Epicyclic orbits in a viscous fluid about a precessing rod: theory and experiments at the micro- and macro-scales.
We present experimental observations and quantified theoretical predictions of the nanoscale hydrodynamics induced by nanorod precession emulating primary cilia motion in developing embryos. We observe phenomena including micron size particles which exhibit epicyclic orbits with coherent fluctuations distinguishable from comparable amplitude thermal noise. Quantifying the mixing and transport physics of such motions on small scales is critical to understanding fundamental biological processes such as extracellular redistribution of nutrients. We present experiments designed to quantify the trajectories of these particles, which are seen to consist of slow orbits about the rod, with secondary epicycles quasicommensurate with the precession rate. A first-principles theory is developed to predict trajectories in such time-varying flows. The theory is further tested using a dynamically similar macroscale experiment to remove thermal noise effects. The excellent agreement between our theory and experiments confirms that the continuum hypothesis applies all the way to the scales of such submicron biological motions.
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA.
Elizabeth L
EL
Bouzarth
Adam
A
Brooks
Roberto
R
Camassa
Hao
H
Jing
Terry Jo
TJ
Leiterman
Richard M
RM
McLaughlin
Richard
R
Superfine
Jonathan
J
Toledo
Leandra
L
Vicci
D001703:Biophysics / Q000379:methods; D002627:Chemistry, Physical / Q000379:methods*; D004058:Diffusion; D036262:Empirical Research; D015233:Models, Statistical; D008962:Models, Theoretical; D053758:Nanoparticles / Q000737:chemistry; D036103:Nanotechnology / Q000379:methods; D012107:Research Design; D012212:Rheology; D013997:Time Factors; D014783:Viscosity