Rotating tensiometer for the measurement of the elastic modulus of deformable particles

In a spinning drop tensiometer, the interfacial tension between two immiscible fluids can be inferred from the equilibrium shape of a drop suspended in a denser rotating immiscible liquid [B. Vonnegut, Rev. Sci. Instrum. 13, 6 (1942)RSINAK0034-674810.1063/1.1769937]. For small deformations of the droplet, an analytical solution for the droplet's shape exists [H. A. Stone and J. W. M. Bush, Q. Appl. Math. 54, 551 (1996)QAMAAY0033-569X10.1090/qam/1402409]. Similarly, we derive an analytical solution for the deformation dynamics of an initially spherical elastic particle suspended in a denser viscous rotating liquid. At long times, the particle attains a steady-state deformed shape that depends on the rotational Bond number, from which it is possible to get a measurement of the particle's elastic modulus, thus giving a proof of concept for a rotating tensiometer. Direct numerical simulations are used to validate the theory and identify its limits of applicability.