Nonlinear approach to flow instability of the orifice-centerline liquid induced by bubble chain rising in shear-thinning fluids

Abstract

The flow characteristics of orifice-centerline liquid induced by bubble chain rising in carboxymethylcellulose (CMC) aqueous solution have been investigated using nonlinear analysis of the velocity measured by Laser Doppler Anemometry. Both axial and radial velocities are determined under various gas flow rates (Q_g), measurement heights (z) and mass concentrations. The results show that for low Q_g, z and dilute solution, the characteristic frequency of the power spectrum is consistent with bubbling frequency, with uniform elliptical shape of reconstructed phase space. Largest Lyapunov exponents λ₁ in radial direction is approximately 10 times that in the axial direction. Whereas for high Q_g, z and concentrated solution, power spectrums are of broad coverage within low frequency range, with the compressed phase portrait and the raised λ₁. Especially, the liquid motion has a special feature of binary fraction in the present experiment.