# 13.9: Counter–Current Flow

This discussion will be only on liquid–liquid systems (which also includes liquid-gas systems). This kind of flow is probably the most common to be realized by the masses. For example, opening a can of milk or juice. Typically if only one hole is opened on the top of the can, the liquid will flow in pulse regime. Most people know that two holes are needed to empty the can easily and continuously. Otherwise, the flow will be in a pulse regime.

Fig. 13.10 Counter–flow in vertical tubes map.

In most cases, the possibility to have counter–current flow is limited to having short length of tubes. In only certain configurations of the infinite long pipes the counter–current flow can exist. In that case, the pressure difference and gravity (body forces) dominates the flow. The inertia components of the flow, for long tubes, cannot compensate for the pressure gradient. In short tube, the pressure difference in one phase can be positive while the pressure difference in the other phase can be negative. The pressure difference in the interface must be finite. Hence, the counter–current flow can have opposite pressure gradient for short conduit. But in most cases, the heavy phase (liquid) is pushed by the gravity and lighter phase (gas) is driven by the pressure difference. woImg{cont/phase/canOne} {cont/phase/can} {Counter Flow In Can} {0.15} {phase:fig:can} {Counter–current flow in a can} {Counter–current flow in a can (the left figure) has only one hole thus pulse flow and a flow with two holes (right picture).} The counter-current flow occurs, for example, when cavity is filled or emptied with a liquid. The two phase regimes occurs'' mainly in entrance to the cavity. For example, Figure 13.11 depicts emptying of can filled with liquid. The air is "attempting'' to enter the cavity to fill the vacuum created thus forcing pulse flow. If there are two holes, in some cases, liquid flows through one hole and the air through the second hole and the flow will be continuous. It also can be noticed that if there is one hole (orifice) and a long and narrow tube, the liquid will stay in the cavity (neglecting other phenomena such as dripping flow.).

Fig. 13.12 Picture of Counter-current flow in liquid–gas and solid–gas configurations. The container is made of two compartments. The upper compartment is filled with the heavy phase (liquid, water solution, or small wood particles) by rotating the container. Even though the solid–gas ratio is smaller, it can be noticed that the solid–gas is faster than

There are three flow regimes that have been observed. The first flow pattern is pulse flow regime. In this flow regime, the phases flow turns into different direction (see Figure 13.12). The name pulse flow is used to signify that the flow is flowing in pulses that occurs in a certain frequency. This is opposed to counter–current solid–gas flow when almost no pulse was observed. Initially, due to the gravity, the heavy liquid is leaving the can. Then the pressure in the can is reduced compared to the outside and some lighter liquid (gas)entered into the can. Then, the pressure in the can increase, and some heavy liquid will starts to flow. This process continue until almost the liquid is evacuated (some liquid stay due the surface tension). In many situations, the volume flow rate of the two phase is almost equal. The duration the cycle depends on several factors. The cycle duration can be replaced by frequency. The analysis of the frequency is much more complex issue and will not be dealt here.

### Annular Flow in Counter–current flow

Fig. 13.13 Flood in vertical pipe.

The other flow regime is annular flow in which the heavier phase is on the periphery of the conduit (In the literature, there are someone who claims that heavy liquid will be inside). The analysis is provided, but somehow it contradicts with the experimental evidence. Probably, one or more of the assumptions that the analysis based is erroneous). In very small diameters of tubes the counter–current flow is not possible because of the surface tension (see section). The ratio of the diameter to the length with some combinations of the physical properties (surface tension etc) determines the point where the counter flow can start. At this point, the pulsing flow will start and larger diameter will increase the flow and turn the flow into annular flow. Additional increase of the diameter will change the flow regime into extended open channel flow. Extended open channel flow retains the characteristic of open channel that the lighter liquid (almost) does not effect the heavier liquid flow. Example of such flow in the nature is water falls in which water flows down and air (wind) flows up. The driving force is the second parameter which effects the flow existence. When the driving (body) force is very small, no counter–current flow is possible. Consider the can in zero gravity field, no counter–current flow possible. However, if the can was on the sun (ignoring the heat transfer issue), the flow regime in the can moves from pulse to annular flow. Further increase of the body force will move the flow to be in the extended "open channel flow.'' In the vertical co–current flow there are two possibilities, flow with gravity or against it. As opposed to the co–current flow, the counter–current flow has no possibility for these two cases. The heavy liquid will flow with the body forces (gravity). Thus it should be considered as non existent flow.

### Contributors

• Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.