Microrheology

Micro-rheological studies reveal properties of fluids at the micron scale. One seeds a flow with small particles (typically a few hundred nanometers in diameter) and observes their motions under light microscopy. Brownian motion jiggles the particles, but particle-tracking algorithms can follow these motions if we illuminate the particles so they form bright spots in videos. Algorithms reveal the visco-elastic nature of the suspending fluids. For example, the mean square displacement of particles in a Newtonian fluid is simply proportional to a particle's molecular viscosity (via the Einstein equation), but more complex non-Newtonian fluids, polymers and protein-laden solutions in hemolymph, for example, behave differently.

The microstructure we can see under light microscopy and the composition or weight fractions of elements in the mixture determine the physical properties of traditional solutes. For nano-structured materials, however, the atomic species present, and their configurations on the atomic scale determine the properties. Surface roughness determines the wetting properties of liquids at both the micro- and nano-scales. Exact molecular shapes rubbing over each other determine boundary conditions and wall slip. Newtonian fluids encountering highly hydrophobic surfaces may slip. A rough surface at molecular dimensions may inhibit slippage. Fabrication technology permits constructing atomically smooth surfaces as well as precisely setting the heights of the micro-channels.

We can model flows in devices and hemocoels having two and three dimensions. In two-dimensional models, we give the channels infinite dimensions and therefore no top or bottom wall boundary conditions. Such two-dimensional views resemble our concept of a hemocoel as a single surface enveloping the hemo-coel that forms when fluid volumes are very small in the smallest insects.

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