(628a) Interfacial Rheology of an Oscillating Spherical Cap

Interfacial viscoelasticity is an important contributor to the stability of emulsions and foams with adsorbed macromolecules and particles. A common method of measuring interfacial mechanics involves blowing a bubble at a capillary tip and measuring the pressure jump across the interface of the expanding or oscillating interface. We have implemented a similar method of measuring apparent interfacial elasticity in a microtensiometer capable of measuring interfacial properties of small (radius ~10^-5 m) droplets.  In this device, the interface forms a spherical cap at the end of a drawn capillary tube that is tens of micrometers in diameter. The imposed pressure inside the spherical cap oscillates sinusoidally with amplitude of the order of 100 Pa and frequencies from 0.05 to 0.5 Hz. The microtensiometer has several advantages for rapid measurement of novel surface active species, including small sample volumes, faster transport timescales, and simple interfacial shape analysis. The common assumption that the interface is a sphere expanding radially in all directions is not valid since the radius of the capillary and the bubble are comparable and the interface is pinned at the edges of the capillary tube. In the present study, we use toroidal coordinates to derive the surface deformation tensor, and show that the deformation of an expanding or oscillating spherical cap pinned at a capillary tip is purely dilatational with a non-uniform dilatation rate along the interface. We discuss the tangential velocity at the interface of the growing bubble in a Newtonian fluid via a solution of the stream function and show the conditions when this flow contributes significantly to the interfacial deformation. The interfacial dilatation rate is greatest at the tip of the spherical cap and smallest at the contact line, leading to the equivalent of a non-viscometric flow for an interface. We use existing interfacial rheological models to derive the expected pressure jump as a function of oscillation frequency and amplitude, the capillary and interfacial radii, and the interfacial mechanics for several model interfaces. We use these model systems to demonstrate the appropriate interpretation of oscillatory interfacial measurements for deforming spherical caps, and apply our model to experiments measuring the interfacial elasticity of particle and surfactant adsorbed interfaces. Finally, we discuss experimental protocols that can allow for the separation of various contributions to the interfacial elasticity.