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From dissipative particle dynamics scales to physical scales: a coarse-graining study for water flow in microchannel

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Abstract

In the present work, dissipative particle dynamics (DPD) simulation of simple flows is studied based on coarse-graining parameter. Reference scales of DPD are expressed in terms of physical units and DPD parameters and equations are expressed in terms of Reynolds number and apparent Peclet number. DPD parameters for a given coarse-graining are calculated by matching the density and viscosity of water and Reynolds number of the flow. The formulation is applied to water flow in microchannels of height 5 and 10 μm and tested for a wide range of coarse-graining parameter varying from 107 to 109. The results are in a good agreement with the continuum formulation and simulated the correct hydrodynamics of water flow in microchannels. By inspecting the microscopic detail of the interaction between the DPD particles, it is found that diffusivity is low for high coarse-graining parameter, which results in higher values of Schmidt number. Parameters are tested within the continuum assumption. It is shown that correct Schmidt number can be achieved using small coarse-graining parameter. Also, it is observed that low diffusivity or high Schmidt number does not affect the hydrodynamics of water.

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Abbreviations

D :

Diffusivity

D h :

Hydraulic diameter

f :

Force

H :

Height of the channel

k B :

Boltzmann constant

L :

Length of the channel

m DPD :

Mass of a DPD particle

n :

DPD number density

M y :

Number of cells in y-direction

N DPD :

Total number of DPD particles

N m :

Coarse-graining parameter

N x :

Number of cells in x-direction

Pe* :

Apparent Peclet number

Re :

Reynolds number

Re cell :

Reynolds number based on cutoff length

r :

Distance

r c :

Cut-off radius

Sc :

Schmidt number

T :

Temperature

t :

Time

u avg :

Average velocity of the flow

u T :

Thermal velocity of the particle

v :

Velocity

α:

Repulsive force parameter

γ:

Dissipative force parameter

μ :

Dynamic viscosity

σ:

Random force parameter

ζ :

Random number

ρ DPD :

Number of DPD Particles in a unit cell

τ w :

Shear stress at the wall

ν :

Kinematic viscosity

ω C, ω D, ω R :

Weight functions

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Acknowledgments

This work is supported by the National Science Foundation grant (NSF-OISE-0530203). The third author would like to thank Arab Fund Fellowship Program for supporting his research stay at URI.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island, 92 Upper College Rd, Kingston, RI, 02881, USA

    Anurag Kumar, Eiyad Abu-Nada & Mohammad Faghri

  2. Department of Mechanical Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan

    Yutaka Asako

  3. iRMB, Technical University Braunschweig, 38106, Braunschweig, Germany

    Manfred Krafczyk

Authors
  1. Anurag Kumar
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  2. Yutaka Asako
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  3. Eiyad Abu-Nada
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  4. Manfred Krafczyk
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  5. Mohammad Faghri
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Correspondence to Anurag Kumar.

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Kumar, A., Asako, Y., Abu-Nada, E. et al. From dissipative particle dynamics scales to physical scales: a coarse-graining study for water flow in microchannel. Microfluid Nanofluid 7, 467 (2009). https://doi.org/10.1007/s10404-008-0398-x

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