# Pendant Capsule Elastometry

## TL;DR

This paper introduces a software tool for analyzing the shape of deflated elastic capsules to determine their elastic properties, enabling non-contact interfacial rheology measurements with applications in material characterization.

## Contribution

It presents a new software implementation for pendant capsule elastometry that accurately fits capsule shapes to determine elastic moduli using various constitutive laws.

## Key findings

- Nonlinear Hookean elasticity is suitable for most capsules.
- Elastic moduli can be tracked over deformation history for hysteresis analysis.
- The method's results agree with traditional rheological measurements.

## Abstract

We provide a C/C++ software for the shape analysis of deflated elastic capsules in a pendant capsule geometry, which is based on an elastic description of the capsule material as a quasi two-dimensional elastic membrane using shell theory. Pendant capsule elastometry provides a new in-situ and non-contact method for interfacial rheology of elastic capsules. Given an elastic model of the capsule membrane, pendant capsule elastometry determines optimal elastic moduli by fitting numerically generated axisymmetric shapes optimally to an experimental image. For each digitized image of a deflated capsule elastic moduli can be determined, if another image of its undeformed reference shape is provided. Within this paper, we focus on nonlinear Hookean elasticity because of its low computational cost its wide applicability, but also discuss and implement alternative constitutive laws. For Hookean elasticity, Young's surface modulus (or, alternatively, area compression modulus) and Poisson's ratio are determined; for Mooney-Rivlin elasticity, the Rivlin modulus and a dimensionless shape parameter are determined; for neo-Hookean elasticity, only the Rivlin modulus is determined, using a fixed dimensionless shape parameter. Comparing results for different models we find that nonlinear Hookean elasticity is adequate for most capsules. If series of images are available, these moduli can be evaluated as a function of the capsule volume to analyze hysteresis or aging effects depending on the deformation history. An additional wrinkling wavelength measurement allows the user to determine the bending modulus, from which the layer thickness can be derived. We verify the method by analyzing several materials, compare the results to available rheological measurements, and review several applications. We make the software available under the GPL license at github.com/jhegemann/opencapsule.