## Saturday, August 21, 2010

### Viscous Critical Force (p165)

The type of liquid flow is situation-dependent. This explains why a bacterium in water experiences laminar flow whereas we don’t. It is a consequence of the amount of force exerted by us or the bacterium.
Looking at equation 5.5 we can understand why.

f(viscous critical force) = η^2 / ρm
η units are Pa.s
ρ units are kg.m^-3

We look at the effect of applied forces with the dimensionless ratio F(applied)/f(crit)
F/f(crit) = Fρm / η^2
For a large ratio value you can see that the equation will be dominated by the density and therefore inertial effects (proportional to mass). This results in Turbulent Flow.
For a small ratio it is the viscosity and thereby the frictional effect that dominates. Result: Laminar Flow.
Obviously if you apply enough force you can also create turbulent flow from a very viscous liquid. Which is one way a bacterium can feed, by using a burst of force to create turbulent flow to capture its food. Whoever said strength isn't everything obviously wasn't a bacterium.

#### 1 comment:

1. It's also a way in which a bacterium can escape from being the food. Of course what needs to be remembered as well is that sometimes the fast approach can have its own dangers, such as with predators who work through the sensing of surrounding turbulent flow. Also, the bacterium would be hoping that it's in a newtonian fluid....i can't imagine being held in an non-newtonian fluid would be advantageous to its escape....though nor also to the predator charging to catch it.
And don't forget as well, you've mentioned that a turbulent flow can be created within even the most viscous liquid, but the opposite situation is also true, where the lack of enough force can create laminar flow out of a non-viscous fluid. Despite this being less likely, it is still possible (even if you have to head to the nanoscale world to observe it).