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Simulation of droplet impingement on a rigid square obstacle in a microchannel using multiphase lattice Boltzmann method

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Abstract

The impingement of a droplet on a rigid square obstacle in a microchannel is simulated numerically using a high-density-ratio pseudo-potential multi-relaxation time LBM. The effects of Reynolds (Re) number, Weber (We) number, contact angle, obstacle size and kinematic viscosity ratio on the droplet dynamics after impact are investigated. It was found that the formation of the liquid film around the obstacle, the expansion of the droplet and its rupture time are all affected by these factors. As the Re number increases, the process of droplet falling along the obstacle is faster and the droplet demonstrates a more intense dynamic behavior. Increasing the We number makes the liquid film around the obstacle thinner and more stretched. Hydrophilicity and hydrophobicity of the obstacle surface play a major role in its surface wetting. For the hydrophobic obstacle wall, the separated sub-droplets move more rapidly toward the channel walls. As the hydrophobicity increases, the small droplet left on the upper surface of the obstacle will bounce upward. The bouncing tendency increases as the kinematic viscosity ratio decreases. As the obstacle size increases, the droplet expands more around it and approaches the channel walls faster.

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Abbreviations

a, b :

Parameters of Carnahan–Starling equation of state

C :

Source term

c :

Lattice speed (lu ts−1)

c s :

Speed of sound (lu ts−1)

D :

Droplet diameter (lu)

e :

Discrete velocity vector (lu ts−1)

f :

Distribution function (mu lu−3)

F :

Total force on each particle (mu lu−2 ts−2)

F m :

Fluid–fluid interaction force (mu lu−2 ts−2)

F ads :

Fluid–solid interaction force (mu lu−2 ts−2)

H :

Maximum horizontal width of the droplet interface (lu)

L :

Maximum vertical width of the droplet interface (lu)

M :

Transformation matrix

n :

Mode of oscillation

P :

Pressure (mu lu−1 ts−2)

Q :

Related to the source term

R :

Gas constant in the EOS

S :

Force term

s 0: s 8 :

Components of relaxation matrix

t :

Time (ts)

T :

Temperature (tu) and Oscillation period (ts)

V :

Macroscopic velocity (lu ts−1)

U :

Velocity of droplet (lu ts−1)

\( {u_{x} ,u_{y} }\) :

Components of velocity field (lu ts−1)

\( w_{\alpha } \) :

Weighting factor in the \( \alpha \) direction

BGK:

Bhatnagar–Gross–Krook

EOS:

Equation of state

LBE:

Lattice Boltzmann equation

LBM:

Lattice Boltzmann method

MRT:

Multi-relaxation time

SRT:

Single relaxation time

Re:

Reynolds number (\( \frac{UD}{\nu_{l}} \))

We:

Weber number (\( \frac{{\rho_{l} U^{2} D}}{\sigma } \))

Ca:

Capillary number (\( \frac{\rho_{l} {\nu_{l}} U}{\sigma } \))

Oh:

Ohnesorge number (\( \frac{{{\text{We}}^{0.5} }}{\text{Re}} \))

\( \nu \) :

Kinematic viscosity (lu2 ts−1)

\( \lambda \) :

Bulk viscosity (lu2 ts−1)

\( \theta \) :

Contact angle (°)

\( \tau \) :

Relaxation time (–)

\( \rho \) :

Density (mu lu−3)

\(\mathbf\Lambda \) :

Relaxation time matrix (–)

\( \sigma \) :

Surface tension coefficient \(({\text{mu \, ts}}^{-2})\)

\( \psi \) :

Interaction potential function (-)

\( \alpha \) :

Lattice direction

Anal:

Analytical

g:

Gas

Num:

Numerical

l:

Liquid

w:

Wall

e:

Energy

\( \zeta \) :

Energy square

j:

Momentum

q:

Energy flux

r:

Ratio

c:

Critical

eq:

Equilibrium

\( \widehat{{}} \) :

Moment space

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran

    Mehdi Bakhshan & Abdolrahman Dadvand

  2. Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology (KIT), Engesserstr. 20, 76131, Karlsruhe, Germany

    Martin Wörner

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  1. Mehdi Bakhshan
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Bakhshan, M., Wörner, M. & Dadvand, A. Simulation of droplet impingement on a rigid square obstacle in a microchannel using multiphase lattice Boltzmann method. Comp. Part. Mech. 8, 973–991 (2021). https://doi.org/10.1007/s40571-020-00384-9

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