1
|
Paul A, Aluru NR. Nonlocal hydrodynamic model for gravity-driven transport in nanochannels. J Chem Phys 2022; 156:204112. [DOI: 10.1063/5.0089447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has been established that Newton’s law of viscosity fails for fluids under strong confinement as the strain-rate varies significantly over molecular length-scales. We thereby investigate if a nonlocal shear stress accounting for the strain-rate of an adjoining region by a convolution relation with a nonlocal viscosity kernel can be employed to predict the gravity-driven isothermal flow of a Weeks–Chandler–Andersen fluid in a nanochannel. We estimate, using the local average density model, the fluid’s viscosity kernel from isotropic bulk systems of corresponding state points by the sinusoidal transverse force method. A continuum model is proposed to solve the nonlocal hydrodynamics whose solutions capture the key features and agree qualitatively with the results of non-equilibrium molecular dynamics simulations, with deviations observed mostly near the fluid–channel interface.
Collapse
Affiliation(s)
- Arghyadeep Paul
- Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - N. R. Aluru
- Walker Department of Mechanical Engineering, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| |
Collapse
|
2
|
Daivis PJ, Hansen JS, Todd BD. Electropumping of nanofluidic water by linear and angular momentum coupling: theoretical foundations and molecular dynamics simulations. Phys Chem Chem Phys 2021; 23:25003-25018. [PMID: 34739012 DOI: 10.1039/d1cp04139h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
In this article we review the relatively new phenomenon of electropumping in nanofluidic systems, in which nonzero net flow results when polar molecules are rotated by external electric fields. The flow is a consequence of coupling of the spin angular momentum of molecules with their linear streaming momentum. By devising confining surfaces that are asymmetric - specifically one surface is more hydrophobic compared to the other - unidirectional flow results and so pumping can be achieved without the use of pressure gradients. We first cover the historical background to this phenomenon and follow that with a detailed theoretical description of the governing hydrodynamics. Following that we summarise work that has applied this phenomenon to pump water confined to planar nanochannels, semi-functionalised single carbon nanotubes and concentric carbon nanotubes. We also report on the energy efficiency of this pumping technique by comparisons with traditional flows of planar Couette and Poiseuille flow, with the surprising conclusion that electropumping at the nanoscale is some 4 orders of magnitude more efficient than pumping by Poiseuille flow.
Collapse
Affiliation(s)
- Peter J Daivis
- School of Science, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia.
| | - J S Hansen
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Roskilde 4000, Denmark.
| | - B D Todd
- Department of Mathematics, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia.
| |
Collapse
|
3
|
Sam A, Hartkamp R, Kumar Kannam S, Babu JS, Sathian SP, Daivis PJ, Todd BD. Fast transport of water in carbon nanotubes: a review of current accomplishments and challenges. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1782401] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Alan Sam
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India
| | - Remco Hartkamp
- Process and Energy Department, Delft University of Technology, Delft, The Netherlands
| | - Sridhar Kumar Kannam
- Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Australia
| | - Jeetu S. Babu
- Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Amritapuri, India
| | - Sarith P. Sathian
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India
| | - Peter J. Daivis
- School of Applied Sciences, RMIT University, Melbourne, Australia
| | - B. D. Todd
- Department of Mathematics, Swinburne University of Technology, Melbourne, Australia
| |
Collapse
|
4
|
de la Torre JA, Duque-Zumajo D, Camargo D, Español P. Microscopic Slip Boundary Conditions in Unsteady Fluid Flows. PHYSICAL REVIEW LETTERS 2019; 123:264501. [PMID: 31951457 DOI: 10.1103/physrevlett.123.264501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Indexed: 06/10/2023]
Abstract
An algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the plateau problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.
