Consequences of the Inverse Viscosity-Temperature Relationship

In Homework Problem 50 of Chapter 1 in Intermediate Physics for Medicine and Biology, Russ Hobbie and I write

Section 1.19

Problem 50. The viscosity of water (and therefore of blood) is a rapidly decreasing function of temperature. Water at 5° C is twice as viscous as water at 35° C. Speculate on the implications of this extreme temperature dependence for the circulatory system of cold-blooded animals. (For a further discussion, see Vogel 1994, pp. 27–31.)

Let’s see what Steven Vogel discusses. The citation is to Life in Moving Fluids: The Physical Biology of Flow.

CONSEQUENCES OF THE INVERSE VISCOSITY-TEMPERATURE RELATIONSHIP

At 5° C water is about twice as viscous (dynamically or kinematically) as at 35° C; organisms live at both temperatures and, indeed, at ones still higher and lower. Some experience an extreme range within their lifetimes—seasonally, diurnally, or even in different parts of the body simultaneously. Does the consequent variation in viscosity ever have biological implications?…

Consider the body temperature of animals. At elevated temperatures less power ought to be required to keep blood circulating if the viscosity of blood follows the normal behavior of liquids. And, in our case, it does behave in the ordinary way—human blood viscosity (ignoring blood’s minor non-Newtonianism) is 50% higher at 20° than at 37° C… Is this a fringe benefit of having a high body temperature? Probably the saving in power is not especially significant—circulation costs only about 6% of basal metabolic rate. More interesting is the possibility of compensatory adjustments in the bloods and circulatory systems of animals that tolerate a wide range of internal temperatures. The red blood cells of cold-blooded vertebrates, and therefore presumably their capillary diameters, are typically larger than either the nucleated cells of birds or the nonnucleated ones of mammals… The shear rate of blood is greatest in the capillaries; must these be larger in order to permit circulation at adequate rates without excessive cost in a cold body?…

Is the severe temperature dependence of viscosity perhaps a serendipitous advantage on occasion? A marine iguana of the Galapagos basks on warm rocks, heating rapidly, and then jumps into the cold Humboldt current to graze on algae, cooling only slowly. Circulatory adjustments as the animal takes the plunge have been postulated…, but no one seems to have looked at whether part of the circulatory reduction in cold water is just a passive consequence of an increase in viscosity. A variety of large, rapid, pelagic fish have circulatory arrangements that permit locomotory muscles to get quite hot when they’re in use…; blood flow ought to increase automatically at just the appropriate time.

A less speculative case is that of Antarctic mammals and birds… [They] must commonly contend with cold appendages, since full insulation of feet and flippers would be quite incompatible with their normal functions. The circulation of such an appendage often includes a [countercurrent] heat exchanger at the base of the limb so that, in effect, a cold-blooded appendage and a warm-blooded body can be run on the same circulatory system without huge loses of heat… Changes in blood viscosity will reduce flow to appendages when they get cold quite without active adjustments within the circulatory systems.

Vogel goes on for another couple pages. I love the way he uses comparative physiology to illustrate physics. He also covers a lot of ground, ranging from the Galapagos islands to Antarctica. Such discussions are typical of Life in Moving Fluids.