Convective flows of a colloidal suspension in a Hele-Shaw cell under vertical vibrations

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Abstract

Numerical simulation of convection of a colloidal binary mixture in a Hele-Shaw cell under vertical vibrations of finite amplitude has been carried out. The boundary of convective instability in a modulated gravity field is found. Bifurcation diagrams are constructed and the concentration distributions of nanoparticles corresponding to various solutions are analyzed. Thermal vibration convective flows are studied in the case of positive thermal diffusion of nanoparticles and their gravitational stratification. It is shown that vibrations, depending on the frequency, can both increase the intensity of the convective flow and weaken it.

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About the authors

I. N. Cherepanov

Perm State National Research University

Author for correspondence.
Email: che-email@yandex.ru
Russian Federation, Perm

B. L. Smorodin

Perm State National Research University

Email: bsmorodin@yandex.ru
Russian Federation, Perm

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Supplementary files

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2. Fig. 1. Geometry of the problem.

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3. Fig. 2. There is no thermal diffusion (ψ = 0). (a) The threshold of mechanical equilibrium stability depending on the frequency; (b) the dependence of the maximum function Ymax of the current on the Rayleigh number at different vibration frequencies compared to the static case.

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4. Fig. 3. Time dependences of the maximum value of the stream function Ψmax and the value of the stream function at a fixed point of the cell Ψloc, as well as the effective gravity geff, taking into account the acceleration in a static and vibration field; ψ = 0 at Ra = 0.4. The dotted line corresponds to the flow in the absence of vibrations. The vertical lines A and B indicate the moments of time for which the distribution fields of the stream function, temperature and concentration in the cell are presented in Fig. 4.

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5. Fig. 4. Fields of the current function, temperature and concentration during convection for different frequencies: (a–b) – ω = 5 10–4 and 5 10–2, corresponding to vertical lines A and B in Fig. 3.

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6. Fig. 5. a) Dependence of the maximum current function on time at Ra=0.2: 1, 2 – ω = 0, 0.01; b) Bifurcation diagrams (dependences of the average value of the maximum current function at different vibration frequencies, Pr=48, Le=5 10–4, Ψ = 8.8, Bm = 0.16; l/H =1.6, Av = 2.

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7. Fig. 6. Dependence of concentration in the center –3, at the lower –1 and upper boundary –2 at Ra = 0.02, ω = 1.2·10–3.

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8. Fig. 7. Distribution of impurity at Ψ = 8.8, Ra = 0.02, ω = 1.2·10–3, the initial frame –1 corresponds to time tstart = 84159, the interval between frames δt = 233.

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9. Fig. 8. Dependence of the maximum value of the current function on time. Ψ = 8.8, Ra = 0.02, ω = 1.2·10–3, vertical lines correspond to the times in Fig. 7.

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10. Fig. 9. Characteristic distribution of impurity at Ra = 0.02, ω = 1.0 10–2.

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