Collapse
Affiliation(s)
- J A de la Torre
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
| | - D Duque-Zumajo
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
| | - D Camargo
- Facultad de Ingeniería y Arquitectura, Universidad Pontificia Bolivariana, CO-230003 Montería, Colombia
| | - Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
| |
Collapse
|
5
|
Camargo D, de la Torre JA, Delgado-Buscalioni R, Chejne F, Español P. Boundary conditions derived from a microscopic theory of hydrodynamics near solids. J Chem Phys 2019; 150:144104. [DOI: 10.1063/1.5088354] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Affiliation(s)
- Diego Camargo
- Facultad de Ingeniería y Arquitectura, Universidad Pontificía Bolivariana, Montería, Colombia
| | - J. A. de la Torre
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Rafael Delgado-Buscalioni
- Departamento de Física Teórica de la Materia Condensada Universidad Autónoma de Madrid, and Condensed Matter Physics Center (IFIMAC), Madrid 28049, Spain
| | - Farid Chejne
- Universidad Nacional de Colombia, Bogotá, Colombia
| | - Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| |
Collapse
|
6
|
Abstract
The fluid dynamics of macroscopic and microscopic systems is well developed and has been extensively validated. Its extraordinary success makes it tempting to apply Navier–Stokes fluid dynamics without modification to systems of ever decreasing dimensions as studies of nanofluidics become more prevalent. However, this can result in serious error. In this paper, we discuss several ways in which nanoconfined fluid flow differs from macroscopic flow. We give particular attention to several topics that have recently received attention in the literature: slip, spin angular momentum coupling, nonlocal stress response and density inhomogeneity. In principle, all of these effects can now be accurately modelled using validated theories. Although the basic principles are now fairly well understood, much work remains to be done in their application.
Collapse
|
7
|
Rees RJ, Spencer MJ. The science and life of Ian K. Snook. MOLECULAR SIMULATION 2015. [DOI: 10.1080/08927022.2016.1091560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
8
|
Bollinger JA, Jain A, Truskett TM. How Local and Average Particle Diffusivities of Inhomogeneous Fluids Depend on Microscopic Dynamics. J Phys Chem B 2015; 119:9103-13. [PMID: 25350488 DOI: 10.1021/jp508887r] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Computer simulations and a stochastic Fokker-Planck equation based approach are used to compare the single-particle diffusion coefficients of equilibrium hard-sphere fluids exhibiting identical inhomogeneous static structure and governed by either Brownian (i.e., overdamped Langevin) or Newtonian microscopic dynamics. The physics of inhomogeneity is explored via the imposition of one-dimensional sinusoidal density profiles of different wavelengths and amplitudes. When imposed density variations are small in magnitude for distances on the scale of a particle diameter, bulk-like average correlations between local structure and mobility are observed. In contrast, when density variations are significant on that length scale, qualitatively different structure-mobility correlations emerge that are sensitive to the governing microscopic dynamics. Correspondingly, a previously proposed scaling between long-time diffusivities for bulk isotropic fluids of particles exhibiting Brownian versus Newtonian dynamics [Pond et al. Soft Matter 2011, 7, 9859-9862] cannot be generalized to describe the position-dependent behaviors of strongly inhomogeneous fluids. While average diffusivities in the inhomogeneous and homogeneous directions are coupled, their qualitative dependencies on inhomogeneity wavelength are sensitive to the details of the microscopic dynamics. Nonetheless, average diffusivities of the inhomogeneous fluids can be approximately predicted for either type of dynamics based on knowledge of bulk isotropic fluid behavior and how inhomogeneity modifies the distribution of available volume. Analogous predictions for average diffusivities of experimental, inhomogeneous colloidal dispersions (based on known bulk behavior) suggest that they will exhibit qualitatively different trends than those predicted by models governed by overdamped Langevin dynamics that do not account for hydrodynamic interactions.
Collapse
Affiliation(s)
- Jonathan A Bollinger
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Avni Jain
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Thomas M Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
9
|
Dalton BA, Glavatskiy KS, Daivis PJ, Todd BD. Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. II. Sinusoidally driven shear and multisinusoidal inhomogeneity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012108. [PMID: 26274126 DOI: 10.1103/physreve.92.012108] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Indexed: 06/04/2023]
Abstract
We use molecular-dynamics computer simulations to investigate the density, strain-rate, and shear-pressure responses of a simple model atomic fluid to transverse and longitudinal external forces. We have previously introduced a response function formalism for describing the density, strain-rate, and shear-pressure profiles in an atomic fluid when it is perturbed by a combination of longitudinal and transverse external forces that are independent of time and have a simple sinusoidal spatial variation. In this paper, we extend the application of the previously introduced formalism to consider the case of a longitudinal force composed of multiple sinusoidal components in combination with a single-component sinusoidal transverse force. We find that additional harmonics are excited in the density, strain-rate, and shear-pressure profiles due to couplings between the force components. By analyzing the density, strain-rate, and shear-pressure profiles in Fourier space, we are able to evaluate the Fourier coefficients of the response functions, which now have additional components describing the coupling relationships. Having evaluated the Fourier coefficients of the response functions, we are then able to accurately predict the density, velocity, and shear-pressure profiles for fluids that are under the influence of a longitudinal force composed of two or three sinusoidal components combined with a single-component sinusoidal transverse force. We also find that in the case of a multisinusoidal longitudinal force, it is sufficient to include only pairwise couplings between different longitudinal force components. This means that it is unnecessary to include couplings between three or more force components in the case of a longitudinal force composed of many Fourier components, and this paves the way for a highly accurate but tractable treatment of nonlocal transport phenomena in fluids with density and strain-rate inhomogeneities on the molecular length scale.
