Instability of Vertical Constant Through Flows in Binary Mixtures in Porous Media with Large Pores

Abstract

A binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical fluid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs are recovered. Sufficient conditions guaranteeing that a secondary steady motion or a secondary oscillatory motion can be observed after the loss of stability are found. When the layer is salted from above, a condition guaranteeing the occurrence of “cold” instability is determined. Finally, the influence of the velocity module on the increasing/decreasing of the instability thresholds is investigated.

Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field

“…We remark that condition (23) continues to be a sufficient condition for the onset of steady instability when the fluid is, initially, at the rest state [10]. Let us assume that (23) holds and let us compare R s in (21) with the critical Rayleigh thermal numbers in [10,22] found, respectively, in the absence of throughflow and in the absence of the magnetic field. When Pe → 0 (negligible throughflow), one has that lim Pe→0…”

“…that is the critical Rayleigh thermal number for the onset of steady instability of a vertical constant throughflow in a binary mixture saturating a horizontal porous layer, found in [22]. In the case (23), in order to look for the influence of the throughflow on the onset of instability, let us remark that…”

“…Just to mention a few, in [16,17], the instability of a vertical throughflow has been analyzed on considering, respectively, the effect of viscous dissipation and a non-Newtonian power-law fluid; in [18] the simultaneous influence of a vertical magnetic field and a rotation on the instability of a vertical throughflow in a clear fluid, is considered. In [19][20][21][22], the instability of a vertical constant throughflow in a binary mixture is analyzed on considering different effects such as the Brinkman law and a uniform rotation. Horizontally periodic throughflows have been analyzed in [23].…”

Instability of Vertical Throughflows in Bidisperse Porous Media

“…When the rest state loses its stability and steady convection occurs, a secondary steady motion, or throughflow, is observable. The stability of fluid motion in porous media finds relevant applications in industrial processes, geophysics, and astronomy and has been analyzed in many papers (see, for example [17][18][19][20][21][22][23][24][25][26] and the references therein).…”

“…In [17][18][19][20][21][22][23][24][25][26], the stability of vertical constant throughflows has been performed incorporating various effects, such as viscous dissipation [17]; chemicals dissolved in the fluid [19,22,25,26]; and an external magnetic field acting on an electrically conducting fluid [23]. The stability of non-constant throughflows was performed in [27].…”