Spreading of a micrometric fluid strip down a plane under controlled initial conditions

We experimentally study the spreading of a small volume of silicon oil down a vertical plane with small Bond number. The initial condition is characterized by a horizontal long fluid strip with cross sectional area $A$ and width $w_0$. We find that the experiments are characterized by a unique nondimensional parameter, $R\propto w_0^4∕\left(a^{2}A\right)$, where $a$ is the capillary length. An empirical criterium to estimate the onset of the contact line instability is established. The later rivulet formation at the contact line leads to a pattern which is characterized by a dominant wavelength. We find that this wavelength is approximately proportional to $R^{-1∕4}$.

Figure 1

Time evolution of the width of the fluid strip, $w$, scaled as suggested by Huppert [1]. The solid line is given by Eq. (2), and the dashed and dotted-dashed lines correspond to the same equation with different prefactors, with $C=9g{A}^{1∕2}∕\left(4\nu \right)$. The time range is the same as used in Fig. 3 of Ref. 1.

Figure 2

Time evolution of the width of the spreading, $w$. The inset is a magnification for very early times, which allows us to see case $E_5$.

Figure 3

Evolution of the width of the spreading $w$, using the scaling defined in Eq. (6). The spreading rate increases for increasing $R$ (see Table ).

Figure 4

Frontline evolution for three experiments: $E_2$ (squares), $E_4$ (triangle down), and $E_6$ (triangle up). The dotted lines are given by Eq. (9). The beginning of the instability is shown by the splitting of the data, which then correspond to the positions of a fingertip and a trough.

Figure 5

Dominant wavelength in the Fourier spectrum of the unstable contact line $\lambda$ in units of $w_0$. The solid line is the power law given by Eq. (10).