TY - JOUR

T1 - Rotating tensiometer for the measurement of the elastic modulus of deformable particles

AU - Villone, Massimiliano M.

AU - Stone, Howard A.

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevFluids.5.083606

DO - 10.1103/PhysRevFluids.5.083606

M3 - Article

AN - SCOPUS:85092050969

SN - 2469-990X

VL - 5

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 8

M1 - 083606

ER -