1
|
Borreguero M, Bezgin D, Adami S, Adams NA. Implicit atomistic viscosities in smoothed dissipative particle dynamics. Phys Rev E 2019; 100:033318. [PMID: 31640035 DOI: 10.1103/physreve.100.033318] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Indexed: 11/07/2022]
Abstract
We apply a standard nonequilibrium dynamics microscopic analysis of transport coefficients to the smoothed dissipative particle dynamics (SDPD) method of steady-shear flow conditions. Extending the research of Ellero et al. [Phys. Rev. E 82, 046702 (2010)PRESCM1539-375510.1103/PhysRevE.82.046702] for smoothed particle hydrodynamics (SPH), we focus, in particular, on velocity and acceleration statistics and on mean-density phenomena. Implicit and explicit fluctuations affect non-Gaussian statistics and effective viscosities whereas only explicit fluctuations affect large-scale dissipation through the fluctuation-dissipation relation. SDPD facilitates the simulation of mesoscopic systems as the resolution scale is defined by the scaling of the random fluctuations. In the kinetic regime, SDPD recovers the behavior of SPH. In the diffusive regime, non-Gaussian behavior occurs, in contrast to SPH. We observe the formation of isotropic randomly oriented structures with high density which are related to the magnitude of thermal fluctuations. It is demonstrated that SDPD produces non-Gaussian acceleration PDF corresponding to that of a turbulent flow field.
Collapse
Affiliation(s)
- Morgane Borreguero
- Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Munich, Germany
| | - Deniz Bezgin
- Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Munich, Germany
| | - Stefan Adami
- Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Munich, Germany
| | - Nikolaus A Adams
- Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Munich, Germany
| |
Collapse
|
2
|
Wang Y, Li Z, Xu J, Yang C, Karniadakis GE. Concurrent coupling of atomistic simulation and mesoscopic hydrodynamics for flows over soft multi-functional surfaces. SOFT MATTER 2019; 15:1747-1757. [PMID: 30672954 PMCID: PMC6414210 DOI: 10.1039/c8sm02170h] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
We develop an efficient parallel multiscale method that bridges the atomistic and mesoscale regimes, from nanometers to microns 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 grafted polydimethylsiloxane (PDMS) 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 slip length, 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 the 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.
Collapse
Affiliation(s)
- Yuying Wang
- CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhen Li
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
| | - Junbo Xu
- CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
| | - Chao Yang
- CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | | |
Collapse
|
3
|
Colagrossi A, Durante D, Bonet Avalos J, Souto-Iglesias A. Discussion of Stokes' hypothesis through the smoothed particle hydrodynamics model. Phys Rev E 2017; 96:023101. [PMID: 28950547 DOI: 10.1103/physreve.96.023101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2017] [Indexed: 11/07/2022]
Abstract
Stokes' hypothesis, the zeroing of the bulk viscosity in a Newtonian fluid, is discussed in this paper. To this aim, a continuum macroscopic fluid domain is initially modeled as a Hamiltonian system of discrete particles, for which the interparticle dissipative forces are required to be radial in order to conserve the angular momentum. The resulting system of particles is then reconverted to the continuum domain via the framework of the smoothed particle hydrodynamics (SPH) model. Since an SPH-consistent approximation of the Newtonian viscous term in the momentum equation incorporates interparticle radial as well as nonradial terms, it is postulated that the latter must be null. In the present work it is shown that this constraint implies that first and second viscosities are equal, resulting in a positive value for the bulk viscosity, in contradiction to the cited Stokes' hypothesis. Moreover, it is found that this postulate leads to bulk viscosity coefficients close to values found in the experimental literature for monoatomic gases and common liquids such as water.
Collapse
Affiliation(s)
- Andrea Colagrossi
- CNR-INSEAN, Marine Technology Research Institute, Rome, Italy and Ecole Centrale Nantes, LHEEA Laboratory, Nantes, France
| | - Danilo Durante
- CNR-INSEAN, Marine Technology Research Institute, Rome, Italy
| | - Josep Bonet Avalos
- Department d'Enginyeria Química, ETSEQ, Universitat Rovira i Virgili, Tarragona, Spain
| | | |
Collapse
|
4
|
Li Z, Lee HS, Darve E, Karniadakis GE. Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts. J Chem Phys 2017; 146:014104. [DOI: 10.1063/1.4973347] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhen Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Hee Sun Lee
- Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA
| | - Eric Darve
- Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| |
Collapse
|
5
|
Heyes DM, Dini D, Smith ER. Equilibrium fluctuations of liquid state static properties in a subvolume by molecular dynamics. J Chem Phys 2016; 145:104504. [PMID: 27634268 DOI: 10.1063/1.4962165] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (∼10), with the variances being inversely proportional to the SV volume, Ω. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes.
Collapse
Affiliation(s)
- D M Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - E R Smith
- Department of Chemical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| |
Collapse
|
6
|
Bian X, Deng M, Tang YH, Karniadakis GE. Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow. Phys Rev E 2016; 93:033312. [PMID: 27078489 DOI: 10.1103/physreve.93.033312] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Indexed: 11/07/2022]
Abstract
We analyze hydrodynamic fluctuations of a hybrid simulation under shear flow. The hybrid simulation is based on the Navier-Stokes (NS) equations on one domain and dissipative particle dynamics (DPD) on the other. The two domains overlap, and there is an artificial boundary for each one within the overlapping region. To impose the artificial boundary of the NS solver, a simple spatial-temporal averaging is performed on the DPD simulation. In the artificial boundary of the particle simulation, four popular strategies of constraint dynamics are implemented, namely the Maxwell buffer [Hadjiconstantinou and Patera, Int. J. Mod. Phys. C 08, 967 (1997)], the relaxation dynamics [O’Connell and Thompson, Phys. Rev. E 52, R5792 (1995)], the least constraint dynamics [Nie et al.,J. Fluid Mech. 500, 55 (2004); Werder et al., J. Comput. Phys. 205, 373 (2005)], and the flux imposition [Flekkøy et al., Europhys. Lett. 52, 271 (2000)], to achieve a target mean value given by the NS solver. Going beyond the mean flow field of the hybrid simulations, we investigate the hydrodynamic fluctuations in the DPD domain. Toward that end, we calculate the transversal autocorrelation functions of the fluctuating variables in k space to evaluate the generation, transport, and dissipation of fluctuations in the presence of a hybrid interface. We quantify the unavoidable errors in the fluctuations, due to both the truncation of the domain and the constraint dynamics performed in the artificial boundary. Furthermore, we compare the four methods of constraint dynamics and demonstrate how to reduce the errors in fluctuations. The analysis and findings of this work are directly applicable to other hybrid simulations of fluid flow with thermal fluctuations.
Collapse
Affiliation(s)
- Xin Bian
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Mingge Deng
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Yu-Hang Tang
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| |
Collapse
|