Basics of Fluid Mechanics, 2014a

13.5. CLASSIFICATION OF LIQUID-LIQUID FLOW REGIMES 539
materials flow in the opposite direction, it is referred as counter–current. In general,
the co-current is the more common. Additionally, the counter–current flow must have
special configurations of long length of flow. Generally, the counter–current flow has a
limited length window of possibility in a vertical flow in conduits with the exception of
magnetohydrodynamics. The flow regimes are referred to the arrangement of the fluids.
The main difference between the liquid–liquid flow to gas-liquid flow is that gas
density is extremely lighter than the liquid density. For example, water and air flow as
oppose to water and oil flow. The other characteristic that is different between the gas
flow and the liquid flow is the variation of the density. For example, a reduction of the
pressure by half will double the gas volumetric flow rate while the change in the liquid
is negligible. Thus, the flow of gas–liquid can have several flow regimes in one situation
while the flow of liquid–liquid will (probably) have only one flow regime.
13.5.1 Co–Current Flow
In Co–Current flow, two liquids can have three main categories: vertical, horizontal,
and what ever between them. The vertical configuration has two cases, up or down.
It is common to differentiate between the vertical (and near vertical) and horizontal
(and near horizontal). There is no exact meaning to the word “near vertical” or “near
horizontal” and there is no consensus on the limiting angles (not to mention to have
limits as a function with any parameter that determine the limiting angle). The flow
in inclined angle (that not covered by the word “near”) exhibits flow regimes not much
different from the other two. Yet, the limits between the flow regimes are considerably
different. This issue of incline flow will not be covered in this chapter.
13.5.1.1 Horizontal Flow
The typical regimes for horizontal flow
are stratified flow (open channel flow,
and non open channel flow), dispersed
bubble flow, plug flow, and annular flow.
For low velocity (low flow rate) of the
two liquids, the heavy liquid flows on the
bottom and lighter liquid flows on the
top 5 as depicted in Figure 13.2. This
Light Liquid
Heavy Liquid
Fig. -13.2. Stratified flow in horizontal tubes
when the liquids flow is very slow.
kind of flow regime is referred to as horizontal flow. When the flow rate of the lighter
liquid is almost zero, the flow is referred to as open channel flow. This definition (open
channel flow) continues for small amount of lighter liquid as long as the heavier flow can
be calculated as open channel flow (ignoring the lighter liquid). The geometries (even
the boundaries) of open channel flow are very diverse. Open channel flow appears in
many nature (river) as well in industrial process such as the die casting process where
liquid metal is injected into a cylinder (tube) shape. The channel flow will be discussed
in a greater detail in Open Channel Flow chapter.
5 With the exception of the extremely smaller diameter where Rayleigh–Taylor instability is an important
issue.