Average properties of bidisperse bubbly flows

Experiments were performed in a vertical channel to study the properties of a bubbly flow composed of two distinct bubble size species. Bubbles were produced using a capillary bank with tubes with two distinct inner diameters; the flow through each capillary size was controlled such that the amount of large or small bubbles could be controlled. Using water and water-glycerin mixtures, a wide range of Reynolds and Weber number ranges were investigated. The gas volume fraction ranged between 0.5% and 6%. The measurements of the mean bubble velocity of each species and the liquid velocity variance were obtained and contrasted with the monodisperse flows with equivalent gas volume fractions. We found that the bidispersity can induce a reduction of the mean bubble velocity of the large species; for the small size species, the bubble velocity can be increased, decreased, or remain unaffected depending of the flow conditions. The liquid velocity variance of the bidisperse flows is, in general, bound by the values of the small and large monodisperse values; interestingly, in some cases, the liquid velocity fluctuations can be larger than either monodisperse case. A simple model for the liquid agitation for bidisperse flows is proposed, with good agreement with the experimental measurements.

Figure 1

Scheme of the capillary array.

Figure 2

Terminal bubble velocity as a function of equivalent diameter. The symbols denote experiments conducted in different liquids: $(\begin{array}{c}•\end{array},\begin{array}{c}○\end{array})$, water; $(\begin{array}{c}♦\end{array},\begin{array}{c}\diamond \end{array})$ water-glycerin 30%; $(\begin{array}{c}\blacksquare \end{array},\begin{array}{c}\square \end{array})$ water-glycerin 50%. The filled and empty symbols refer to small and large bubbles, respectively. The lines show the predictions of Moore [23] for the three liquids used here: (–), $\mathrm{Mo}=2.6\times {10}^{-8}$; (- - -), $\mathrm{Mo}=3.9\times {10}^{-6}$; (-$·$- $·)$, $\mathrm{Mo}=3.1\times {10}^{-5}$.

Figure 3

Typical monodisperse bubbly flows. Images obtained for different liquids for a gas volume fraction of $\alpha =0.02$. The top and bottom rows show images obtained for the small and large capillary array, respectively. Water, (a) and (d); water-glycerin (70-30), (b) and (e); water-glycerin (50-50), (c) and (f). The size of each image is approximately $5\times 5,{\mathrm{cm}}^2$.

Figure 4

Ratio of bubble velocities, ${\mathrm{\Gamma }}_1=U_b^L/U_b^S$, and ratio of liquid velocity variances, ${\mathrm{\Gamma }}_2={\langle U_l^2\rangle }^L/{\langle U_l^2\rangle }^S$, as a function of gas volume fraction. All data is for monodisperse flows. The symbols denote experiments conducted in different liquids: $\left(\begin{array}{c}○\end{array}\right)$, water; $\left(\begin{array}{c}\diamond \end{array}\right)$ water-glycerin 30%; $\left(\begin{array}{c}\square \end{array}\right)$ water-glycerin 50%. The asterisks (of each color) on (a) at $\alpha =0$ represent the values corresponding to isolated bubbles, taken from Fig. 2.

Figure 5

Typical bidisperse bubbly flows. Images obtained for different liquids for a gas volume fraction of $\alpha =0.02$. The top, middle and bottom rows show flows for the three values of the parameter $R$ (1/3, 1 and 3), respectively. Water, (a), (d), and (g); water-glycerin (70-30), (b), (e), and (h); water-glycerin (50-50), (c), (f), and (i).

Figure 6

Bubble velocity, $U_b^i$, as a function of gas volume fraction for bidisperse flows with $i$ being $S$ or $L$ for small and large bubbles, respectively (left and right columns, respectively). The symbols denote experiments for different liquids: $(\begin{array}{c}•\end{array},\begin{array}{c}○\end{array})$ water; $(\begin{array}{c}♦\end{array},\begin{array}{c}\diamond \end{array})$ water-glycerin 70-30%; $(\begin{array}{c}\blacksquare \end{array},\begin{array}{c}\square \end{array})$ water-glycerin 50-50%. The filled and empty symbols refer to small and large bubbles, respectively. The continuous and dashed lines denote the bubble velocity for the monodisperse case for small and large bubbles, respectively. The asterisks (of each color) at $\alpha =0$ represent the values corresponding to isolated bubbles, taken from Fig. 2. (a) $\mathrm{S}\text{−}\mathrm{bubbles},R=1/3$, (b) $\mathrm{L}\text{−}\mathrm{bubbles},R=1/3$, (c) $\mathrm{S}\text{−}\mathrm{bubbles},R=1$, (d) $\mathrm{L}\text{−}\mathrm{bubbles},R=1$, (e) $\mathrm{S}\text{−}\mathrm{bubbles},R=3$, and (f) $\mathrm{L}\text{−}\mathrm{bubbles},R=3$.

