Inferring elastic moduli of droplets in acoustic fields

Abstract

The acoustic radiation force, as seen in apparati such as acoustic levitators, continues to find applications in materials science, manufacturing, and medical fields. One example of the utilization of an acoustic levitator is measuring the progress of clotting blood droplets. One of the largest advantages of using acoustic levitation is that the process is a minimal contact method. In some biological and chemical processes, surface contact can corrupt measurements, and acoustic levitation avoids these issues by using the acoustic radiation force to contain and manipulate the blood drop. The deformation of Newtonian liquid droplets via acoustic levitation has been well studied. In that case, the shape of the droplet is governed by the surface tension and shape curvature (Young-Laplace equilibrium). The quasi-static deformation of elastic droplets in acoustic levitators, however, has not yet been investigated. In this thesis, we explore the application of acoustic levitation to the characterization of the deformation of soft elastic droplets. This thesis consists of three main efforts. To start, the history of the acoustic radiation force and its applications are discussed. Next, a generalized theory for the acoustic radiation pressure acting on droplets of sizes similar to the acoustic wavelength is presented. We model the droplet as an incompressible, isotropic, linear elastic solid undergoing small deformations, under the conditions that the deformation is axisymmetric, with a purely radial traction condition, where the traction condition is derived from the acoustic radiation pressure. The quasi-static displacement and stress within the droplet is then solved for utilizing two potentials developed by Love (1926). We conclude by testing the validity of the theory by measuring the deformation and location of soft alginate gel spheres with known material properties in an acoustic levitator.