Dewetting of evaporating thin films over nanometer-scale topographies

A lubrication model is used to study dewetting of an evaporating thin film layer over a solid substrate with a nanometer-scale topography. The effects of the geometry of the topography, the contact angle, the film thickness, and the slippage on the dewetting have been studied. Our results reveal that the evaporation enhances the dewetting process and reduces the depinning time over the topography. Also it is shown that the depinning time is inversely proportional to the slippage and increasing the contact angle may considerably reduce the depinning time, while the film thickness increases the depinning time.

Figure 1

Dewetting of a film over a topography. The film moves to the right because of the dewetting.

Figure 2

(a) The typical profile of the DJP. (b) The zeros for different given value of $B$.

Figure 3

Initial conditions for the dewetting process. The slope is 2.17°. It is assumed that the dewetting starts near the topography. Initial thickness of the liquid film is equal to 20. All parameters are dimensionless.

Figure 4

Effect of the evaporation on the dynamic of the dewetting of the film over a trapezoidal topography. Time evolution of the flow of the film is shown. For both cases $C$ = 0.21, $B$ = 0, and total time is 2 500 000. Both axes are nondimensional. (a) Nonevaporating film. (b) The evaporating film with $C_1$ = 1.0, $C_2$ = 0.0049, and $R$ = 1.

Figure 5

The effect of $C_2$ on the rate of dewetting of film. $C_1$ = 1.0, $C$ = 0.21, and $B$ = 0.0 for all the cases. The results are for time = 8500. The topography is a sinusoidal curve. Increasing $C_2$ considerably increases the rate of dewetting.

Figure 6

The effect of $C_1$ on the rate of dewetting. $C_2$ = 0.05, $C$ = 0.21, $B$ = 0, and $R$ = 1 for all the cases. The results are for time = 8500. The topography is a sinusoidal curve. Increasing $C_1$ increases the dewetting rate.

Figure 7

Dewetting of evaporating films over the steps; time evolution of flow of the film is shown for different intervals. (a) Liquid can pass through the upward step with no interaction. (b) Pinning of contact line for a downward step. The liquid front is blocked and after a certain time it passes over the topography. For both cases $C_1$ = 1.0, $C_2$ = 0.05, $C$ = 0.21, $B$ = 0, and $R$ = 1.

Figure 8

The contact angle (degree) of the pinned area for a nonevaporating case during the pinning for $d$ = 2. $\theta =53.4t^{{*}^{-0.31}}$ can well represent the data points.

Figure 9

The effect of the evaporation on the depinning time of a downward step. (a) The initial condition and the downward step topography with height 2. (b) $C_2$ has an important role on the depinning time. (c) $C_1$ is inversely proportional to the depinning time. (d) The depinning time increases by increasing height of the step (d). All the parameters are dimensionless and $R$ = 1.0.

Figure 10

The effect of the step slope on the depinning time over a downward step. (a) A downward step with a height equal to 3 and a slope equal to 2°. (b) The time as a function of the slope angle (λ). $C_2$ = 0.05, $C$ = 0.21, and $R$ = 1. The depinning time increases with the slope size.

Figure 11

(a) The effect of dimensionless parameter $C$ in the DJP on the depinning time for an evaporating film with $C_2$ = 0.05, $B$ = 0, and $R$ = 1 for all the cases. The step height is 2. (b) Comparing the case with $C_1$ = 0.1, $C_2$ = 0.05, $B$ = 0, and $R$ = 1 to power law curve, $t^{*}=469864C^{-0.899}$.

Figure 12

The effect of dimensionless parameter $B$ in the DJP on the depinning time for an evaporating film with $C_1$ = 1.0, $C_2$ = 0.05, $C$ = 0.21, and $R$ = 1 for all the cases. The step height is 2.

Figure 13

The effect of the step height on the depinning time for an evaporating film. The topography is a downward step with the height 2. Depinning time increases smoothly with the film thickness enhancement. $C_1$ = 0.1, $C_2$ = 0.05, $C$ = 0.21, $B$ = 0, and $R$ = 1 for all the cases.

Figure 14

The effect of the different slip lengths on the depinning of a thin evaporating film. The topography is a downward step with the height equal to 2. Depinning time is decreased byincreasing the slippage. $C_2$ = 0.1, $C$ = 0.21, $B$ = 0, and $R$ = 1 for all the cases.