The schematics above shows the flows in a liquid (eg water) which is being pushed into motion at point (shown by red and green arrows*). The flows are shown by what are called streamlines (in blue) which show the paths water molecules in the water follow as they are moved by the flowing liquid. The two flows are what are called Stokes flows because they obey Stokes’ equation – which is just the low inertia limit of the Navier-Stokes equation all simple liquids like water follow. Inertia is irrelevant for small scale (say millimetres or smaller) flows. The difference between the two flows is that there is a wall (in black) on the left, while on the right the flowing liquid is in the middle of the liquid, far from any wall.
In both the cases above the force the liquid is being pushed with, is the same. But the flows are clearly very different. On the right there is basically a jet of fluid moving from left to right. The force (green arrow) pulls in fluid and fires it out to the right, into a jet that broadens out as it moves away from where the force is. There is no wall to obstruct the jet.
But on the left the flow is very different. Walls have two effects on the flow. The first is that they are impermeable to the liquid, it cannot flow into or out of it. This prevents the simple jet of liquid seen on the right; the impermeable wall blocks it.
The second effect is due to friction between the (static) wall and the liquid. This friction means that the liquid immediately in contact with the static wall is also static*, it is stuck to the wall. This friction inhibits flow from the top left by the wall down towards to force (red arrow), and flow from the bottom left up towards the force.
Combined, these two effects turn the simple jet on the right into the weaker jet surrounded by the two oval vortices on the left. A lot of the flowing liquid now circulates instead of being simply pushed from left to right. And, although you can’t see this from the streamlines above, the jet is a lot weaker and shorted ranged. The flow speed decreases as one over the distance from the force, for a jet in the middle of the liquid, while it decreases as one over the distance cubed for the jet near the wall.
And these flow patterns are not just pretty. We often want to inject one liquid into another, using a pressure differential to generate the forces. And the schematics above show how different it is when you inject one liquid into another through a pore in a surface, or via a long thin pipette in the middle of the liquid.
* The flows are due to what is often called a Stokeslet, which is what you get if you push on a liquid at a point, in the limit where the flows are Stokes flows.
** This is are what are called no-slip boundary conditions on the flowing liquid.
Chance & Necessity 