Rivulet flow of generalized Newtonian fluids
Al Mukahal, F. H. H. and Duffy, B. R. and Wilson, S. K. (2018) Rivulet flow of generalized Newtonian fluids. Physical Review Fluids, 3 (8). 083302. ISSN 2469990X (https://doi.org/10.1103/PhysRevFluids.3.083302)
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Abstract
Steady unidirectional gravitydriven flow of a uniform thin rivulet (i.e. a rivulet with small transverse aspect ratio) of a generalised Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the shear rate, and the explicit solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behaviour of these two fluids. In addition, the general behaviour of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux, as well as the behaviour of rivulets of strongly shearthinning Carreau and Ellis fluids, are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three nondimensional parameters and of an Ellis fluid on two of its three nondimensional parameters leads to the expected dependence of the behaviour of the rivulet on these parameters (namely that increasing the viscosity of the fluid leads to a larger rivulet), the nonmonotonic dependence of the viscosity of an Ellis fluid on the non dimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behaviour of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shearthinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of nonzero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a nonconstant powerlaw viscosity, leading to a pluglike velocity profile with large magnitude in the narrow central region of the rivulet.
ORCID iDs
Al Mukahal, F. H. H., Duffy, B. R. ORCID: https://orcid.org/0000000326877938 and Wilson, S. K. ORCID: https://orcid.org/0000000178419643;

Item type: Article ID code: 64569 Dates: DateEvent6 August 2018Published19 June 2018AcceptedKeywords: Newtonian fluid, viscosity, Carreau fluids, Ellis fluids, rivulets, Physics, Mathematics, Physics and Astronomy(all), Mathematical Physics, Fluid Flow and Transfer Processes Subjects: Science > Physics
Science > MathematicsDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 22 Jun 2018 09:36 Last modified: 09 Dec 2021 01:49 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/64569