Complex fluids and complex flows near surfaces are encountered in biological systems and in numerous technological applications, such as microfluidics and coatings. Understanding the dynamics of such fluids and flows is of both technological and fundamental importance. In my PhD dissertation, under the supervision of Prof. Satish Kumar, we investigated three different problems involving complex fluids and complex flows.

a) The dynamics of polyelectrolytes near complex surfaces is important for the development of polyelectrolyte multilayers, the understanding of protein complexation, and microfluidics. In the first problem, we probe the effects of external fields, such as electrostatic and hydrodynamic, on the static and dynamic properties of polyelectrolyte molecules near complex surfaces [1-7]. We found that surface heterogeneities not only affect the condition required for adsorption but also the conformation of adsorbed chains. In the presence of an imposed flow, polyelectrolyte adsorption is determined by the competition between electrostatic and hydrodynamic forces. We propose a desorption criterion and put forward numerous strategies for controlling the adsorption/desorption of polyelectrolyte molecules. The diffusion dynamics of an adsorbed polymer chain was also probed, and we found that it is sensitive to chain flexibility and solvent quality.

b) Linear dynamical systems can have solutions that grow substantially at short times, even though they decay at long times. One method to study this so-called transient growth, which can put the system into a regime where nonlinear interactions are no longer negligible, is to study the response of the linearized Navier-Stokes equations to external disturbances. In the second problem, we apply this method to study the effects of external disturbances on channel flows of Oldroyd-B fluids [8-9]. We found that in addition to inertia, even elasticity can amplify disturbances. Our analysis of the Reynolds-Orr equation demonstrates that the energy-exchange term involving the streamwise/wall-normal polymer stress component and the wall-normal gradient of the streamwise velocity is the main driving force for amplification in flows with strong viscoelastic effects. We also found that viscoelastic effects introduce additional timescales and promote development of flow patterns with smaller time constants than in Newtonian fluids.

c) In gravure printing and coating processes, the print quality as well as coating thickness is affected by the amount of liquid that gets transferred from the cells, engraved on the surface of the gravure roll, to the substrate. In the last project, we aim to better understand the cell-emptying process, and to suggest ways of increasing liquid removal from the cell [10]. We found that the liquid removal from the cell can be significantly increased either by increasing the ratio of cell width to cell height, or by increasing the vertical velocity of the substrate.

References

1. Nazish Hoda and Satish Kumar, "Brownian dynamics simulations of polyelectrolyte adsorption onto charged patterned surfaces", Langmuir, 23, 1741 (2007)

2. Nazish Hoda and Satish Kumar, "Kinetic theory of polyelectrolyte adsorption in shear flow", J. Rheol., 51, 799 (2007).

3. Nazish Hoda and Satish Kumar, "Brownian dynamic simulations of polyelectrolyte adsorption onto topographically patterned surfaces", Langmuir, 23, 11747 (2007)

4. Nazish Hoda and Satish Kumar, "Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interactions", J. Chem. Phys., 127, 234902 (2007)

5. Nazish Hoda and Satish Kumar, "Theory of Polyelectrolyte adsorption onto surfaces patterned with charge and topography", J. Chem. Phys., 128, 124907 (2008)

6. Nazish Hoda and Satish Kumar, "Brownian dynamics simulations of polyelectrolyte adsorption in shear flow: Effect of hydrophobicity and charge patterning", J. Chem. Phys., 128, 164907 (2008)

7. Nazish Hoda and Satish Kumar, "Parameters influencing diffusion dynamics of an adsorbed chain", Phys. Rev. Lett. (submitted)

8. Nazish Hoda, Mihailo R. Jovanovic, and Satish Kumar, "Energy amplification in channel flows of viscoelastic fluids", J. Fluid Mech., 601, 407-424 (2008)

9. Nazish Hoda, Mihailo R. Jovanovic, and Satish Kumar, "Frequency Responses of the 2D/3C Model in Channel Flows of Oldroyd-B Fluids", J. Fluid Mech. (submitted)

10. Nazish Hoda and Satish Kumar, "Boundary integral simulations of gravure cell emptying", Phys. Fluids (submitted)