To image the flow produced by biomimetic cilia beating with a tilted conical beat shape, fluids are seeded with one micron red latex fluorescent microspheres (FluoSpheres). (Throughout this thesis I will interchangeably use microspheres, tracers, and tracer particles to indicate the particles I utilize to track flow in biomimetic cilia arrays.) Depending on the fluid, the microspheres may or may not be PEGylated, a process which binds low molecular weight polyethylene glycol (PEG) to a microsphere’s surface to reduce (or neutralize) its surface charge. If using polymer solutions such as mucus or guar, coating microspheres’ surfaces with PEG reduces the potential that beads will become attached to the polymer matrix and cease their thermal and/or driven motion. In an aqueous solution such as buffer
PEGylation does not affect the motion of microspheres. Additionally, in some polymer so-
lutions such as agarose, diffusion measurements taken by David Hill, a research associate
with the Cystic Fibrosis Center at UNC-Chapel Hill, also indicate that PEGylation has little effect on microsphere motion.
To investigate the flow above and below the array of biomimetic cilia, the focal plane of the objective is changed in increments of tens of microns, and both brightfield and flu- orescent videos are taken using a Pulnix camera, model TM-6710CL (JAI, Inc.), and an EDT-PCI DV (Engineering Design Team) frame grabber card. With fluorescence, videos may be captured close to and within the cilia layer without interference from moving cilia. In each video, the fluorescent microspheres are tracked using CISMM’s Video Spot Tracker (cismm.org/downloads), and velocities are extracted using in-house Matlab scripts.
Chapter 6
Fluid Transport in Aqueous and
Viscoelastic Fluids
The thrust of this thesis thus far has concentrated on the design and realization of fab- ricated microstructures in the same physical parameter space as biological cilia. Because biological cilia are responsible for propelling both aqueous and viscoelastic fluids, creating an identically sized biomimetic system has been an important endeavor. In hydrodynam- ics, viscous and viscoelastic fluids are characterized by a group of dimensionless numbers which represent the dominant forces and timescales in a fluid. In order to use an experi- mental apparatus, such as biomimetic cilia, at a larger scale and accurately represent fluidic phenomena, all dimensionless numbers characterizing the experiment must be equivalent (Metzner et al., 1966). For purely viscous fluids, this is a relatively simple undertaking as the Reynolds number is the significant dimensionless number that must be scaled. Any purely viscous fluid may be utilized in a macro-scale experiment, producing similar results to a micro-scale experiment, if the Reynolds number is equivalent. For viscoelastic fluids, the Reynolds number, Deborah number, and Weissenberg number must all be scaled with the physical dimensions of the experiment. This scaling is nearly impossible unless the
exact same fluid is used every time; it is difficult to make any generalization concerning
all three dimensionless numbers for viscoelastic fluids (Metzner et al., 1966). For these reasons, core-shell biomimetic cilia are an ideal system for the study of fluid propulsion at the micro-scale, being the only system currently capable of viscoelastic fluid propulsion at the scale of biological cilia.
In addition to dimensionless numbers, the field of fluid dynamics has developed a num- ber of constitutive relations to understand how, for a particular fluid, stress and shear (or strain) rate are related. Purely viscous fluids, also called Newtonian fluids, which exhibit a linear relationship between stress and shear rate with a proportionality constant that is the fluid’s viscosity, are understood analytically for a number of problems with simple geome- tries. The introduction of a little complexity, however, may require the use of computational methods. As such, very little is understood about viscoelastic fluids, or non-Newtonian flu- ids, which are fluids that exhibit a time dependent response to an applied stress or strain.
In this chapter, I will first give a brief review of the relevant hydrodynamics including an overview of the three significant dimensionless numbers used to describe both viscous and viscoelastic fluids, the governing equation in fluid dynamics, the Navier-Stokes equation, and canonical solutions for both viscous and linear viscoelastic fluids, including Stokes’ 1st and 2nd problems. Following this will be an analysis and extensive discussion of the characteristics of fluid flow driven by biomimetic cilia in both aqueous (Section 6.2) and viscoelastic (Section 6.3) fluids. Biological cilia are responsible for driving flow in multiple kinds of fluids including both buffer-like (aqueous) and mucus-like (viscoelastic) fluids.
environments.
Our theoretical understanding of viscous and viscoelastic fluids far surpasses our ex- perimental understanding, especially as it pertains to biological systems. By using simple theoretical models for viscous and viscoelastic fluids and treating my biomimetic cilia tips as a single moving boundary (also known as coarse-graining), I am able to gain insight into the fluid dynamics of the system and apply this insight to both embryonic nodal cilia and lung epithelial cilia.
In the purely viscous, or aqueous, fluid, both FFPDMS and core-shell cilia are ca- pable of driving transport with the tilted conical beat shape. The hydrodynamic model which supports the experimental data considers the motion of all cilia as a single translat- ing plane and is a superposition of two canonical solutions to the low Reynolds number Navier-Stokes equation. This model was first identified in our publication in 2010 (Shields et al., 2010) and has been expounded upon in significant detail by Adam Shields in his dissertation (Shields, 2010).
In viscoelastic fluids, FFPDMS cilia are incapable of maintaining a sufficiently large
amplitude to attain flow, and thus all presented results were collected with core-shell bioimimetic cilia. The data for flow in a viscoelastic fluid at low Reynolds number is markedly differ-
ent than purely viscous flow, and to better understand these differences, I first apply the
purely viscous models to the viscoelastic data. These models are quickly shown to be in- sufficient at explaining the fluid dynamics and a model which better incorporates the elastic