5. Channel Flows with Permeable Partitions

Channel flow is one of the widely used ways of transportation of gas, fluids, various emulsions, and suspensions. Of the two types of channel flow—open and pipe flow—we are interested in the second type. These flows are distinguished by a great variety of pattern depending on the cross-sectional configuration and nature of the change of the latter along the length of a channel. In most cases, the channel walls are impermeable and the fluid flow is unchangeable. However, in some cases, the channel walls may be permeable (perforated or made of porous material), which leads to the inflow (or outflow) of the additional amount of fluid into the channel. As a result, the average flow rate through the channel increases (decreases). The channels may be curved (tortuous) and have branches or connections with other channels. Common to all channel flows is the presence of a pressure differential at the fluid transportation section. Thus, it is natural to attribute the flow of a real viscous fluid through the capillaries or porous medium to the channel currents.