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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 2
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Original Articles

Stationary contact line formation and particle deposition in dip coating

&
Pages 132-144 | Received 09 Oct 2015, Accepted 11 Feb 2016, Published online: 13 Jul 2016
 

ABSTRACT

The stationary contact line formation and particle deposition in the evaporation regime of dip coating is investigated numerically by solving the conservation equations of mass, momentum, energy, vapor mass fraction, and particle concentration. A sharp-interface level-set method for tracking the liquid–gas interface is extended to include the effect of phase change and to treat the particle deposition as well as the liquid–gas–solid contact line on a moving substrate. The computations demonstrate that the particle deposition occurs spontaneously near the stationary contact line and the deposition thickness depends on the deposition rate constant and the substrate withdrawal velocity.

Nomenclature

c=

= specific heat

dp=

= particle diameter

Dp=

= diffusion coefficient of particles in liquid

Dv=

= diffusion coefficient of vapor in air

Da=

= Damkohler number

F=

= fraction function

g=

= gravity

h=

= grid spacing

hlg=

= latent heat of vaporization

H=

= height

kd=

= particle deposition rate constant

L=

= domain length

=

= mass flux across the interface

M=

= molecular mass

n=

= unit normal vector

p=

= pressure

t=

= time

T=

= temperature

u=

= flow velocity vector, (u, v)

Vw=

= substrate withdrawal velocity

Wl=

= liquid film thickness

Wp=

= particle deposition thickness

x, y=

= Cartesian coordinates

Yp=

= particle volume fraction

Yv=

= vapor mass fraction

α=

= step function

β=

=

κ=

= interface curvature

λ=

= thermal conductivity

μ=

= dynamic viscosity

ρ=

= density

σ=

= surface tension coefficient

τ=

= artificial time

ϕ=

= distance function from the liquid–gas interface

Subscripts=
a, v=

= air, vapor

CL=

= liquid–gas–solid contact line

f=

= fluid

g, l=

= gas, liquid

I=

= interface

o=

= initial

p=

= particle

sat=

= saturation

w=

= wall

=

= ambient

Nomenclature

c=

= specific heat

dp=

= particle diameter

Dp=

= diffusion coefficient of particles in liquid

Dv=

= diffusion coefficient of vapor in air

Da=

= Damkohler number

F=

= fraction function

g=

= gravity

h=

= grid spacing

hlg=

= latent heat of vaporization

H=

= height

kd=

= particle deposition rate constant

L=

= domain length

=

= mass flux across the interface

M=

= molecular mass

n=

= unit normal vector

p=

= pressure

t=

= time

T=

= temperature

u=

= flow velocity vector, (u, v)

Vw=

= substrate withdrawal velocity

Wl=

= liquid film thickness

Wp=

= particle deposition thickness

x, y=

= Cartesian coordinates

Yp=

= particle volume fraction

Yv=

= vapor mass fraction

α=

= step function

β=

=

κ=

= interface curvature

λ=

= thermal conductivity

μ=

= dynamic viscosity

ρ=

= density

σ=

= surface tension coefficient

τ=

= artificial time

ϕ=

= distance function from the liquid–gas interface

Subscripts=
a, v=

= air, vapor

CL=

= liquid–gas–solid contact line

f=

= fluid

g, l=

= gas, liquid

I=

= interface

o=

= initial

p=

= particle

sat=

= saturation

w=

= wall

=

= ambient

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