# Capillary micromechanics: Measuring the elasticity of microscopic soft objects

Original entry: Darren Yang, AP225, Fall 2010

## Reference

Capillary micromechanics: Measuring the elasticity of microscopic soft objects. Hans M. Wyss, Thomas Franke, Elisa Mele and David A. Weitz, *Soft Matter* **6**, 4550-4555 (2010).

## Summary

The authors present a simple method to measure the elastic properties of microscopic deformable particles. The elastic properties of microscopic particles are determined by measuring the pressure-induced deformation of soft particles as they are forced through a tapered glass microcapillary. This method can determine the compressive and the shear modulus of a deformable object in one single experiment.

## Background

At low particle concentrations suspensions of soft objects exhibit a viscoelastic response similar to hard spheres, but as the concentration increases they can behave much differently. Since the particles are deformable, at a higher concentration, the suspensions of particles exhibit a lower viscosity as the particles deform and shrink. While existing techniques such as atomic force microscopy (AFM) or micropipette aspiration can be used to characterize a mechanical response at small scales, these methods are often difficult to carry out, as they require localizing each particle under a microscope. In addition, they probe a highly localized response at the surface of a soft particle but do not readily provide information on the elastic response of the entire particle. Thus, in this article the author present a much simpler and direct method for characterizing the mechanics of microscopic soft objects. The approach directly characterizes the elastic properties of entire soft objects. They use a microfluidic setup where particles are deformed in tapered microcapillaries; direct imaging of their deformation with an optical microscope enables us to characterize both the compressive and the shear modulus of a soft particle in a single experiment.

## Method

The experimental setup is summarized in Figure 1. A dilute suspension of soft particles flows towards the tapered tip of a microcapillary as a result of an applied pressure difference. For low pressure values < 10,000 Pa the authors use the height difference of the sample reservoir and outlet of the microcapillary tip to apply a hydrostatic pressure, and much higher pressures can be achieved by connecting the sample reservoir to a pressure regulator. As a single particle blocks the flow of fluid, the particle deforms until the pressure-induced external stresses are balanced by its internal elastic stress. The pressure-dependence of the shape and size of the particle is thus a direct measure of its elastic properties.

Figure 1. Schematic of the experimental setup.

To verify the method, the authors use the most general type of elastic material, which is both deformable and compressible. The use microgel particles to test the both elastic properties of shear resistance and compressibility. The particles consist of a sparse, crosslinked polymer network of poly-acrylamide, with a background fluid of water; the elastic properties of this system can be conveniently tuned by adjusting the concentration of polymer and of the cross-linker during synthesis.

## Results

Typical results are shown in the series of images in Figure 2A, where a particle is shown under an applied pressure difference that increases from p = 100 Pa in the top image to 300 Pa in the bottom image. As the pressure is increased it becomes more elongated and is compressed along the radial direction as it moves closer to the tip of the capillary.

The surface of the particle that is in contact with the glass walls has the shape of a tapered band with circular cross section. The authors use the length (L) and the average radius (R) of this band as a measure of the length and the radius of the particle, respectively. As the pressure is increased, L increases, while R decreases (Figure 2B). Moreover, a significant change in volume is also observed; the particle is compressed as the applied pressure is increased (Figure 2B). The compressive modulus of the particle is given by the slope of the compressive stress as a function of the volumetric strain, K ≈ 4.5 kPa (Figure 2D). The elastic shear modulus is the slope of the differential stress (pwall – p)/2 as a function of εr – εz, G ≈ 0.8 kPa (Figure 2E).

Figure 2. (A) Series of images of a microgel particle being deformed as the applied pressure increases; from top to bottom: p = 100 Pa, 150 Pa, 200 Pa, 250 Pa, 300 Pa. (B) Change of the particle geometry. (C) Schematic of deformation. (D) Compressive stress as a function of the volumetric strain; the dashed line is a linear fit to the data; the compressive modulus of the particle is given by the slope of this curve, K ≈ 4.5 kPa. (E) Differential stress (pwall – p)/2 as a function of εr – εz; the elastic shear modulus is the slope of the linear fit curve, G ≈ 0.8 kPa.

The authors demonstrated that this approach enables the quantification of the full elastic response of soft particles, expressed in terms of the compressive modulus K and the shear modulus G from a single experiment. This approach enables us to derive the average properties of an entire soft object, while other methods such as atomic force microscopy (AFM) are more suited to characterize the localized response at nanometer length scales.