Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Dilatational and shear rheology of soluble and insoluble monolayers with a Langmuir trough

HYPOTHESIS

The surface dilatational and shear moduli of surfactant and protein interfacial layers can be derived from surface pressures measured with a Wilhelmy plate parallel, ΔΠpar and perpendicular ΔΠperp to the barriers in a Langmuir trough.

EXPERIMENTAL

Applying area oscillations, A0+ ΔAeiωt, in a rectangular Langmuir trough induces changes in surface pressure, ΔΠpar and ΔΠperp for monolayers of soluble palmitoyl-lysophosphatidylcholine (LysoPC), insoluble dipalmitoylphosphatidylcholine (DPPC), and the protein β-lactoglobulin to evaluate Es∗+Gs∗=A0ΔΠparΔA and Es∗-Gs∗=A0ΔΠperpΔA. Gs∗ was independently measured with a double-wall ring apparatus (DWR) and Es∗ by area oscillations of hemispherical bubbles in a capillary pressure microtensiometer (CPM) and the results were compared to the trough measurements.

FINDINGS

For LysoPC and DPPC, A0ΔΠparΔA≅A0ΔΠperpΔA meaning Es∗≫Gs∗ and Es∗≅A0ΔΠparΔA≅A0ΔΠperpΔA. Trough values for Es∗ were quantitatively similar to CPM when corrected for interfacial curvature. DWR showed G∗ was 4 orders of magnitude smaller than Es∗ for both LysoPC and DPPC. For β-lactoglobulin films, A0ΔΠparΔA>A0ΔΠperpΔA and Es∗ and Gs∗ were in qualitative agreement with independent CPM and DWR measurements. For β-lactoglobulin, both Es∗ and Gs∗ varied with film age and history on the trough, suggesting the evolution of the protein structure.