Skip to main content
SpringerLink
Log in

Viscous heating in nanoscale shear driven liquid flows

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

Three-dimensional Molecular Dynamics (MD) simulations of heat and momentum transport in liquid Argon filled shear-driven nano-channels are performed using 6–12 Lennard–Jones potential interactions. Work done by the viscous stresses heats the fluid, which is dissipated through the channel walls, maintained at isothermal conditions through a recently developed interactive thermal wall model. Shear driven nano-flows for weak wetting surfaces (ε wf /ε ≤ 0.6) are investigated. Spatial variations in the fluid density, kinematic viscosity, shear- and energy dissipation rates are presented. Temperature profiles in the nano-channel are obtained as a function of the surface wettability, shear rate and the intermolecular stiffness of wall molecules. The energy dissipation rate is almost a constant for ε wf /ε ≤ 0.6, which results in parabolic temperature profiles in the domain with temperature jumps due to the well known Kapitza resistance at the liquid/solid interfaces. Using the energy dissipation rates predicted by MD simulations and the continuum energy equation subjected to the temperature jump boundary conditions developed in [Kim et al. Journal of Chemical Physics, 129, 174701, 2008b], we obtain analytical solutions for the temperature profiles, which agree well with the MD results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Allen MP, Tildesley DJ (1989) Computer simulation of liquids. Oxford University Press, New York

    Google Scholar 

  • Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Maris HJ, Merlin R, Phillpot SR (2003) Nanoscale thermal transport. J Appl Phys 93(2):793–818

    Article  Google Scholar 

  • Cieplak M, Koplik J, Banavar JR (1999) Applications of statistical mechanics in subcontinuum fluid dynamics. Physica A 274(1–2):281–293

    Article  Google Scholar 

  • Cieplak M, Koplik J, Banavar JR (2001) Boundary conditions at a fluid–solid interface. Phys Rev Lett 86(5):803–806

    Article  Google Scholar 

  • Evans DJ, Hoover WG (1986) Flows far from equilibrium via molecular-dynamics. Annu Rev Fluid Mech 18:243–264

    Article  MathSciNet  Google Scholar 

  • Ge ZB, Cahill DG, Braun PV (2006) Thermal conductance of hydrophilic and hydrophobic interfaces. Phys Rev Lett 96(18):186101

    Article  Google Scholar 

  • Jabbarzadeh A, Atkinson JD, Tanner RI (1999) Wall slip in the molecular dynamics simulation of thin films of hexadecane. J Chem Phys 110(5):2612–2620

    Article  Google Scholar 

  • Kapitza PL (1941) The study of heat transfer in helium II. J Phys 4(1–6):181–210

    Google Scholar 

  • Karniadakis G, Beskok A, Aluru N (2005) Microflows and nanoflows fundamentals and simulation. In: Microflows and nanoflows fundamentals and simulation. Springer Science, New York

  • Khare R, dePablo J, Yethiraj A (1997) Molecular simulation and continuum mechanics study of simple fluids in non-isothermal planar couette flows. J Chem Phys 107(7):2589–2596

    Article  Google Scholar 

  • Kim BH, Beskok A, Cagin T (2008a) Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solid–liquid interfaces. Microfluid Nanofluidics 5(4):551–559

    Article  Google Scholar 

  • Kim BH, Beskok A, Cagin T (2008b) Molecular dynamics simulations of thermal resistance at the liquid–solid interface. J Chem Phys 129:174701

    Article  Google Scholar 

  • Koplik J, Banavar JR (1995) Continuum deductions from molecular hydrodynamics. Annu Rev Fluid Mech 27:257–292

    Article  Google Scholar 

  • Koplik J, Banavar JR, Willemsen JF (1988) Molecular-dynamics of poiseuille flow and moving contact lines. Phys Rev Lett 60(13):1282–1285

    Article  Google Scholar 

  • Koplik J, Banavar JR, Willemsen JF (1989) Molecular-dynamics of fluid-flow at solid-surfaces. Phys Fluids A 1(5):781–794

