Liquid/liquid Mixing Pattern in a Mechanically-stirred Vessel

Abstract

In order to find out effect of operating factors on mixing pattern which affects liquid/liquid mass transfer rate drastically, cold model experiment was carried out with liquid paraffin or tetradecane as a dispersed phase and ion-exchanged water as a continuous phase in a mechanically stirred vessel. There exist three types of liquid/liquid mixing pattern in a mechanical agitation. I: region where each liquid phase separates and has no dispersion, II: region where vortex of dispersed phase (liquid/liquid interface) arrives at impeller position and its dispersion begins into continuous phase, III: region where gas/liquid interface as well as liquid/liquid one arrives at impeller position and dispersion occurs heavily. The transition of I–II accelerated along with the increases in rotation speed, ratio of dispersion phase volume to continuous one, density of dispersion phase, impeller diameter and vessel diameter, and the decrease in impeller depth. The transition of II–III accelerated along with the increases in rotation speed, density of dispersion phase and impeller diameter, and the decrease in impeller depth.

The multi regression equation for the transition of I–II is expressed as,   

where H: distance between free surface of oil and upper part of impeller (mm), H_oil: bath depth of dispersed phase(mm), N: rotation speed(rpm), V_oil/V_w: ratio of dispersion phase volume to continuous one(–), d_i: impeller diameter(mm). D: vessel diameter(mm), ρ_d: density of dispersion phase(kg/m³), whereas that on transition of II–III is H ∝ N^2.18d_i^1.96ρ_d^1.33.

1. Introduction

Slag/metal reaction caused by solid/liquid or liquid/liquid system is one of the most basic and important practices to remove the impurities in steel melt, typically known as gas injection¹⁾ or mechanical stirring.^2,3,4) Cold model experiment has been a helpful method to understand the slag/metal transport phenomena. Therefore, there are many studies in this domain.⁵⁾ For mechanical stirring operation, Nakai et al.⁶⁾ showed that desulfurization rate increased remarkably when vortex caused by mechanical stirring came at the impeller position and the flux dispersed in steel melt. There are also studies of the effect of baffles^7,8) on the dispersion behavior^9,10) of particles into liquid in a mechanically agitated bath.

On the other hand, in case of liquid/liquid mechanical stirring, it is likely that penetration of the dispersion layer into an impeller position affects liquid/liquid mass transfer rate as Nakai et al.⁶⁾ indicated in the solid/liquid system. However, there are few studies on mixing pattern vs. operating factors of liquid/liquid system during mechanical agitation processes in the field of steelmaking except study on impeller diameter and mechanical offset suitable for complete dispersion of the dispersion phase worked in the field of chemical engineering.¹¹⁾

In this water model study, liquid paraffin and tetradecane were chosen as dispersion phase and effect of operating factors such as rotation speed, impeller depth were made clear in a mechanically agitated vessel.

2. Experimental

Schematic view of experimental apparatus is shown in Fig. 1. Liquid paraffin or tetradecane as dispersion phase and ion-exchanged water as continuous phase were charged in an acrylic tank. Inner diameter of a vessel is denoted as D mm and bath depth of static continuous and dispersed phases is represented as H₀ mm. Four blades of impeller whose diameter is expressed as d_i mm, thickness as b_i mm and width as w_i mm was used as shown schematically in Fig. 2. The impeller was set in the central axis of the vessel. Visual observation was carried out to obtain a relation between characteristic mixing pattern and impeller position, which means vortex depth of liquid/liquid interface or gas/liquid interface was measured with a ruler. Photography was made for liquid paraffin colored with oil-based ink.

Fig. 1.

Schematic view of experimental apparatus of mechanical stirring.

Fig. 2.

Schematic view of impeller.

