Acoustically Levitated Droplets

Acoustic pressure has been used to levitate drops of surfactant solution in liquid or air. One may deduce a drop's surface tension from its oscillation frequency (either its natural frequency, or the frequency response to a driving oscillation in the acoustic pressure). This method of measuring surface tension does not produce isotherms. (Tian et al., 1997, online)

Basic Assumptions

• The drop's equilibrium shape is a sphere
• We assume the drop's shape is axisymmetric throughout its oscillations
• Although the drop can oscillate in various modes, we restrict our analysis to the basic (L=2) mode, in which the droplet elongates and contracts along the central axis:

  

(Holt et al., 1997, online; Trinh et al., 1987, binder)

If we ignore the effects of viscosity in the droplet and the surrounding substance, we can write the droplet's frequency as

f_L² = (L (L+2) (L-1) s)/ (d R³)

where L is the mode (2 in our case), d is the density of the droplet, s is the surface tension, and R is the radius of the equilibrium sphere. (Trinh et al., 1987, binder) A detailed treatment of viscosity and elasticity leads to a significantly more complicated equation. (c.f. Tian et al., 1997, online)

This method produces uncertainties in surface tension around 5%. (c.f. Trinh et al., 1987, binder)

Pendant and Sessile Drops

A pendant drop:

A sessile drop:

Surface tension can be measured by taking pictures of drop shapes and fitting the Laplace equation of capillarity to their contours. The basic form of this equation is:

Here, is the change in pressure across the interface, is the surface tension, and R₁ and R₂ are the radii of curvature. (Adamson, 1990, Measurement binder) The fit may use standard measurements, such as the drop width and height, or it may take several points from a digitized profile of the drop. (c.f. Adamson, 1990, Measurement binder and del Río and Neumann, 1997, online)

ADSA (Axisymmetric Drop Shape Analysis) is a popular program for determining surface tension, created by the group of A.W. Neumann at the University of Toronto. (del Río and Neumann, 1997, online) This program solves the following form of the Laplace equation numerically:

(Jennings and Pallas, 1988, binder)

where b is the curvature at the origin and c is the capillary constant:

(del Río and Neumann, 1997, online)

The program takes the density of the fluid and the local gravity as parameters. It varies curvature, surface tension, and scaling factors to find a good fit to the experimental data. When used with static droplets, the method has an error of less than 1%. (del Río and Neumann, 1997, online)

ADSA has been used to make oscillating droplets into a film balance.

Surfactant is spread at the drop's surface using a syringe, or allowed to adsorb from solution. (c.f. Wege et al., 1999, online and Prokop et al., 1998, binder) The drop's volume can be varied with time using a syringe or a microinjector at the top of the capillary. This produces changes in the surface area and surface tension.

Advantages of the ADSA film balance:

• Small volume
• Easy to spread a known amount of surfactant at the surface
• Rapid rates of surface area change compared to Langmuir-Wilhelmy balance

Disadvantages of the ADSA film balance:

• Loss of surfactant due to spreading on capillary (especially at low surface tension)
• Possible resolution problems at low surface tension (more often a problem with sessile drops, which have not been used in a film balance)
• Capillary must be very smooth to preserve axisymmetry

(Wege et al., 1999, online)