    Article  Google Scholar 

  • Liem SY, Brown D, Clarke JHR (1992) Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method. Phys Rev A 45(6):3706–3713

    Article  Google Scholar 

  • Nagayama G, Cheng P (2004) Effects of interface wettability on microscale flow by molecular dynamics simulation. Int J Heat Mass Transf 47(3):501–513

    Article  MATH  Google Scholar 

  • Ohara T, Torii D (2005) Molecular dynamics study of thermal phenomena in an ultrathin liquid film sheared between solid surfaces: the influence of the crystal plane on energy and momentum transfer at solid–liquid interfaces. J Chem Phys 122:214717

    Google Scholar 

  • Priezjev NV (2007) Rate-dependent slip boundary conditions for simple fluids. Phys Rev E 75(5):051605

    Google Scholar 

  • Priezjev NV, Darhuber AA, Troian SM (2005) Slip behavior in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys Rev E 71(4):041608

    Google Scholar 

  • Sofos F, Karakasidis T, Liakopoulos A (2009a) Transport properties of liquid argon in krypton nanochannels: anisotropy and non-homogeneity introduced by the solid walls. Int J Heat Mass Transf 52(3–4):735–743

    Article  MATH  Google Scholar 

  • Sofos F, Karakasidis T, Liakopoulos A (2009b) Non-equilibrium molecular dynamics investigation of parameters affecting planar nanochannel flows. Contemp Eng Sci 2(6):283–298

    Google Scholar 

  • Tenenbaum A (1983) Local equilibrium in stationary states by molecular-dynamics. Phys Rev A 28(5):3132–3133

    Article  Google Scholar 

  • Tenenbaum A, Ciccotti G, Gallico R (1982) Stationary non-equilibrium states by molecular-dynamics—fourier law. Phys Rev A 25(5):2778–2787

    Article  Google Scholar 

  • Thomas JA, McGaughey AJH (2007) Effect of surface wettability on liquid density, structure, and diffusion near a solid surface. J Chem Phys 126(3):034707

    Google Scholar 

  • Thompson PA, Robbins MO (1990) Shear-flow near solids—epitaxial order and flow boundary-conditions. Phys Rev A 41(12):6830–6837

    Article  Google Scholar 

  • Thompson PA, Troian SM (1997) A general boundary condition for liquid flow at solid surfaces. Nature 389(6649):360–362

    Article  Google Scholar 

  • Tseng HC, Wu JS, Chang RY (2008) Shear thinning and shear dilatancy of liquid n- hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: temperature, pressure, and density effects. J Chem Phys 129(1):014502

    Google Scholar 

  • Volz S, Saulnier JB, Lallemand M, Perrin B, Depondt P, Mareschal M (1996) Transient Fourier-law deviation by molecular dynamics in solid argon. Phys Rev B 54(1):340–347

    Article  Google Scholar 

  • Xu P, Cagin T, Goddard WA (2005) Assessment of phenomenological models for viscosity of liquids based on nonequilibrium atomistic simulations of copper. J Chem Phys 123(10):104506

    Google Scholar 

  • Xue L, Keblinski P, Phillpot SR, Choi SUS, Eastman JA (2004) Effect of liquid layering at the liquid–solid interface on thermal transport. Int J Heat Mass Transf 47(19–20):4277–4284

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace Engineering Department, Old Dominion University, Norfolk, VA, 23529, USA

    Bo Hung Kim & Ali Beskok

  2. Chemical Engineering Department, Texas A&M University, College Station, TX, 77840, USA

    Tahir Cagin

Authors
  1. Bo Hung Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Beskok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tahir Cagin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Beskok.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, B.H., Beskok, A. & Cagin, T. Viscous heating in nanoscale shear driven liquid flows. Microfluid Nanofluid 9, 31–40 (2010). https://doi.org/10.1007/s10404-009-0515-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-009-0515-5

Keywords

Search

Navigation