Drops spreading on fluid surfaces: Transition from Laplace to Marangoni regime

We show the occurrence of two distinguished classical regimes of wetting, namely, Laplace and solutal Marangoni, during the spreading of oil drops on a surfactant-laden aqueous phase in a single surfactant-oil-water system. The spreading kinetics is found to follow a power-law behavior not only in the Laplace and Marangoni regimes, but also in the transition regime. Our experimental findings are corroborated with the scaling laws. The results demonstrate that increasing the surfactant concentration across the critical micelle concentration is instrumental to obtain the Laplace to Marangoni transition. Moreover, this transition does not depend on surfactant chemistry; instead, it depends on the adsorption/desorption kinetics of surfactant molecules to/from the interfaces that are created or annihilated during drop spreading.

Figure 1

(a) Schematic representation of the experimental setup used to study spreading of an oil drop on aqueous surfactant solutions. The top view of a $5\mu \mathrm{l}$ decane drop spreading on (b) 0.6 mM and (c) 2.0 mM aqueous CTAB solution as a function of time. The scale bar for each image in (b) and (c) represents 2 cm. A dashed circle is drawn to enable easy identification of the spreading drop from the background. (d) Spreading kinetics of oil drops on aqueous CTAB solutions of different concentrations. In all spreading experiments, the surfactant solution was taken in a Petri dish of diameter $d_p=12.6$ cm, filled up to a height $L=4$ mm, and allowed to equilibrate for 6 h before introducing a decane drop of volume, $V=5\mu \mathrm{l}$. Schematic representation of the surfactant dynamics that occur during the spreading and the corresponding flow profile in (f) the Laplace regime ($C<C_{\text{CMC}}$), which is characterized by the power-law scaling $R\sim t^{1/8}$ [Eq. (1)], and (g) the Marangoni regime ($C>C_{\text{CMC}}$), which is characterized by the power-law scaling $R\sim t^{\frac{3}{4}+\frac{m}{2}}$ [Eq. (4)].

Figure 2

Effect of (a) substrate liquid height ($L$) and (b) Petri dish diameter ($d_p$) and drop volume ($V$) on the power-law exponent ($n$) for the spreading of a decane drop on an aqueous CTAB solution of concentrations varying across CMC. (c) Spreading kinetics of decane drops on aqueous Triton X-100 solutions when the concentration of the surfactant is varied across CMC ($C_{\text{CMC}}=0.25$ mM). Other experimental conditions are the same as those described in the caption of Fig. 1.