## 3 Result
### The Film Shape at the Initial Stage  
Inside the distributor slot, the liquid flow can be described by a symmetric parabolic velocity profile. The liquid is accelerated by the hydrostatic pressure exerted by the liquid in the pressure tank and decelerated by viscous friction at the slot walls, modeled by the no-slip condition at both walls. Far from the outlet, a semi-parabolic profile of liquid velocity is expected. The liquid is accelerated by  
Figure 2: Dependence of the time-averaged film thickness on the downstream coordinate: (**a**) water–glycerol solution (WGS1), \(Q_{L}=10.3\) mL/s, \(V_{G}=22\) m/s; (**b**) WGS1, \(Q_{L}=10.3\) mL/s, \(V_{G}=43\) m/s. the interfacial shear force exerted by the gas stream and decelerated by viscous friction at the pipe inner wall. Gravity may either accelerate or decelerate the flow depending on flow orientation. The transition from one state to the other requires a certain time and consequently, the distance for the liquid to travel. The thickness of the liquid film changes with a downstream distance from the slot thickness at the slot outlet to the \"equilibrium\" value far from the slot, which depends on the balance between the gas drag force, gravity, liquid inertia, and viscous friction. For thin liquid films, the thickness decreases rapidly at the beginning, then decays exponentially; see, e.g., Figure 2c in [29], where the thickness of the liquid film at \(Re_{\text{L}}=30\) flowing downwards in absence of gas flow is investigated. For thicker water films flowing downwards, it was found in the same paper that the film thickness is kept on a relatively constant level, close to the thickness of the slot, for a certain distance and then undergoes rapid decrease to the \"equilibrium\" value. The length of the \"thick\" film was found to grow with a liquid flow rate and decrease with gas velocity. Examples of the time-averaged profiles of film thickness along a downstream coordinate are shown in the top parts of subfigures in Figure 2 as blue and red lines for the downward and upward flow, respectively. Examples of raw instantaneous frames with superimposed interface positions are given in the bottom parts of each subfigure; the frame for the downward flow is above the one for the upward flow. For the downward flow, the shape of the initial film is a relatively long plateau of a film with a thickness slightly larger than that of the slot (0.5 mm); further downstream, the thickness drops to a thinner \"equilibrium\" value. In the case of upward flow, the film gets noticeably thicker than the slot just after the slot outlet (Figure 2a). On the other hand, this \"thick film\" stage is much shorter than in a downward flow. When the gas superficial velocity is high (Figure 2b), the difference between the upward and downward flows becomes less pronounced: the transition to the \"equilibrium\" film stage occurs at nearly the same downstream distance, and at the initial stage the film is only slightly thicker in upward flow. To analyze the effect of flow conditions on the film shape at the initial stage, two parameters were measured: maximum time-averaged film thickness, \(H_{\text{max}}\), and the distance at which the \"equilibrium\" film thickness is reached, \(X\). Figure 3 shows the behavior of \(H_{\text{max}}\) for different conditions. There is a prominent effect of flow orientation. In upward flow, \(H_{\text{max}}\) decreases with \(V_{\text{G}}\). At the lowest \(V_{\text{G}}=15\) m/s it even exceeds the joint thickness of the slot (0.5 mm) and the gas-feeding tube (0.3 mm), thus protruding by 0.1-0.2 mm into the gas core. At a larger \(V_{\text{G}}\), \(H_{\text{max}}\) is smaller than 0.8 mm and gets close to the slot thickness at the largest \(V_{\text{G}}\). In upward flow, the gravity assists the accumulation of liquid behind the slot outlet. The gas drag is strong enough to prevent the liquid from flowing down the dry inner side of the gas-feeding tube, so the liquid is gathered in the \"pocket\" on top of the end of the gas-feeding tube.