Experimental conditions are shown in Table 1 where baselines are underlined. D = H₀ = 400 mm and d_i, b_i, W_i = 116 mm, 67 mm, 31 mm were used except the experiment where these factors were changed. Rotation speed, N was changed 0–410 rpm, volumetric ratio of dispersed to continuous phase V_oil/V_w was 0–5.0 × 10^–1, although its baseline was 1.2 × 10^–1. Densities of liquid paraffin and tetradecane used for the experiments were 828 and 763 kg/m³, respectively. When static depths of liquid paraffin and water were defined as H_oil and H_W, these values were calculated as Table 2 for D = H₀ = 400 mm and Table 3 for D = H₀ = 300 mm.

Table 1. Experimental condition for mechanical stirring.

Variables
Vessel inner diameter, D (mm)	300, 400
Bath depth, H0 (mm)	300, 400
Impeller diameter, di (mm)	116, 165
Impeller thickness, bi (mm)	67, 85
Impeller width, wi (mm)	31, 42
Rotating speed, N (rpm)	0 – 410
Impeller depth, H (mm)	5– 275
Ratio of dispersion phase to water volume, Voil/Vw (–)	0 –5.0 × 10–1
Dispersion phase	liquid paraffin, tetradecane

Table 2. Static bath depths of oil and water under a given V_oil/V_w (D = H₀ = 400 mm).

Voil/Vw (–)	Hoil (mm)	Hw (mm)
5.9 × 10–2	22	378
1.2 × 10–1	42	358
2.3 × 10–1	74	326

Table 3. Static bath depths of oil and water under a given V_oil/V_w (D = H₀ = 300 mm).

Voil/Vw (–)	Hoil (mm)	Hw (mm)
5.9 × 10–2	17	283
1.2 × 10–1	31	269
2.3 × 10–1	57	243

3. Results and Discussion

3.1. Mixing Patterns of Single Liquid Phase and Liquid/liquid Double Phases

Mixing patterns of water and liquid paraffin/water at N = 189 rpm and H = 233 mm are shown in Fig. 3. V_oil/V_w of liquid/liquid equals to 1.2 × 10^–1. The formed vortex of a single liquid phase (Fig. 3(a)) is different from liquid/liquid phase (Fig. 3(b)). As shown in Fig. 3(b), liquid/liquid interface reaches the impeller, whereas gas/liquid one drawn in dotted line exists upward. The interface depth of liquid/liquid is larger and that of gas/liquid in liquid/liquid flow is less than that of gas/liquid in a single phase.

Fig. 3.

Comparison between mixing patterns of mechanical stirring in single and two liquid phases (N = 189 rpm , H = 233 mm, D = H₀ = 400 mm).

3.2. Mixing Pattern of Liquid/liquid System

When impeller depth is changed at N = 146 rpm and V_oil/V_W = 1.2 × 10^–1, mixing pattern is also changed as shown in Fig. 4. Three types of mixing patterns in liquid/liquid system are recognized. I is the region where liquid/liquid interface does not arrive at the impeller (Fig. 4(a)), II is the region where liquid/liquid interface attains at the impeller position and a part of liquid paraffin disperses in water (Fig. 4(b)) and III is the region where gas/liquid interface touches the impeller (Fig. 4(c)). Transitions of I→II→III occur along with the decrease in impeller depth.

Fig. 4.

Change in mixing pattern according to impeller position (N = 146 rpm, V_oil/V_W = 1.2 × 10^–1).

The above three mixing patterns are recognized when rotation speed is changed at V_oil/V_w = 1.2 × 10^–1 and H = 233 mm in Fig. 5. Figure 5(a) is the region I at N = 137 rpm, Fig. 5(b) is II at N = 231 rpm and Fig. 5(c) is III at N = 360 rpm. Transitions of I→II→III arise with the increase in rotation speed.

Fig. 5.

Change in mixing pattern according to rotating speed (H = 233 mm, V_oil/V_W = 1.2 × 10^–1).

