Effects of Contact-Line Pinning on the Adsorption of Nonspherical Colloids at Liquid Interfaces

The effects of contact-line pinning are well known in macroscopic systems but are only just beginning to be explored at the microscale in colloidal suspensions. We use digital holography to capture the fast three-dimensional dynamics of micrometer-sized ellipsoids breaching an oil-water interface. We find that the particle angle varies approximately linearly with the height, in contrast to results from simulations based on the minimization of the interfacial energy. Using a simple model of the motion of the contact line, we show that the observed coupling between translational and rotational degrees of freedom is likely due to contact-line pinning. We conclude that the dynamics of colloidal particles adsorbing to a liquid interface are not determined by the minimization of interfacial energy and viscous dissipation alone; contact-line pinning dictates both the time scale and pathway to equilibrium.

Figure 1

(a) Schematic showing the cross section through the long axis of an ellipsoidal particle breaching an interface. Simulations assuming the interfacial energy is minimized at each time step predict trajectories (solid lines) that are nonmonotonic in both the center-of-mass position and polar angle [32, 33]. Our experimental results (shaded ellipses) show a monotonic increase in both the height and polar angle. See also the movie in Supplemental Material [36]. (b) Schematic of contact-line motion for one scenario in (a). A line shows where the contact line moves in the frame of reference of the particle after time $\mathrm{\Delta }t$. The dynamic contact angles at two points are shown.

Figure 2

Schematic of the experimental setup. (a) The sample is illuminated with a red collimated laser ($\lambda =660\mathrm{nm}$). A counterpropagating infrared laser ($\lambda =785\mathrm{nm}$) is used to gently push the particles against gravity toward the interface. In the coordinate system used here, the imaging axis lies along $z$, and the interface is at $z=0$. The center-of-mass position and the polar angle $\theta$ of the particle are defined relative to the laboratory frame by a unit vector $\mathbf{u}$ that points along the long axis of the ellipsoid. (b) A typical hologram of an ellipsoid at an interface. See also the movie in Supplemental Material [36].

Figure 3

The height (a) and polar angle $\theta$ (b) of ellipsoids after they breach (breach at $t=0\mathrm{s}$) appear correlated (example marked with blue circles). To compare data from particles of different aspect ratios on the same plot, we normalize the center-of-mass height relative to the interface [33] to obtain $z_{\mathrm{COM}}=z/\sqrt{2a^2+b^2}$, where $a$ and $b$ are the semiminor and semimajor axes of the spheroid. (c) The polar angle varies with the height. Our model (red), based on contact-line hopping over defects, produces almost linear relationships between $z$ and $\theta$ for the particles from the experiments.

Figure 4

(a) A hydrophilic spherocylinder (${\alpha }_E<\pi /4$; hemispherical caps drawn in dotted lines) can reach a local minimum in the interfacial energy when the contact angle $\alpha ={\alpha }_E$. (b) Experimental data showing that a hydrophilic silica spherocylinder freely rotates about the $z$ axis once it has attached to the interface (shaded region), but its polar angle remains fixed. Arrows indicate the particle’s polar and azimuthal angles at the time points indicated by the red dotted lines.