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Mannheimer and Schechter model revisited: Viscosimetry of a (non-)Newtonian and curved interface
Phys. Rev. Fluids 4, 054002 – Published 13 May, 2019
DOI: https://doi.org/10.1103/PhysRevFluids.4.054002
Abstract
The impact of a Newtonian or non-Newtonian interface, possibly curved due to wetting effects, on the surface viscosimetry method historically developed by Mannheimer and Schechter [Mannheimer and Schechter, J. Colloid Interface Sci. 32, 195 (1970); Mannheimer and Schechter, J. Colloid Interface Sci. 32, 212 (1970)] is investigated theoretically and numerically in this paper. The Reynolds number is considered small enough for inertial effects to be negligible and thus for surface shear viscosity to be preferentially studied. The classical Boussinesq-Scriven law is modified by a shear-dependent viscosity governed by the Carreau constitutive law. The case of a curved interface is also investigated whether the liquid is hydrophilic or hydrophobic (liquid metals), which is revealed to be relevant for a liquid with a significant capillary length. The shallow-channel layout is found to be particularly well suited to the detection of a non-Newtonian liquid surface whatever its mechanical behavior: shear thinning or shear thickening. A key to evaluating the parameters involved in a surface viscosity model is to carry out a series of experiments at various rotation speeds, with preferably a nonwetting contact angle. Indeed, it is demonstrated that such a contact angle tends to amplify non-Newtonian effects, especially for a carrier fluid with a significant capillary length.
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