3.3. Effect of Operating Factors on Liquid/liquid Mixing Pattern

Mixing patterns and their transitions in the cases of various N and H under V_oil/V_w = 1.2 × 10^–1 are shown in Fig. 6. Liquid paraffin and tetradecane were used for a dispersion phase. As shown in transition curves of I–II and II–III, both of liquid/liquid and gas/liquid vortex depths for liquid paraffin were deeper than those for tetradecane at the same rotation speed, and larger rotation speed for tetradecane was necessary compared with that for liquid paraffin at the same vortexes. There indicate that tetradecane is harder to form the vortex than the liquid paraffin. It seems to be due to the density differences, that is, the density of liquid paraffin is larger than tetradecane.

Fig. 6.

Mixing pattern and its transition for different dispersion phase.

The mixing patterns and their transitions for various V_oil/V_w and N are shown in Fig. 7 where the dispersion phase was liquid paraffin. To transit from I to II, the larger rotation speed was required along with the decrease in V_oil/V_w, which implies that the liquid/liquid interface depth decreases with smaller V_oil/V_w at the same N and H in the region I. However, the transitions of II–III had no change even if V_oil/V_w was changed. It was found that the region where the vortex arrives at the impeller in a single water phase expressed by V_oil/V_w = 0 exists at the transition of II–III.

Fig. 7.

Mixing pattern and its transition according to V_oil/V_w (liquid paraffin).

As H_oil and H_w have different values according to V_oil/V_w as shown in Tables 2 and 3, it is effective to rearrange the transition of I–II of Fig. 7 with H–H_oil instead of H. Figure 8 shows the mixing patterns and their transition. The transition curve of a single water phase was also drawn here. The transition curves of I–II approached II–III according as V_oil/V_w approached 0.

Fig. 8.

Mixing pattern and its transition according to V_oil/V_w (liquid paraffin).

The mixing patterns and their transitions for tetradecane/water mixing are shown in Fig. 9. The transition curves of I–II approached to II–III, which is the same tendency as shown in Fig. 8.

Fig. 9.

Mixing pattern and its transition according to V_oil/V_w (tetradecane).

Based on these results, the schematic views of mixing patterns and their transitions in case of various V_oil/V_w are drawn in Fig. 10. The upper stage is for I and II, whereas lower one is for III. When V_oil/V_w was larger, the vortex of dispersed phase was formed deeply and its mixing pattern became II. However, under the same N and H, mixing pattern changed from II to I for smaller V_oil/V_w. On the other hand, the mixing pattern of III and its transition to II was independent of V_oil/V_w.

Fig. 10.

Change in mixing pattern according to V_oil/V_W.

3.4. Effect of Impeller and Vessel Diameters on Mixing Pattern

Figure 11 shows the mixing patterns and their transitions where impeller diameter was changed. Both of D and H₀ were fixed to 400 mm and V_oil/V_w was also kept at 1.2 × 10^–1. Under larger impeller diameter, the vortex was formed deeply and the transitions of I–II and II–III occurred at lower rotation speed, which means larger impeller is more effective for liquid/liquid mixing.

Fig. 11.

Mixing pattern and its transition according to impeller.

The mixing patterns and their transitions are shown in Fig. 12 when both of vessel diameter and bath depth were changed. Impeller size of d_i, b_i, and W_i was fixed to 116 mm, 67 mm and 31 mm, respectively, and V_oil/V_w was also kept at 1.2 × 10^–1. It was found that larger D and H₀ required less rotation speed to transit the mixing pattern from I to II, although the transition of II–III was not affected by the vessel size and bath depth.

Fig. 12.

Mixing pattern and its transition according to vessel size.

3.5. Quantitative Relations Among Operating Factors on Transitions of I–II and II–III

A multi-regression analysis was carried out in order to find the relation among operating factors quantitatively. Using the data of sections 3.3 and 3.4, the equation of transition of I–II was expressed as follows:   

$$\text{H}-{\text{H}}_{\text{oil}}={\text{10}}^{-\text{20}\text{.4}}{\text{N}}^{\text{2}\text{.52}}{{\text{(V}}_{\text{oil}}{\text{/V}}_{\text{w}}\text{)}}^{\text{0}\text{.357}}{\text{d}}_{\text{i}}{\hspace{0.17em}}^{\text{1}\text{.71}}{\text{D}}^{\text{0}\text{.399}}{\rho }_{\text{d}}{\hspace{0.17em}}^{\text{4}\text{.43}}$$(1)

where correlation coefficient, R² equals 0.923. As seen from Eq. (1), N, V_oil/V_w, d_i, D and ρ_d had positive correlation with H–H_oil.

