMM). Our results from this hybrid method compare very well with full MD simulations of flow cases up to a membrane thickness of 150 nm, beyond which any full MD simulation is computationally intractable. We proceed to use the SeN-IMM to predict the flow in membranes of thicknesses 150 nm–2 μm, and compare these results with both a modified Hagen–Poiseuille flow equation and experimental results for the same membrane configuration. We also find good agreement between experimental and our numerical results for a 1-mm-thick membrane made of CNTs with diameters around 1.1 nm. In this case, the hybrid simulation is orders of magnitude quicker than a full MD simulation would be.

A hybrid molecular–continuum method for unsteady compressible multiscale flows

We present an internal-flow multiscale method (‘unsteady-IMM’) for compressible, time-varying/unsteady flow problems in nano-confined high-aspect-ratio geometries. The IMM is a hybrid molecular–continuum method that provides accurate flow predictions at macroscopic scales because local microscopic corrections to the continuum-fluid formulation are generated by spatially and temporally distributed molecular simulations. Exploiting separation in both time and length scales enables orders of magnitude computational savings, far greater than seen in other hybrid methods. We apply the unsteady-IMM to a converging–diverging channel flow problem with various time- and length-scale separations. Comparisons are made with a full molecular simulation wherever possible; the level of accuracy of the hybrid solution is excellent in most cases. We demonstrate that the sensitivity of the accuracy of a solution to the macro–micro time-stepping, as well as the computational speed-up over a full molecular simulation, is dependent on the degree of scale separation that exists in a problem. For the largest channel lengths considered in this paper, a speed-up of six orders of magnitude has been obtained, compared with a notional full molecular simulation.

Multiscale simulation of nanofluidic networks of arbitrary complexity

We present a hybrid molecular-continuum method for the simulation of general nanofluidic networks of long and narrow channels. This builds on the multiscale method of Borg et al. (Microfluid Nanofluid 15(4):541–557, 2013; J Comput Phys 233:400–413, 2013) for systems with a high aspect ratio in three main ways: (a) the method has been generalised to accurately model any nanofluidic network of connected channels, regardless of size or complexity; (b) a versatile density correction procedure enables the modelling of compressible fluids; (c) the method can be utilised as a design tool by applying mass-flow-rate boundary conditions (and then inlet/outlet pressures are the output of the simulation). The method decomposes the network into smaller components that are simulated individually using, in the cases in this paper, molecular dynamics micro-elements that are linked together by simple mass conservation and pressure continuity relations. Computational savings are primarily achieved by exploiting length-scale separation, i.e. modelling long channels as hydrodynamically equivalent shorter channel sections. In addition, these small micro-elements reach steady state much quicker than a full simulation of the network does. We test our multiscale method on several steady, isothermal network flow cases and show that it converges quickly (within three iterations) to good agreement with full molecular simulations of the same cases.

Hybrid molecular–continuum methods: From prototypes to coupling software

In this contribution, we review software requirements in hybrid molecular–continuum simulations. For this purpose, we analyze a prototype implementation which combines two frameworks–the Molecular Dynamics framework MarDyn and the framework Peano for spatially adaptive mesh-based simulations–and point out particular challenges of a general coupling software. Based on this analysis, we discuss the software design of our recently published coupling tool. We explain details on its overall structure and show how the challenges that arise in respective couplings are resolved by the software.

A hybrid molecular-continuum simulation method for incompressible flows in micro/nanofluidic networks

We present a hybrid molecular-continuum simulation method for modelling nano- and micro-flows in network-type systems. In these types of problem, a full molecular dynamics (MD) description of the macroscopic flow behaviour would be computationally intractable, or at least too expensive to be practical for engineering design purposes. Systems that exhibit multiscale traits, such as this, can instead be solved using a hybrid approach that distinguishes the problem into macroscopic and microscopic dynamics, modelled by their respective solvers. The technique presented in this study is an extension and addition to a hybrid method developed by Borg et al. (J Comput Phys 233:400–413, 2013) for high-aspect-ratio channel geometries, known as the internal-flow multiscale method (IMM). Computational savings are obtained by replacing long channels in the network, which are highly scale-separated, by much smaller, but representative, MD simulations, without a substantial loss of accuracy. On the other hand, junction components do not exhibit this length-scale separation, and so must be simulated in their entirety using MD. The current technique combines all network elements (junctions and channels) together in a coupled simulation using continuum conservation laws. For the case of steady, isothermal, incompressible, low-speed flows, we use the conservation of mass and momentum flux equations to derive a set of molecular-continuum constraints. An algorithm is presented here that computes at each iteration the new constraints on the pressure differences to be applied over individual MD micro-elements (channels and junctions), successively moving closer to macroscopic mass and momentum conservation. We show that hybrid simulations of some example network cases converge quickly, in only a few iterations, and compare very well to the corresponding full MD results, which are taken as the most accurate solutions. Major computational savings can be afforded by the IMM-type approximation in the channel components, but for steady-state solutions, even greater savings are possible. This is because the micro-elements are coupled to a steady-state continuum conservation expression, which greatly speeds up the relaxation of individual micro-components to steady conditions as compared to that of a full MD simulation. Unsteady problems with high temporal scale separation can also be simulated, but general transient problems are beyond the capabilities of the current technique.

