hydrodynamically coupled Brownian dynamics simulations for flow of non-Newtonian fluids

*Vishal Ahuja is a PhD student in the research group Computational Chemical Physics. His supervisors are prof.dr. W.J. Briels from the faculty of Science and Technology and prof.dr.ir. J. van der Gucht from the Wageningen University. *

The flow of non-Newtonian fluids, polymer solutions in particular, has been a subject of research for several decades. Owing to the complexity of this subject, many fundamental questions are still open for discussion even today. Particularly, the flow of these complex fluids through complex geometries is a poorly understood subject, and over time the knowledge in this field has been growing with advances in both experimental as well as simulation techniques. In this thesis, we have described a novel simulation technique that we have developed for studying this problem. With this technique, we have provided a new methodology to study the bulk flow of polymer solutions as well as their flow through porous media.

In Chapter 2, we have presented a coarse-grain particle based simulation technique in which we couple the Brownian motion of the polymers with the flow of a 'background fluid' implicitly present at the positions of the centers-of-mass of the polymers. The polymers are represented by the positions of their centers-of-mass and interact with each other based on pair potentials. As our test system, we used a potential that is commonly used for modeling star polymer solutions. Furthermore, the polymers are also influenced by the flow of the background fluid, which is calculated by solving a modified version of the Navier-Stokes equation on a moving grid of nodes, which in this case are positioned at the centers-of-mass of the polymers. The modification to the Navier-Stokes equation is essentially the addition of an extra force term, which is actually the force felt by the polymers at that position due to the interaction with the other polymers. This method of transmitting the polymer force to the fluid, which then affects back the flow of the polymers is based on the Galilean invariant, first order Brownian dynamics algorithm developed by Padding and Briels [J. Chem. Phys. 141, 244108 (2014)]. This makes the flow of the background fluid non-Newtonian and also couples it to the polymers. This coupling is straightforward as the fluid blobs are assumed to be implicitly present at the positions of the centers-of-mass of the polymers. We have applied this method to study the flow of our model star polymer solution between two infinite solid plates. For this purpose, we applied appropriate boundary conditions at the solid-fluid interface using the method developed by Morris et al. [J. Comp. Phys. 136, 214 (1997)].

Although the method described in Chapter 2 gives good results and is computationally very efficient, yet there a couple of limitations of this method, \textit{viz.} one is not free to choose the resolution of the background fluid as it is by definition the concentration of the polymers, and one is not free to choose the equation of the state for the fluid either if the method is used as is. Therefore, we envisaged that the model can be improved by using two different types of particles for the polymers and the fluid. However, the coupling between the two would not be obvious like the previous method because now the fluid blobs are not present at the position of the centers-of-mass of the polymers anymore. So we developed a novel approach which we call Hydrodynamically Coupled Brownian Dynamics (HCBD), in which we couple the polymer blobs and the fluid blobs (which are now independent entities), using a special interaction term that we constructed in such a way that the momentum is conserved locally. We describe the development of this technique along with simple applications in Chapter 3, where we chose the Flory-Huggins potential to describe the interactions between the polymers and also introduced memory into the system using the Responsive Particle Dynamics (RaPiD) method. Using this model, we studied the rheology of model linear polymer solutions for two different concentrations by simulating their responses to a homogeneous shear using the Lees-Edwards method and to a varying shear environment using the Reverse Poiseuille Flow technique. We observed that the polymers are coupled very well with the fluid, which is evident from the absence of a lag between their flows. Furthermore, we observed the characteristic shear-thinning and cross-flow migration phenomenon, that have been observed experimentally.

In Chapter 4, we used our novel HCBD technique to couple the background fluid with a less coarse and hence more realistic polymer model \textit{viz.} RaPiD with Finitely Extensible Non-Linear Elastic (FENE) dumbbells. In this polymer model, the polymers are represented as a finitely extensible non-linear elastic dumbbell instead of a point particle as in the case of RaPiD. This brings, in addition to the external quasi elastic memory term of RaPiD, intra-molecular elasticity in the system and allows us to study elastic instabilities exhibited by polymer solutions. We simulated the flow of this model polymer solution for two different concentrations in a homogeneous shear field. For the highest concentration, we observe the well known shear banding phenomenon and study its time evolution. Moreover, we found that at certain shear rates the resulting bands themselves become unstable and spontaneously form microstructures such as 'shear rolls' and 'streaks'.

In Chapter 5, we have presented the flow of our model polymer solution through a periodic array of cylindrical and cuboidal structures in two extreme flow directions. The complex geometries were constructed in such a way that they mimic various configurations of porous media. The porosity was maintained the same for the two different types of porous media and also the same pressure drop was applied across the media. Furthermore, two different, extreme current directions were chosen in both cases. We observed the differences in the emerging flow patterns and polymer concentrations in the two different media. There are interesting correlations between the polymer concentrations and the flow profiles as a result of cross-flow migration of the polymers. This highlights an advantage of our coarse-grain particle-based model in contrast to conventional CFD methods, as our method allows polymers to distribute heterogeneously over the accessible volume.

Thus, we have developed a novel computational technique (HCBD), which can be used to couple any Brownian Dynamics based polymer model with a background fluid model based on Smoothed Particle Hydrodynamics. We have shown that with our model we can study the flow of polymer solutions through porous media, which is one of the main applications of this work. An important aspect of our method is that it is not limited to studying flow of polymer solutions but can be easily extended to study the flow of viscoelastic surfactants or multiphase flow through porous media to understand how polymer solutions displace oil from an oil reservoir. This can greatly help improve the understanding of polymer flooding operations in Enhanced Oil Recovery. The additional oil recovered from the reservoirs can then be used for making petrochemical products or fuels to provide additional energy to the global market whose energy consumption is ever-increasing. Our work can also be used to improve the understanding of other operations in the chemical industry, such as polymer extrusion and food processing. It is thus a new tool which can be used to further the scientific understanding for various phenomena of interest related to a wide range of non-Newtonian fluids using computer simulations.