On the other hand, the transition of II–III is not affected by V_oil/V_w, H_oil and D as shown in Figs. 7, 8 and 12. Therefore, a multi-regression analysis was carried out without the above factors and equation for transition of II–III was given as follows:   

$$\text{H}={\text{10}}^{-\text{11}\text{.1}}{\text{N}}^{\text{2}\text{.18}}{\text{d}}_{\text{i}}{\hspace{0.17em}}^{\text{1}\text{.96}}{\rho }_{\text{d}}{\hspace{0.17em}}^{\text{1}\text{.33}}$$(2)

where correlation coefficient, R² equals 0.99. As seen from Eq. (2), N, d_i and ρ_d has positive correlation with H.

The quantitative relations of the transitions of I–II and II–III were obtained from Eqs. (1) and (2), respectively. The regions I, II and III in this experiment have been affirmed by pilot plant test carried out by liquid slag and metal.¹²⁾ However, the dimensional analysis with dimensionless numbers including more factors than this experiment is needed in order to apply the quantitative relation to the slag/metal system.

4. Conclusions

Liquid/liquid cold model experiments of mixing pattern and its transition was carried out with liquid paraffin or tetradecane as a dispersed phase and ion-exchanged water as a continuous phase in a mechanically stirred vessel.

(1) Vortex of dispersed phase in liquid/liquid flow was able to arrive at impeller, although vortex of a single phase flow did not penetrate into impeller position under the same operating condition.

(2) There existed three types of liquid/liquid mixing patterns in a mechanical agitation. I: region where each liquid phases separate and have no dispersion, II: region where vortex of dispersed phase (liquid/liquid interface) arrives at impeller position and its dispersion begins into continuous phase, III: region where gas/liquid interface in addition to liquid/liquid interface arrives at impeller position and dispersion occurs hard.

(3) The transition of I–II was accelerated along with the increases in rotation speed, ratio of dispersion phase volume to continuous one, density of dispersion phase, impeller diameter and vessel diameter, and the decrease in impeller depth.

(4) The transition of II–III was accelerated along with the increases in rotation speed, density of dispersion phase and impeller diameter, and the decrease in impeller depth.

(5) The multi regression equation on transition of I–II was as follows:   

$$\text{H}-{\text{H}}_{\text{oil}}\propto {\text{N}}^{\text{2}\text{.52}}{{\text{(V}}_{\text{oil}}{\text{/V}}_{\text{w}}\text{)}}^{\text{0}\text{.36}}{\text{d}}_{\text{i}}{\hspace{0.17em}}^{\text{1}\text{.71}}{\text{D}}^{\text{0}\text{.40}}{\rho }_{\text{d}}{\hspace{0.17em}}^{\text{4}\text{.43}}$$

where H: impeller depth(mm), H_oil: bath depth of dispersed phase(mm), N: rotation speed(rpm), V_oil/V_w: ratio of dispersion phase volume to continuous one(–), d_i: impeller diameter(mm), D: vessel diameter(mm), ρ_d: density of dispersion phase(kg/m³).

(6) The multi regression equation on transition of II–III was as follows:   

$$\text{H}\propto {\text{N}}^{\text{2}\text{.18}}{\text{d}}_{\text{i}}{\hspace{0.17em}}^{\text{1}\text{.96}}{\rho }_{\text{d}}{\hspace{0.17em}}^{\text{1}\text{.33}}$$

Acknowledgements

This work was carried out under the project of NEDO (New Energy and Industrial Technology Development Organization), entitled “Research and development project on enhancement of usage of hard-to-use ferrous scrap”.

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