Relationship between the pull-up speed and film thickness

Controlled by pull-up speed and viscosity of coating liquid

⇒ Generally, a faster pull-up speed results in a thicker film, while a slower pull-up speed results in a thinner film.

Case a：When the pull-up speed is high and the viscosity of the coated liquid is high

The film thickness in this case is determined by the balance between viscous resistance and gravity.

$h=C\sqrt{\frac{\mathrm{\eta U}}{\mathrm{\rho g}}}$

Case b：When the pull-up speed is sufficiently slow and the viscosity of the coating liquid is low

The surface tension at a gas and liquid interface governs the film thickness, and the following relationship holds.

$h=\frac{0.94{\left(\mathrm{\eta U}\right)}^{\frac{2}{3}}}{{\gamma }^{\frac{1}{6}}\sqrt{\mathrm{\rho g}}}$

U is the pull-up speed (m/s)、$\mathrm{;7}$ is viscosity (Pa・s = kg・m/s)、$\rho$ is density of coating liquid (kg/m³).
$\gamma$ is the surface tension of a liquid (N/m).
g is gravitational acceleration (m/s²).
C is coefficient (0.8 for Newtonian fluid)
In dip coating, Newtonian fluid is basically used as the coating liquid.