Collapse
Affiliation(s)
- Benjamin A Dalton
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - Kirill S Glavatskiy
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - Peter J Daivis
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - B D Todd
- Department of Mathematics, Faculty of Science, Engineering and Technology, and Centre for Molecular Simulation, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia
| |
Collapse
|
10
|
Glavatskiy KS, Dalton BA, Daivis PJ, Todd BD. Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. I. Sinusoidally driven shear and sinusoidally driven inhomogeneity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062132. [PMID: 26172686 DOI: 10.1103/physreve.91.062132] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2014] [Indexed: 06/04/2023]
Abstract
We present theoretical expressions for the density, strain rate, and shear pressure profiles in strongly inhomogeneous fluids undergoing steady shear flow with periodic boundary conditions. The expressions that we obtain take the form of truncated functional expansions. In these functional expansions, the independent variables are the spatially sinusoidal longitudinal and transverse forces that we apply in nonequilibrium molecular-dynamics simulations. The longitudinal force produces strong density inhomogeneity, and the transverse force produces sinusoidal shear. The functional expansions define new material properties, the response functions, which characterize the system's nonlocal response to the longitudinal force and the transverse force. We find that the sinusoidal longitudinal force, which is mainly responsible for the generation of density inhomogeneity, also modulates the strain rate and shear pressure profiles. Likewise, we find that the sinusoidal transverse force, which is mainly responsible for the generation of sinusoidal shear flow, can also modify the density. These cross couplings between density inhomogeneity and shear flow are also characterized by nonlocal response functions. We conduct nonequilibrium molecular-dynamics simulations to calculate all of the response functions needed to describe the response of the system for weak shear flow in the presence of strong density inhomogeneity up to the third order in the functional expansion. The response functions are then substituted directly into the truncated functional expansions and used to predict the density, velocity, and shear pressure profiles. The results are compared to the directly evaluated profiles from molecular-dynamics simulations, and we find that the predicted profiles from the truncated functional expansions are in excellent agreement with the directly computed density, velocity, and shear pressure profiles.
Collapse
Affiliation(s)
- Kirill S Glavatskiy
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria, 3001, Australia
| | - Benjamin A Dalton
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria, 3001, Australia
| | - Peter J Daivis
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria, 3001, Australia
| | - B D Todd
- Department of Mathematics, Faculty of Science, Engineering and Technology, and Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria, 3122, Australia
| |
Collapse
|
11
|
Bollinger JA, Jain A, Truskett TM. Structure, thermodynamics, and position-dependent diffusivity in fluids with sinusoidal density variations. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:8247-8252. [PMID: 24984592 DOI: 10.1021/la5017005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids.
Collapse
Affiliation(s)
- Jonathan A Bollinger
- McKetta Department of Chemical Engineering, University of Texas at Austin , Austin, Texas 78712, United States
| | | | | |
Collapse
|
12
|
Dalton BA, Daivis PJ, Hansen JS, Todd BD. Effects of nanoscale density inhomogeneities on shearing fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052143. [PMID: 24329250 DOI: 10.1103/physreve.88.052143] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2013] [Indexed: 06/03/2023]
Abstract
It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.
Collapse
Affiliation(s)
- Benjamin A Dalton
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - Peter J Daivis
- School of Applied Sciences, RMIT University, GPO Box 2476 Melbourne, Victoria 3001, Australia
| | - J S Hansen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - B D Todd
- Mathematics, Faculty of Engineering and Industrial Sciences, and Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
| |
Collapse
|