*3.2. The Entrapment of Slag in Ladle*

For the entrapment of the top slag in the ladle, the influence of the bottom gas flow rate, number of porous plugs and thickness of the slag layer to the top slag entrapment in the ladle was studied with an image processing method in the water model.

#### 3.2.1. The Entrapment of Slag in Ladle with Single Porous Plug

In the water model, the entrapment of the top slag during bottom blowing was videoed to analyse the influence of the bottom gas flow rate to entrapment, Figure 5, and in the experiment the thickness of oil (simulating the slag layer) was 14 mm. It was found that as the bottom blowing gas flow rate was less than 0.143 m3/h, the fluctuation at the interface between the oil and water was gentle (Figure 5a,b), the escape of bubbles caused the little disturb at the interface between the oil and water and the horizontal flow at the interface driven by the upper flow around the bubble column caused the oil layer thickening at the area around the bubble escaping region. As the bottom flow rate was increased above 0.143 m3/h, the escape of bubbles caused the obvious disturb at the interface between the oil and water, the horizontal flow at the interface caused the oil layer obviously thickening at the area around the bubble escaping region, as shown in Figure 5c–f, the oil bump was formed at that area, the shear of horizontal flow resulted in the small droplet divided from the oil bump and the entrapment was formed, most of the oil droplets were soon floated up to the top oil layer. When the bottom gas flow rate was above 0.333 m3/h (Figure 5g,h), the entrapment worsened, most of the oil droplets were not floated up to the top oil layer, instead, they were dragged into the deep region in the water model by the downward flow.

*Processes* **2019**, *7*, 479

**(c) (d)** 

**Figure 5.** The influence of the air flow rate to the entrapment in the water model simulating the ladle with a single porous plug and OLT of 14 mm: (**a**) Q = 0.0475 m3/h; (**b**) Q = 0.095 m3/h; (**c**) Q = 0.143 m3/h; (**d**) Q = 0.191 m3/h; (**e**) Q = 0.238 m3/h; (**f**) Q = 0.286 m3/h; (**g**) Q = 0.333 m3/h; (**h**) Q = 0.381 m3/h.

The area without the slag covering, which was caused by the bubbles-escaping at the top of the bath, was called the slag eye. The area of the slag eye in the water model with a single porous plug at different bottom gas flow rates and slag thicknesses was summarized in Table 4, which was measured from the digital image of the top of the water model during bottom blowing. From Table 4, it was found that the area of the slag eye increased as the increase of the bottom gas flow rate. The reason was that as the bottom gas flow rate increased, the rise velocity of the plume increased and then the horizontal velocity at the liquid-oil interface was also raised, the increase of the horizontal velocity raised the repulsive force at the interface between the water and oil and the area of the slag eye increased. On the other hand, as the raise of the top oil thickness, the work to repulsive the oil at the top of the water model, which overcame the interfacial tension and viscous force, increased and the area of the slag eye decreased at the same bottom gas flow rate.

**Table 4.** The areas of the slag eye at different air flow rate and oil thickness in the water model with a single porous plug.


Figure 6 showed the relation between entrapping the depth of the top oil in the water model with a single porous plug, bottom flow rate and oil thickness. It was shown that at the same bottom flow rate the entrapping depth increased as the increase of oil thickness, and at the same oil thickness the entrapping depth increased as the bottom flow rate, but when the bottom flow rate was above a certain level, the entrapping depth would not increase as the increase of the flow rate. The reason was that as the bottom flow rate increased, more of the oil layer at the top of the water model was repulsed from the bubble escaping region of the plume, the horizontal velocity of water increased, the velocity of the downward flow around the plume also increased, the bump of the oil layer increased, Figure 5, the shear forced on the bump of the oil layer increased, and all these factors caused oil entrapping in the water model raising. From Figure 6, the critical bottom flow rates for oil entrapment in the water model were in the range of 0.095–0.143 m3/h (18–24 m3/h for prototype ladle).

**Figure 6.** The influence of air flow rate to entrapping depth in the water model with a single porous plug.
