Friday, May 20, 2011

Non-Newtonian Fluids and the Rheology of Blood

In Chapter 1 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I explain the difference between a Newtonian fluid and a non-Newtonian fluid.
“A fluid can support a viscous shear stress if the shear strain is changing. One way to create such a situation is to immerse two parallel plates, each of area S, in the fluid, and to move one parallel to the other … The variation of velocity between the plates gives rise to a velocity gradient dvx/dy

In order to keep the top plate moving and the bottom plate stationary, it is necessary to exert a force of magnitude F on each plate: to the right on the upper plate and to the left on the lower plate. The resulting shear stress or force per unit area is in many cases proportional to the velocity gradient:

F/S = η dvx/dy . (1.33)

The constant η is called the coefficient of viscosity … Fluids that are described by Eq. 1.33 are called Newtonian fluids. Many fluids are not Newtonian.”
At the end of the chapter, we give an example of a biologically important non-Newtonian fluid.
Blood is not a Newtonian fluid. The viscosity depends strongly on the fraction of volume occupied by red cells (the hematocrit).”
An excellent review of blood's fluid behavior can be found in the article “Rheology of Blood” by Edward Merrill (Physiological Reviews, Volume 49, Pages 863-888, 1969). Rheology is the part of fluid mechanics that deals with non-Newtonian fluids. Merrill explains clearly the difference between a Newtonian fluid with a high viscosity and a Non-Newtonian fluid.
“A Newtonian liquid is one in which the viscosity, at fixed temperature and pressure, is independent of the shear stress. Thus, a non-Newtonian liquid is one in which the viscosity depends on shear stress. Water and honey are Newtonian, but many aqueous suspensions of fine particulate matter such as water-base paint, plaster, and oil emulsions are non-Newtonian. The distinction is qualitatively obvious if one imagines two spoons, one in a pot of honey (Newtonian) and the other in a pot of mayonnaise (non-Newtonian emulsion). The honey is harder to stir (has a higher viscosity) than the mayonnaise, but when the spoons are removed and held above the pots, the honey continues to drizzle off its spoon, whereas the mayonnaise coating the other spoon clings indefinitely to it without flow, thus exhibiting 'infinite' viscosity.”
An important concept when discussing the rheology of blood is yield stress. Merrill explains
“Blood … exhibits a 'yield stress.' This means that, if …one increases from zero the stress, but keeps it less than a critical value, the response will be elastic … On removal of the stress, the shape of the blood film will be unaltered, i.e., no flow will have occurred. However, if the yield stress is exceeded, irreversible deformation will occur.”
In other words, it acts like a solid at low stress, and a fluid at high stress. Merrill concludes by discussing the physiological significance of the non-Newtonian nature of blood.
“In summary, the relevance of blood rheology to physiological fluid mechanics is to make stopping of flows easier, starting of flows more difficult, and slow flows more energy consuming than would be expected if blood were a simple, cell-less, micromolecular fluid of equal viscosity--and these effects are increasingly emphasized with increase of hematocrit and fibrinogen concentration.”
Besides blood, another dramatic example of a non-Newtonian fluid is a mixture of corn starch and water. My Oakland University colleague Alberto Rojo (who’s office is next door to mine) has made a fun video demonstrating how you can “walk on water” by taking advantage of this mixture's non-Newtonian properties. The effect is fascinating.

1 comment:

  1. Thank you for sharing this information.
    It will really helpful to solve my confusion

    Process $ Chemical Engineering