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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 |