# Reynolds Number Insights in Biology What if you could shrink small enough to live in a drop of water?

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Reynolds Number Insights in Biology What if you could shrink small enough to live in a drop of water? http://www.flickr.com/photos/nebarnix/878049616/

Fantastic Voyage! Scientists aboard a sub are shrunk to micro-scale. They ride and swim through the blood. Theoretically, could this work? http://www.microbiologybytes.com

Just because something works big doesn’t mean it will work small (or vice versa) Are the concerns of a blue whale swimming the same as those of a copepod? Two Blue Whales. Credit: A. Lombardi Copyright © 2008 Field Studies Council

Before we can answer that question, we have to look at fluid dynamics! courtesy Cesareo de La Rosa Siqueira. [http://www.mcef.ep.usp.br/staff/jmeneg/cesareo/Cesareo_HomePage. html].

Laminar vs. Turbulent Flow Move the straw through the water very slowly. Describe the fluid movement around the straw Repeat, moving the straw more quickly. How does fluid movement differ with the speed?

Which is laminar?

This is laminar Very smooth! But very sticky! What conditions yielded laminar flow?

This is turbulent Very chaotic! But not as sticky! What conditions yielded turbulent flow?

Let’s look at factors of concern to a swimmer Inertia

Let’s look at factors of concern to a swimmer Inertia Viscosity

Let’s look at factors of concern to a swimmer Inertia Viscosity Density

Let’s look at factors of concern to a swimmer Inertia Viscosity Density Speed

Which factors can you observe? Wind the fish CAREFULLY! Time its swim across the tank. Measure the distance (cm) it travelled. Calculate its speed. Complete 3 runs and fill in the data table.

A swimmer at the nano scale faces a different set of problems. Water becomes very sticky – meaning viscosity dominates! Does that mean we can’t model a nano- scale swimmer at the macro scale?

No! That’s what Reynolds number (Re) is for. Measure your swimmer. Use the information provided to calculate the Reynolds number.

No! That’s what Reynolds number (Re) is for.

Swimmer Swimming Speed (cm/s) Body Length (cm) Re Blue whale Person Minnow 630 100 1 2400 180 15 Calculate the Re for each of these animals

For a big animal, Re is high Swimmer Reynold ’ s Number (Re) Blue whale swimming Person swimming Minnow 300,000,000 4,000,000 1000

Turbulent flow high Re A Reynolds number greater than 2000 is considered to be turbulent flow.

Swimmer Swimming Speed (cm/s) Length (cm)Re Copepod E. coli Electron transport protein.5.001 ?.15.0002 1 X 10 -7 But what about something small?

Object Reynold ’ s Number (Re) Copepod E. coli Electron transport protein 10.00004.0000025

Laminar flow at low Re

We can model a copepod at large scale if we can match the Re What can we reasonably change in our model to accomplish a smaller Re?

Can we change the size of our model? Probably not. Even if possible, small size would be difficult to manage.

What about the speed of our swimmer? Again, possible but not practical. Winding slightly enough to effectively change the speed would be difficult at best.

Can we easily change density? Yes! But even the least dense liquid at room temperature is only 2/3 as dense as water. And that would only lower Re by the same amount.

That leaves us with viscosity! By replacing water with a shampoo mixture we can raise the viscosity by a factor or 3000!  = dynamic viscosity of fluid (for water =.01)

Reynolds number in higher viscosity Wind the fish CAREFULLY! Time its swim across the tank. Measure the distance (cm) it travelled. Calculate its speed. 3 times and average Calculate its Reynolds number (Re)

Cnidarians fire small harpoons called nematocysts (or cnidoblasts) at their prey Courtesy of James Cook Uni

But a nematocyst is only 10mm, so Re should be low How do they overcome viscosity to fire these small projectiles so rapidly? Photo courtesy of Dr. Zoltan Takacs

What could compensate for the small size and make the nematocysts turbulent? Average velocity = 1860 cm/s Nearly 70 km/h or 42 mph Not impressed? –Speed is attained within 13 micrometers –Acceleration required is about 5,000,000 g’s! Figure from Nüchter et al. 2006.

Things behave differently at different size scales! As things get smaller, viscosity becomes more important. Re can be used to model movement at small scales.

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