Oscillatory convection in binary mixtures: Thermodiffusion, solutal buoyancy, and advection

Abstract

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numer-

Unstable periodic solution controlling collision of localized convection cells in binary fluid mixture

“…The ECGL equations are derived by Riecke from the equations describing two-dimensional convection of a binary fluid mixture within the Boussinesq approximation by imposing infinite Prandtl number, free-slip-permeable boundary conditions, and small Lewis number [21]. The equations are amplitude equations for the envelope of traveling waves that come in via a Hopf bifurcation [4,6], and another mode C in addition to A and B arises due to small Lewis number [21,22]. Other types of amplitude equations for traveling wave convection have been studied [23][24][25].…”

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

“…It is transported away into the well mixing convection bulk and replaced at the interface location by neutral ('yellow/green') δC. Note that increasing u beyond v p causes the appearence of closed streamlines of the velocity field in the frame comoving with the phase velocity of a traveling roll [16,24,68]. These closed streamlines regions are responsible for the characteristic roll structure of the C field in Fig When r is increased v + F tends to become (more) negative: convection to the right of the +interface can now, with increased heating, better invade the quiescent fluid to the left of it and thus ∂ r v + F (r, ψ) < 0.…”

“…The transient oscillatory growth of convection was investigated by numerical simulations [15]. Nonlinear standing wave solutions were obtained only recently [16,17]. Freely propagating convection fronts that connect subcritically bifurcating nonlinear TW convection with the stable quiescent fluid do not seem to have been investigated in detail beyond some first preliminary results [18,19,20].…”

Collisions of localized convection structures in binary fluid mixtures

“…In fact, the buoyancy difference between regions with different concentrations has already been identified in [11] as the cause of the traveling convection waves. However, the oscillatory behavior [3,6,8,9,[12][13][14][15][16][17][18][19][20][21][22] appears not only in the form of spatially extended, fully relaxed, nonlinear TW convection, but also in TW fronts moving into the quiescent fluid. Also, a mostly unstable standing wave solution branches out of the conductive state at the common Hopf bifurcation threshold.…”