Hybrid molecular-continuum methods for micro- and nanoscale liquid flows

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Many flows at microscale and below are characterised by an inherent multiscale nature and accurate numerical modelling of the phenomena involved is the cornerstone for enhancing the applicability of micro and nanofluidics in the industrial environment. This paper presents a hybrid molecular-continuum strategy named as point wise coupling for studying complex micro- and nanoscale flows. In this strategy one performs continuum simulations and uses a molecular solver for computing flow properties. The hybrid methodology utilises a numerical procedure to minimise the cost of the computationally expensive molecular solver. Simulations have been carried out for a slip Poiseuille flow test case. The hybrid results are in good agreement with analytical solutions and pervious molecular simulations.This study is funded by the EPSRC, MoD and AWE through the grant EP/D051940-JGS 607, as well as from the European Commission under the 6th Framework Program (Project: DINAMICS, NMP4-CT-2007-026804)

Multiscale simulation strategies and mesoscale modelling of gas and liquid flows

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.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 is focused on hybrid molecular-continuum methods and reviews different coupling strategies, including geometrical decomposition in conjunction with state- and flux coupling, pointwise coupling, the heterogeneous multiscale method and the equation free approach. The different applications of these methods are briefly discussed

Computational uncertainty in hybrid atomistic-continuum frameworks

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Over the past decade micro and nanofluidics emerged as vital tools in the ongoing drive towards the development of nano-scale analysis and manufacturing systems. Accurate numerical modelling of the phenomena involved at these scales is ssential in order to speed up the industrial design process for nanotechnology. However a parameter often ignored in hybrid simulations is the uncertainty level introduced in the numerical modelling of phenomena taking place at micro and nanoscales. The main interest of the present study is the propagation of the inherent atomistic fluctuations to the continuum solver in the case of multiscale modelling and hybrid solvers

Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.Comment: 52 page

A Particle-based Multiscale Solver for Compressible Liquid-Vapor Flow

To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid-vapor flow with a sharp interface between the phases. The local phase dynamics at the interface can be interpreted as a Riemann problem for which we develop a multiscale solver in the spirit of the heterogeneous multiscale method, using a particle-based microscale model to augment the macroscopic two-phase flow system. The application of a microscale model makes it possible to use the intrinsic properties of the fluid at the microscale, instead of formulating (ad-hoc) constitutive relations

Concurrent coupling of atomistic simulation and mesoscopic hydrodynamics for flows over soft multi-functional surfaces

We develop an efficient parallel multiscale method that bridges the atomistic and mesoscale regimes, from nanometer to micron and beyond, via concurrent coupling of atomistic simulation and mesoscopic dynamics. In particular, we combine an all-atom molecular dynamics (MD) description for specific atomistic details in the vicinity of the functional surface, with a dissipative particle dynamics (DPD) approach that captures mesoscopic hydrodynamics in the domain away from the functional surface. In order to achieve a seamless transition in dynamic properties we endow the MD simulation with a DPD thermostat, which is validated against experimental results by modeling water at different temperatures. We then validate the MD-DPD coupling method for transient Couette and Poiseuille flows, demonstrating that the concurrent MD-DPD coupling can resolve accurately the continuum-based analytical solutions. Subsequently, we simulate shear flows over polydimethylsiloxane (PDMS)-grafted surfaces (polymer brushes) for various grafting densities, and investigate the slip flow as a function of the shear stress. We verify that a "universal" power law exists for the sliplength, in agreement with published results. Having validated the MD-DPD coupling method, we simulate time-dependent flows past an endothelial glycocalyx layer (EGL) in a microchannel. Coupled simulation results elucidate the dynamics of EGL changing from an equilibrium state to a compressed state under shear by aligning the molecular structures along the shear direction. MD-DPD simulation results agree well with results of a single MD simulation, but with the former more than two orders of magnitude faster than the latter for system sizes above one micron.Comment: 11 pages, 12 figure

Modelling solid/fluid interactions in hydrodynamic flows: a hybrid multiscale approach

With the advent of high performance computing (HPC), we can simulate nature at time and length scales that we could only dream of a few decades ago. Through the development of theory and numerical methods in the last fifty years, we have at our disposal a plethora of mathematical and computational tools to make powerful predictions about the world which surrounds us. From quantum methods like Density Functional Theory (DFT); going through atomistic methods such as Molecular Dynamics (MD) and Monte Carlo (MC), right up to more traditional macroscopic techniques based on Partial Differential Equations (PDEs) discretization like the Finite Element Method (FEM) or Finite Volume Method (FVM), which are respectively, the foundation of computational Structural Analysis and Computational Fluid Dynamics (CFD). Many modern scientific computing challenges in physics stem from combining appropriately two or more of these methods, in order to tackle problems that could not be solved otherwise using just one of them alone. This is known as multi-scale modeling, which aims to achieve a trade-off between computational cost and accuracy by combining two or more physical models at different scales. In this work, a multi-scale domain decomposition technique based on coupling MD and CFD methods, has been developed to make affordable the study of slip and friction, with atomistic detail, at length scales otherwise impossible by fully atomistic methods alone. A software framework has been developed to facilitate the execution of this particular kind of simulations on HPC clusters. This have been possible by employing the in-house developed CPL_LIBRARY software library, which provides key functionality to implement coupling through domain decomposition.Open Acces