Figure 7

Bubble velocity ratio, ${\mathrm{\Gamma }}_1=U_b^L/U_b^S$, as a function of gas volume fraction for bidisperse flows. The symbols denote experiments conducted in different liquids: $\left(\begin{array}{c}○\end{array}\right)$, water; $\left(\begin{array}{c}\diamond \end{array}\right)$ water-glycerin 70-30%; $\left(\begin{array}{c}\square \end{array}\right)$ water-glycerin 50-50%. The asterisks (of each color) at $\alpha =0$ represent the values corresponding to isolated bubbles, taken from Fig. 2. (a) ${\mathrm{\Gamma }}_1,R=1/3$, (b) ${\mathrm{\Gamma }}_1,R=1$, and (c) ${\mathrm{\Gamma }}_1,R=3$.

Figure 8

Liquid velocity variance, ${\langle U_l\rangle }^2$, as a function of gas volume fraction for bidisperse flows. The symbols denote experiments conducted in different liquids: $\left(\begin{array}{c}•\end{array}\right)$, water; $\left(\begin{array}{c}♦\end{array}\right)$ water-glycerin 70-30%; $\left(\begin{array}{c}\blacksquare \end{array}\right)$ water-glycerin 50-50%. The continuous and dashed lines denote the liquid velocity variance for the monodisperse case for small and large bubbles, respectively. (a) $R=1/3$, (b) $R=1$, and (c) $R=3$.

Figure 9

Liquid velocity variance ratio, ${\mathrm{\Pi }}^S$ and ${\mathrm{\Pi }}^L$ (left and right columns, respectively), as a function of gas volume fraction for bidisperse flows. The symbols denote experiments for different liquids: $(\begin{array}{c}•\end{array},\begin{array}{c}○\end{array})$, water; $(\begin{array}{c}♦\end{array},\begin{array}{c}\diamond \end{array})$ water-glycerin 70-30%; $(\begin{array}{c}\blacksquare \end{array},\begin{array}{c}\square \end{array})$ water-glycerin 50-50%. The filled and empty symbols refer to either ${\mathrm{\Pi }}^S$ or ${\mathrm{\Pi }}^L$, respectively. (a) $\mathrm{small}\mathrm{bubbles},R=1/3$, (b) $\text{large}\text{bubbles},R=1/3$, (c) $\mathrm{small}\mathrm{bubbles},R=1$, (d) $\mathrm{large}\mathrm{bubbles},R=1$, (e) $\mathrm{small}\mathrm{bubbles},R=3$, and (f) $\mathrm{large}\mathrm{bubbles},R=3$.

Figure 10

Ratio of liquid velocity fluctuations, ${\mathrm{\Pi }}^S$ as a function of the gas volume fraction ratio, $R$, for the three liquids tested in this study: $\left(\begin{array}{c}○\end{array}\right)$ water; $\left(\begin{array}{c}\diamond \end{array}\right)$ water-glycerin 70-30%; $\left(\begin{array}{c}\square \end{array}\right)$ water-glycerin 50-50%. The lines show the predictions from Eq. (15). For water: $n=0.8,\overline{{\mathrm{\Gamma }}_1}=0.85,{\kappa }^{*}=1.95,{\kappa }_{\text{int}}^{*}=-0.8$ (red lines); for water-glycerin 70-30%: $n=0.8,\overline{{\mathrm{\Gamma }}_1}=0.89,{\kappa }^{*}=1.63,{\kappa }_{\text{int}}^{*}=-0.5$ (black lines); and for water-glycerin 50-50%: $n=0.4,\overline{{\mathrm{\Gamma }}_1}=1.32,{\kappa }^{*}=1.41,{\kappa }_{\text{int}}^{*}=-0.52$ (blue lines). For all cases, the continuous lines represent the predictions considering ${\kappa }_{\text{int}}^{*}=0$ (no interaction).