A device for continuous and flexible adjustment of liquid-liquid slug size in micro-channels

Abstract

In liquid-liquid segmented flow slug size determines the interfacial area as well as the intensity of Taylor vortices and is thus an important operational parameter, decisive for mass transfer performance of biphasic micro-reactors and -extractors. Resulting slug sizes conventionally depend on material properties, flow and geometric parameters of the mixing point of the liquids. To evade tedious material specific design of the mixing point, modular devices, which allow active adjustment of developing slug sizes, are desirable. Such a slug generator is presented in this study. By altering the mixing point geometry during operation, it allows continuous manipulation of the slug formation process and thus slug size. The slug generation process in this device is investigated experimentally and with help of CFD simulations in order to identify its geometric influences. The findings lead to an optimized device design, whose capability to generate slugs of adjustable size and with low dispersity is demonstrated experimentally.

Appendix

Simplified model to predict slug length by geometric considerations

Fig. 17

Geometric parameters of the slug mixing point geometry

Determination of volume contribution of growth stage

Similar triangles ∆ABC~∆ADE

$$ \frac{\overline{BC}}{\overline{AC}}=\frac{\overline{DE}}{\overline{AE}} $$

(4.1)

$$ \frac{r_k}{\sqrt{{\left(h+l\right)}^2+{r_k}^2}}=\frac{r_s}{\Delta x+l-{r}_s+s} $$

(4.2)

$$ \mathrm{with}\ {\beta}_2=\arctan \left(\frac{h}{r_k-{r}_o}\right) $$

(4.3)

$$ l={r}_o\tan \left(\ {\beta}_2\right) $$

(4.4)

$$ s={r}_s-\sqrt{{r_s}^2-{r_{d,i}}^2} $$

(4.5)

for clear arrangement introducing

$$ \hat{a}=\frac{r_k}{\sqrt{{\left(h+{r}_o\tan \left(\ {\beta}_2\right)\right)}^2+{r_k}^2}} $$

$$ \hat{b}=\Delta x+{r}_o\tan \left(\ {\beta}_2\right) $$

$$ \hat{c}={r_{d,i}}^2 $$

(4.6)

$$ \mathrm{thus}\ \frac{r_k}{\sqrt{{\left(h+l\right)}^2+{r_k}^2}}=\frac{r_s}{\Delta x+l-{r}_s+s}\kern1em \leftrightarrow \kern1em \hat{a}=\frac{r_s}{\hat{b}-\sqrt{{r_s}^2-\hat{c}}} $$

(4.7)

$$ \mathrm{rearrangement}\ \mathrm{yields}\ {r}_s={\hat{a}}^2\ast \left(\frac{\frac{\hat{b}}{\hat{a}}-\sqrt{-\frac{\hat{c}}{{\hat{a}}^2}+{\hat{b}}^2+\hat{c}\ }}{1-{\hat{a}}^2}\right) $$

(4.8)

Volume contribution of growth stage

$$ {\mathrm{V}}_{S,G}=\frac{4}{3}\pi\ {r_s}^3 $$

(4.9)

Determination of the duration of the detachment process

$$ {u}_{c, MP}=\frac{{\dot{V}}_c}{\pi \cdotp \left({r_{MP}}^2-{\left({r}_{d,i}+w\right)}^2\right)} $$

(4.10)

$$ {r}_{MP}=\frac{\Delta x\ }{\tan \left(\ {\beta}_2\right)}+{r}_o $$

(4.11)

Experimentally determined correlation

$$ {\tau}_{detach}=2.194\ast {u_{c, MP}}^{-0.878} $$

(4.12)

Volume contribution of detachment stage

$$ {V}_{S,D}={\dot{V}}_d\ {\tau}_{detach} $$

(4.13)

Calculation of slug length

$$ {V}_{slug}={V}_{S,G}+{V}_{S,D} $$

(4.14)

Slug lengths assuming a cylindrical shape with spherical caps and ignoring wall film

$$ {L}_s=\frac{V_{slug}-\frac{4}{3}\pi\ {r_o}^3}{\pi\ {r_o}^2}+2{r}_o $$

(4.15)