In situ measurement of the viscoelastic modulus of gels using pure twist-theory

We propose a simple method to measure the viscoelasticity of hydrogels. Our method is based on twisting a flat-ended circular indenter on a thin layer of gel. Since poroelastic flow is suppressed under pure shear, such a method allows direct and separate measurement of the solid gel network's viscoelastic properties. A potential advantage of this method is that it is possible to carry it out in situ, e. g. under cell culture conditions, and with high-throughput. We use the correspondence principle to determine the relationship between the applied torque and the history of twist by solving an elasticity problem. A solution is obtained using the finite element and Hankel transform methods. The relation between the applied torque and the history of twist can be expressed in a simple closed-form expression involving the relaxation function of the gel, the thickness of the gel layer and the indenter radius.