Multiscale simulation strategies and mesoscale modelling of gas and liquid flows

This paper presents a review of multiscale simulation strategies for the modelling of micro- and nanoscale flows. These have been developed in the last two decades in an attempt to bridge the application gap between molecular and continuum simulation methods preventing the simulation of many micro- and nanofluidic devices. The paper focuses on hybrid molecular-continuum methods and reviews different coupling strategies, including geometrical decomposition in conjunction material state and flux coupling. point wise coupling, the heterogeneous multiscale method and the equation-free approach. Different applications of these methods are briefly discussed.

On the behaviour of fluidic material at molecular dynamics boundary conditions used in hybrid molecular-continuum simulations

This paper presents an investigation of the behaviour of the density profile of fluidic material confined by a force field, as it occurs across molecular-continuum mechanics boundaries in multiscale, hybrid molecular-continuum simulations. A theoretical model for the density profile across the boundary is derived. Furthermore, numerical experiments to validate the density profile and thickness of the relaxation zone are performed using molecular dynamics for a Lennard-Jones fluid in gaseous, liquid and supercritical state conditions. The simulation results show excellent agreement with the theoretical model.

Coupling strategies for hybrid molecular—continuum simulation methods

The paper presents numerical issues with regard to the development of hybrid molecular—continuum computational methods for macro and nanoscale modelling of nanoflows and materials. The implementation is based on a hybrid solution interface between the continuum and molecular regions. Two different approaches for the transfer of the mass, momentum, and energy fluxes onto the boundary of the molecular dynamics domain, are considered: (a) momentum transfer by force and (b) momentum transfer by velocity reversing. Simulations performed for a static fluid and free flow between molecular and continuum boundaries have shown that in the case of the momentum-transfer-by-force approach, the width of the relaxation zone depends linearly on the number of boundary atoms onto which the force is applied to, and for a free-flow this approach is numerically unstable. On the other hand, the momentum transfer by velocity reversing was found to lead to correct results with regard to energy conservation and variables distribution within the hybrid solution interface and was numerically stable both for static and free-flow test cases.

Coupled applications on distributed resources

Coupled models are set to become increasingly important in all aspects of science and engineering as tools with which to study complex systems in an integrated manner. Such coupled, hybrid simulations typically communicate data between the component models of which they are comprised relatively infrequently, and so a Grid is expected to present an ideal architecture on which to run them. In the present paper, we describe a simple, flexible and extensible architecture for a two-component hybrid molecular-continuum coupled model (hybrid MD). We discuss its deployment on distributed resources and the extensions to the RealityGrid computational-steering system to handle coupled models.

Structure of a tethered polymer under flow using molecular dynamics and hybrid molecular-continuum simulations

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely jointed chain (FJC) and is modelled by Lennard-Jones (LJ) beads interacting through the FENE potential. The solvent (modelled as a LJ fluid) and a weakly attractive wall are treated at the molecular level. At large shear rates the polymer becomes more elongated than predicted by existing theoretical scaling laws. Also, along the normal-to-wall direction the structure observed for the FJC is, surprisingly, very similar to that predicted for a semiflexible chain. Comparison with previous Brownian dynamics simulations (which exclude both solvent and wall potential) indicates that these effects are due to the polymer–solvent and polymer–wall interactions. The hybrid simulations are in perfect agreement with the MD simulations, showing no trace of finite size effects. Importantly, the extra cost required to couple the MD and CFD domains is negligible.

MULTISCALE FLOW SIMULATIONS USING PARTICLES

▪ Abstract Flow simulations are one of the archetypal multiscale problems. Simulations of turbulent and unsteady separated flows have to resolve a multitude of interacting scales, whereas molecular phenomena determine the structure of shocks and the validity of the no-slip boundary condition. Particle simulations of continuum and molecular phenomena can be formulated by following the motion of interacting particles that carry the physical properties of the flow. In this article we review Lagrangian, multiresolution, particle methods such as vortex methods and smooth particle hydrodynamics for the simulation of continuous flows and molecular dynamics for the simulation of flows at the atomistic scale. We review hybrid molecular-continuum simulations with an emphasis on the computational aspects of the problem. We identify the common computational characteristics of particle methods and discuss their properties that enable the formulation of a systematic framework for multiscale flow simulations.

Continuum level treatment of electronic polarization in the framework of molecular simulations of solvation effects

The hybrid molecular–continuum model for polar solvation considered in this paper combines the dielectric continuum approximation for treating fast electronic (inertialess) polarization effects and a molecular dynamics (MD) simulation for the slow (inertial) polarization component, including orientational and translational solvent modes. The inertial polarization is generated by average charge distributions of solvent particles, composed of permanent and induced (electronic) components. MD simulations are performed in a manner consistent with the choice of solvent and solute charges such that all electrostatic interactions are scaled by the factor 1/ε∞, where ε∞ is the optical dielectric permittivity. This approach yields an ensemble of equilibrium solvent configurations adjusted to the electric field created by a charged or strongly polar solute. The electrostatic solvent response field is found as the solution of the Poisson equation including both solute and explicit solvent charges, with accurate account of electrostatic boundary conditions at the surfaces separating spatial regions with different dielectric permittivities. Both equilibrium and nonequilibrium solvation effects can be studied by means of this model, and their inertial and inertialess contributions are naturally separated. The methodology for computation of charge transfer reorganization energies is developed and applied to a model two-site dipolar system in the SPC water solvent. Three types of charge transfer reactions are considered. The standard linear-response approach yields high accuracy for each particular reaction, but proves to be significantly in error when reorganization energies of different reactions were compared. This result has a purely molecular origin and is absent within a conventional continuum solvent model.