Abstract
In the present work the Soret-induced convection of binary and ternary mixtures with negative separation ratios in a square cavity heating from above in the gravity field is investigated. The parameters of the binary mixtures coincide with the parameters of binary mixtures constituting the ternary mixture, which allows one to observe the effect of adding one more solute to the binary mixture. Analysis of the temporal dependences of the integral characteristics of the convection of binary and ternary mixtures shows that an increase in the separation ratio of the binary mixture value or the net separation ratio of the ternary mixture value leads to an acceleration of the instability onset. The magnitude of the jump in the intensity of the flow that accompanies the instability onset also increases with the separation ratio modulus of the mixture. Dependences of the time of the instability onset, the maximum value of the modulus of the stream function attained at the moment of instability onset, and the corresponding to this time moment components concentration difference between the centers of horizontal boundaries on the separation ratio of the binary mixture and on the separation ratio of the second component at a fixed separation ratio of the first solute for the ternary mixture are presented. The temporal evolution of the structures of the emerging flow and the fields of solutes concentration are observed. It is shown that the adding of one more solute to the binary mixture leads to an acceleration of the instability onset, an increase in the intensity of the flow and a decrease in the concentration difference between the horizontal boundaries.
Highlights
In the present work the Soret-induced convection of binary and ternary mixtures with negative separation ratios in a square cavity heating from above in the gravity field is investigated
The parameters of the binary mixtures coincide with the parameters of ternary mixture in the limiting case of the zero equality of the separation ratio of the one component, which allows one to observe the effect of adding one more solute to the binary mixture
Analysis of the temporal dependences of the integral characteristics of the convection of binary and ternary mixtures shows that an increase in the separation ratio of the binary mixture value or the net separation ratio of the ternary mixture value leads to an acceleration of the instability onset
Summary
Рассмотрим термоконцентрационную конвекцию в квадратной полости с длиной стороны L , заполненной жидкой смесью из n компонент. 1. Будем считать, что отклонения температуры T и концентраций компонент Ci ( i 1, , n 1 ) от некоторых значений T0 и Ci0 , принимаемых за начало отсчета, малы, так что вызываемые ими отклонения плотности смеси от значения. 0 T0 ,Ci0 также малы и можно считать плотность линейно зависящей от температуры и концентраций компонент:. Уравнения свободной термоконцентрационной конвекции многокомпонентной смеси в приближении Буссинеска имеют вид (см., например, [18, 19]):. D – матрица коэффициентов молекулярной диффузии, DT – вектор коэффициентов термодиффузии. Что векторы концентраций компонент смеси и коэффициентов термодиффузии являются псевдовекторами, поэтому здесь и далее такие и истинные векторы обозначаются поразному. Уравнения свободной конвекции многокомпонентной смеси в безразмерной форме при использовании прежних обозначений для безразмерных переменных принимают вид:.
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