On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size

Liu, Chong; Li, Zhigang

doi:10.1063/1.3621858

Cited by 68 publications

(53 citation statements)

References 38 publications

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“…Therefore, the geometrical boundaries of each sub-domain cannot be determined in advance, as they result from molecular dynamics. Taking into consideration that we need to discretize the equations to perform simulations and numerical experiments, and that we are dealing at the very validity limit of continuous flow models [29], our chance of getting close to helpful and interesting solutions in this way is not very likely.…”

Section: Principal Thoughts About Strategic Choicesmentioning

confidence: 99%

“…Therewith, we analyze cellular compensatory mechanisms for replacing the molecules consumed by polymerization, subject to the principle of mass conservation. Cytosol has a colloidal-water constitution which, in first approximation, leads to considering it as an incompressible and viscous fluid and modeling its motion by Navier-Stokes equations for incompressible fluid flow [29],…”

Section: Modeling Cytosolic Flow As a Means To Drive Passive Transpormentioning

confidence: 99%

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Mathematical-Computational Simulation of Cytoskeletal Dynamics

Moura

Kritz

Leal

et al. 2016

Mathematical Modeling and Computational Intelligence in Engineering Applications

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Actin and microtubules are components of the cytoskeleton, and are key mediators of neuron growth and maintenance. Knowing how they are regulated enhances our understanding of neural development, ageing, degeneration, and regeneration. However, biological investigation alone will not unravel the complex cytoskeletal machinery. We expect that inquiries about the cytoskeleton can be significantly enhanced if their physico-chemical behavior is concealed and summarized in mathematical and computational models that can be coupled to concepts of biological regulation. Our computational modeling concerns the mechanical aspects associated with the dynamics of relatively simple, finger-like membrane protrusions called filopodia. Here we propose an alternative approach for representing the displacement of molecules and cytoplasmic fluid in the extremely narrow and long filopodia and discuss strategies to couple the particle-in-cell method with algorithms for laminar flow to model the two phases of actin dynamics: polymerization into filaments which are pulled back into the cell and compensatory G-actin drift towards its tip to supply polymerization. We use nerve cells of the fruit fly Drosophila as an effective, genetically amenable biological system to generate experimental data as the basis for the abstract models and their validation.

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Section: Principal Thoughts About Strategic Choicesmentioning

confidence: 99%

Section: Modeling Cytosolic Flow As a Means To Drive Passive Transpormentioning

confidence: 99%

Mathematical-Computational Simulation of Cytoskeletal Dynamics

Moura

Kritz

Leal

et al. 2016

Mathematical Modeling and Computational Intelligence in Engineering Applications

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“…Liu and Li showed that when the channel height was sufficiently large, the Navier-Stokes equation was still valid; While for a very small channel height, the Navier-Stokes equation failed (Liu and Li, 2011). Roohi and Darbandi (2009) modified the Navier-Stokes equation for solving the velocity distribution in micro/nano channel flows by using the slip boundary conditions and the viscosity coefficient (i.e.…”

Section: The Modified Navier-stokes Equation Modelmentioning

confidence: 99%

“…By using the Lennard-Jones potential model in MDS, Liu and Li (2011) showed that the Navier-Stokes equation can be valid for the channel height greater than 50nm, regardless of the fluid-wall interaction; For a nano channel height on the 1nm scale, MDS should normally be used to simulate the fluid flow inside the channel to capture the special flow characteristic; The flow was heavily dependent on the fluid-wall interaction.…”

Section: Full Mds Modelmentioning

confidence: 99%

“…It often fails to predict a micro/nano scale flow (Chan and Horn, 1985;Cheikh and Kopper, 2003;Craig et al, 2001;Liu and Li, 2011;Zhu and Granick, 2001). In this circumstance, a lot of models have been proposed for depicting micro/nano channel flows, include the full MDS model, the quasi-continuum model, the modified Navier-Stokes equation model, the dissipative particle dynamics method, the lattice Boltzman method, the multiscale hybrid model and the flow factor approach model.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of Micro/Nano Channel Flows

Zhang¹

2017

Frontiers in Heat and Mass Transfer

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This paper reviews the models for the fluid flow in micro/nano channels developed previously. These models include the full MDS (molecular dynamics simulation) model, the quasi-continuum model, the modified Navier-Stokes equation model, the dissipative particle dynamics method, the lattice Boltzman method, the multiscale hybrid model and the flow factor approach model. It was pointed out that most of the models have their own imperfections like huge time and computer storage consumption for simulating a system of realistic size or inaccuracy because of the model limitation. It was also mentioned that the most challenging is to develop efficient models for simulating engineering flows which often occur in much longer channels than currently simulated on a computer. These welcome models should be sufficiently accurate with fast calculation and acceptable computer storage consumption.

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Combined effects of surface roughness and physically adsorbed layer in hydrodynamic journal bearing with multiscale approach

Zhang

2023

Z Angew Math Mech

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Numerical calculations were made for the film pressure and carried load of the hydrodynamic journal bearing with very large eccentricity ratios, that is, very low clearances when the combined effects of surface roughness and physically adsorbed layer were considered. The shaft was rotating with perfectly smooth surface, and the sleeve was stationary with the nanoscale sinusoidal surface roughness. The fluid piezo‐viscous effect was also incorporated. Owing to the coexistence of the nanoscale adsorbed layer and the macroscopic intermediate continuum fluid film, the multiscale approach was used to simultaneously solve this sandwich film lubrication problem. It was found that owing to low bearing clearances the effect of the adsorbed layer normally very significantly increases the lubricant film pressure, depending on the fluid‐bearing surface interaction; While at the same time both the surface roughness effect and the fluid piezo‐viscous effect are particularly significant compared to those classically calculated, owing to the local more severe film squeezing and the resulting local higher pressures. By considering the effect of the adsorbed layer, the surface roughness more significantly increases the load‐carrying capacity of the journal bearing for very large eccentricity ratios, especially for a strong fluid‐bearing surface interaction. It is suggested that in modeling the hydrodynamic journal bearing for large eccentricity ratios, the combined effects of the surface roughness, physically adsorbed layer and fluid piezo‐viscous property should be considered.

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On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size

Cited by 68 publications

References 38 publications

Mathematical-Computational Simulation of Cytoskeletal Dynamics

Mathematical-Computational Simulation of Cytoskeletal Dynamics

Modeling of Micro/Nano Channel Flows

Combined effects of surface roughness and physically adsorbed layer in hydrodynamic journal bearing with multiscale approach

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