Linear Three Dimensional Instability of Viscoelastic Fluid Layers Flowing Down Cylindrical Walls

Abstract

In this paper we present results of the three dimensional linear instability of a viscoelastic thin film flowing down a vertical cylinder. The Oldroyd B fluid model is used. It is shown that the destabilizing effects of viscoelasticity appear in two ways: by increasing the growth rate and by promoting the appearance of more azimuthal modes for a smaller radius of the cylinder.

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

“…The linear evolution equation calculated below, reduces to that of Joo [18] when the radius of the cylinder tends to infinity and in the absence of thermocapillary effects. In the lack of thermocapillary effects the equation reduces to that in [37]. The results of this paper are new not only because of the combination of viscoelasticity [37] and thermocapillarity [31] in flow on the surface of a cylinder, but also because the problem investigated is three dimensional.…”

“…In the lack of thermocapillary effects the equation reduces to that in [37]. The results of this paper are new not only because of the combination of viscoelasticity [37] and thermocapillarity [31] in flow on the surface of a cylinder, but also because the problem investigated is three dimensional. This can be seen in the review section on thin film flow down cylinders presented in Dávalos-orozco [17].…”

“…In Moctezuma-Sánchez and Dávalos-Orozco [37] the viscoelastic Oldroyd's constitutive equation model was used to investigate the longwave linear instability of a fluid film flowing down a cylinder. The corresponding linear equation reduces to that obtained by Joo [18] (without power-law fluid effects) when the radius of the cylinder tends to infinity.…”

“…The corresponding linear equation reduces to that obtained by Joo [18] (without power-law fluid effects) when the radius of the cylinder tends to infinity. In particular, the interest in [37] is to determine the relevance of the azimuthal modes in the presence of viscoelasticity. It is found that the most unstable mode is always the axial one.…”

“…A comparison is done with the results of the isothermal [37] flow and the Newtonian fluid [31] flow. The Oldroyd's fluid model is selected for the constitutive equation of the fluid.…”