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

Abstract

<span style="font-size:9.0pt;font-family: " times="" new="" roman";mso-fareast-font-family:simsun;mso-bidi-font-family:mangal;="" mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:hi"="" lang="EN-GB">The flow characteristics of orifice<b style="mso-bidi-font-weight:normal"><span style="font-size:9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" simsun;mso-bidi-font-family:mangal;mso-ansi-language:en-gb;mso-fareast-language:="" zh-cn;mso-bidi-language:hi"="" lang="EN-GB">-</span></b><span style="font-size:9.0pt; font-family:" times="" new="" roman";mso-fareast-font-family:simsun;mso-bidi-font-family:="" mangal;mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:="" hi"="" lang="EN-GB">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 (<i style="mso-bidi-font-style:normal">Q</i>_g), measurement heights (<i style="mso-bidi-font-style:normal">z</i>) and mass concentrations. The results show that for low <i style="mso-bidi-font-style:normal">Q</i>_g, <i style="mso-bidi-font-style:normal">z</i> and <span style="font-size:9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" simsun;mso-bidi-font-family:mangal;mso-ansi-language:en-gb;mso-fareast-language:="" zh-cn;mso-bidi-language:hi;mso-bidi-font-weight:bold"="" lang="EN-GB">dilute <span style="font-size:9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" simsun;mso-bidi-font-family:mangal;mso-ansi-language:en-gb;mso-fareast-language:="" en-us;mso-bidi-language:hi;mso-bidi-font-weight:bold"="" lang="EN-GB">solution,<span style="font-size:9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" simsun;mso-bidi-font-family:mangal;mso-ansi-language:en-gb;mso-fareast-language:="" en-us;mso-bidi-language:hi"="" lang="EN-GB"> the characteristic frequency of the power spectrum is consistent with bubbling frequency, with uniform elliptical shape of reconstructed phase space. Largest <span style="font-size:9.0pt;font-family: " times="" new="" roman";mso-fareast-font-family:advpstim;mso-bidi-font-family:mangal;="" mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:hi"="" lang="EN-GB">Lyapunov exponent<span style="font-size:9.0pt;font-family:" times="" new="" roman";="" mso-fareast-font-family:simsun;mso-bidi-font-family:mangal;mso-ansi-language:="" en-gb;mso-fareast-language:en-us;mso-bidi-language:hi;mso-bidi-font-style:italic"="" lang="EN-GB">s <i>λ</i>_{<span style="font-size:9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" simsun;mso-bidi-font-family:mangal;mso-ansi-language:en-gb;mso-fareast-language:="" en-us;mso-bidi-language:hi"="" lang="EN-GB">1</span>}<span style="font-size: 9.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:simsun;mso-bidi-font-family:="" mangal;mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:="" hi"="" lang="EN-GB"> in<span style="font-size:9.0pt; font-family:" times="" new="" roman";mso-fareast-font-family:simsun;mso-bidi-font-family:="" mangal;mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:="" hi"="" lang="EN-GB"> radial direction is approximately 10 times that in the axial direction. Whereas for high <i style="mso-bidi-font-style:normal">Q</i>_g, <i style="mso-bidi-font-style:normal">z</i> and concentrated solution, power spectrums are of broad coverage within low frequency range, with the compressed phase portrait and the raised <i>λ</i>₁. Especially, the liquid motion has a special feature of binary fraction in the present experiment.</span></span></span></span></span></span></span></span></span>