Liquid Droplets on a Highly Deformable Membrane

We examine the deformation produced by microdroplets atop thin elastomeric and glassy free-standing films. Because of the Laplace pressure, the droplets deform the elastic membrane thereby forming a bulge. Thus, two angles define the droplet or membrane geometry: the angles the deformed bulge and the liquid surface make with the film. These angles are measured as a function of the film tension, and are in excellent agreement with a force balance at the contact line. Finally, we find that if the membrane has an anisotropic tension, the droplets are no longer spherical but become elongated along the direction of high tension.

Figure 1

(a) Schematic of the side view of liquid droplets on the top and bottom side of the film, not to scale. (b) Microscope images of the side view of a droplet (left) and bulge (right). The top half of the image is the direct visualization of the droplet or bulge, while the bottom half corresponds to a reflection off the film itself. The curves represent spherical cap fits to the profiles. The scale bar represents $20\mu \mathrm{m}$. (c) Schematic of a droplet and bulge with the relevant angles identified. The expanded view shows the interfacial and mechanical tensions acting on the contact line.

Figure 2

(a) The droplet contact angle, (b) the bulge contact angle, and (c) the total internal liquid angle plotted as a function of the normalized tension [see Eq. (1)] for glycerol on SIS (circles) and glycerol on PnBMA (squares). The curves are Eq. (2) and Eq. (3) with ${\theta }_y$ given by the Young’s angle of glycerol on SIS (represented by the dotted horizontal lines). The dashed black lines are bounds to the theory due to uncertainty in ${\theta }_y$. The uncertainty in the theoretical curve for ${\theta }_b$ is on the order of the thickness of the curve itself. (d) $(\cos {\theta }_y-\cos \alpha )/{\sin }^2{\theta }_y$ as a function of $\gamma /2T_{\mathrm{in}}$ for four liquid-substrate combinations. The black line is the theoretical prediction. The vertical and horizontal error bars stem from uncertainties in the measured values of ${\theta }_d$ and ${\theta }_b$.

Figure 3

(a) The tension as measured with PEG compared to those measured with glycerol on the same SIS sample. The black line is a linear fit to the data. (b) The tension as measured with micropipette deflection correlated to those measured with glycerol on SIS (circles) and PnBMA (squares). The black line represents the theoretical relationship, where the thickness of the line is indicative of its upper and lower bound given uncertainties in ${\theta }_y$. Error bars for liquid tensions stem from uncertainties in determining ${\theta }_d$ and ${\theta }_b$, whereas error bars for pipette tensions arise from uncertainties in the spring constant of the pipette as well as in measuring the deformation of the film.

Figure 4

(a) Top view of a water droplet atop a SIS film with isotropic tension ($T_x=T_y$). The droplet is round when viewed from above. (b) Top view of a water droplet atop a SIS film which has been stretched in the $y$ direction ($T_y>T_x$). A white circle is superimposed to emphasize that the droplet is elongated along the direction of high tension. The scale bar represents $50\mu \mathrm{m}$.