Instability of thermocapillary liquid layers for Oldroyd-B fluid

Abstract

The linear stability analysis of Oldroyd-B fluid for thermocapillary liquid layers is carried out. Results are presented for linear flow and return flow with Prandtl numbers of 0.02 and 100. Three kinds of instabilities are found: oblique wave, streamwise wave, and spanwise stationary mode, whose properties are all significantly affected by elasticity. For the first, the critical Marangoni number increases with elasticity. For the second, the work done by perturbation stress fluctuates in vertical direction. The last becomes the preferred mode when the elasticity is high enough and its perturbation energy comes from the Marangoni force caused by perturbation temperature while dissipates by perturbation stress. Their mechanisms are discussed and the comparisons are made with Newtonian fluid.

Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient

“…Thus, a validation by using the results obtained in their studies is difficult. Instead, a three-way validation using the results obtained by Smith & Davis (1983a,b) and Hu, He & Chen (2016) for a purely HTG and Perez-Garcia & Carneiro (1991) for a purely VTG, is presented below. Smith & Davis (1983b) analysed surface-wave instabilities in a liquid layer subjected to a purely HTG.…”

“…The results presented in figure 1 show an excellent agreement between Smith & Davis (1983b) and the present numerical approach, thereby validating the latter. Smith & Davis (1983b), however, did not present the eigenspectrum; thus, to achieve an independent validation for our numerical technique, the eigenspectrum obtained using Present numerical approach Hu et al (2016) 0.000026 + 0.031995i 0.000026…”

“…The four leading eigenvalues in the eigenspectrum for a liquid layer subjected to a purely HTG obtained using our numerical approach and those taken from Hu et al (2016) with Pr = 0.02, Ma = 6.15, k = 0.0251676, m = 0.389187, Bo = 0, Bi = 0 and Ca = 0. The agreement between the two columns validates our numerical technique.…”

Rayleigh–Bénard convection in viscoelastic liquid bridges

“…Among such formulations, widespread success has been enjoyed by the so-called Oldroyd-B framework owing to its relative simplicity and the remarkable possibility to derive it starting from the self-consistent framework of continuum mechanics (Bird et al 1987;Revuz & Yor 1994;Alves, Oliveira & Pinho 2003;Bonito et al 2011;Lappa 2019a). This archetype and related variants have been used by several investigators to investigate the typical dynamics of both thermogravitational and thermocapillary flows in viscoelastic fluids (Green 1968;Vest & Arpaci 1969;Sokolov & Tanner 1972;Eltayeb 1977;Rosenblat 1986;Martínez-Mardones & Pérez-Garcíıa 1990, 1992Larson 1992;Khayat 1994Khayat , 1995Martínez-Mardones et al 1996;Park & Lee 1996;Parmentier et al 2000;Park & Ryu 2001a,b, 2002Li & Khayat 2005;Park et al 2009;Park & Lim 2010;Hu, He & Chen 2016;Lappa & Ferialdi 2018a;Park 2018).…”

Linear stability of thermocapillary liquid layers of a shear-thinning fluid

“…The shear thinning combined with elastic effects is produced in the polymer processing, which have great impacts on the flow. The effect of viscoelasticity on the stability of thermocapillary liquid layers has been investigated in some previous studies, [15][16][17] which show that the instability can be markedly affected by elasticity.…”