The FENE-Fraenkel spring force law has been implemented in code previously used to study bead-FENE-spring chains in flow. Changes were made to the code as it was found that the level of precision used by the code was insufficient to handle calculations with the FENE-Fraenkel spring force law. A further alteration was introduced to solve the cu- bic polynomial Equation (2.7.22) explicitly rather than with a Newton-Raphson iterative scheme, to remove the guesswork required in trialling a first guess for a root.
Comparisons with analytical zero-shear results indicate that the code behaves as the the- ory predicts. The data obtained is also comparable to the simulation work by Hsieh et al. [48], with similar patterns observed in the scale of “noise” of the output when parame- ters are changed to increase the spring stiffness. Small discrepancies with data in [48] do exist, but these are minimised with the a suitable choice of parameters, particularly with the use of a small time-step size. Changes to the code that were required to counteract issues caused by a lack of precision may be an underlying cause of the increased noise in our simulations compared with the data published by Hsieh et al. [48]. Simulations of the alignment of FENE-Fraenkel spring dumbbells in shear flows show increased alignment with high shear rates, similar to modelling data published by McLachlan et al. [89]. Since these simulations are for the study of polymers, further simulations should to be car- ried out with chains (i.e.more than 2 beads) in shear and extensional flow, to see how the alignment parameter changes over time in these flow regimes. These simulations should be performed with a wider range of strain rates, natural length and extensibility parame- ter values than used here. However, attention would need to be paid to how realistic the choice of parameters are, with respect to the behaviour of polymers in reality. In addition,
these simulations should also include excluded volume and hydrodynamic interactions, particularly as longer chains with more beads will increase the prevalence of these inter- actions. The code, as published here, is able to implement these interactions. Finally, an extension on the inclusion of excluded volume interactions would be the inclusion of bending potentials, as discussed by Holleran and Larson [46]; instead of a freely-jointed chain, there would be restrictions on the proximity of springs to each other, reflecting the finite flexibility of polymers in real life.
DNA has been extensively studied with linear dichroism spectroscopy; in many cases, DNA molecules were aligned using Couette shear flow [97]. The behaviour of DNA molecules has also been studied in different flow regimes, using microfludic devices and microscopy. A number of these experiments have used extensional flow to control the motion of DNA molecules [135]. However there have not been any attempts to study DNA using linear dichroism in an extensional flow setting.
This chapter considers LD experiments performed to observe the alignment of DNA molecules in three flow regimes: Couette shear flow using existing equipment already developed in our lab, and pressure-driven (Poiseuille) and extensional flows using mi- crofluidic devices manufactured from polydimethylsiloxane (PDMS). Preliminary exper- iments were performed using test designs to determine if LD experiments with planar microfluidic devices were feasible. The development of an extensional flow microflu- idic device was considered, with further experiments performed to ascertain the ability of these devices to align DNA molecules for LD experiments in different types of fluid flow.
4.1
LD experiments using Couette Flow
LD experiments typically use a circular-dichroism spectropolarimeter with a rectangular beam of light passing through a sample chamber and then into a photomultiplier tube for detection. Two devices are used for LD experiments in this thesis — a Jasco J-815 CD spectropolarimeter and a BioLogic MOS-450 spectropolarimeter. Both devices use a Xenon arc lamp to generate a spectrum of light with wavelengths between 180 nm in the “near-UV” range and 1100 nm in the infra-red range. A polariser and a photoelas- tic modulator are used to generate two linear polarisations of the beam, such that they polarisations are perpendicular to one another.
For Couette flow LD experiments, a setup where a small volume, roughly 70µl, of fluid sample is placed in a rotating quartz cuvette, with a stationary quartz rod placed in the centre (see Figure 4.1) was previously developed in our lab [82, 83]. The light beam passes through a focussing lens, through the cylindrical cuvette setup (see Figure 1.3) and then into a photomultiplier tube for detection.
The principle behind the use of Couette flow for LD experiments is that it a shear flow (see Figure 1.2). In particular, polymer molecules in shear flow align with the long axis parallel to the shear axis. So in this setup, the short axes of polymer molecules in a sample are aligned radially.
Stationary Rod 2.5 mm
3 mm
Rotating cuvette 250 μm annular gap for
sample
Rotation speed ≈ 3000rpm velocity profile in Indicative fluid
Couette Flow
Plane polarised light passed through the
sample
Transmitted light to photodetector
Figure 4.2:Schematic of a Couette flow cell for LD experiments.