Pressure and Electrokinetically Driven Flows of Viscoelastic Fluids through a Model Porous System

Abstract

The flow of viscoelastic fluids through a porous media such as polymer or wormlike mi cellar solutions is encountered in many pragmatic applications ranging from enhanced oil recovery (EOR) process to soil remediation. This particular flow system deserves special attention in the complex fluids research community due to the occurrence of the viscoelastic instability phenomenon resulting from the interaction between the non linear elastic stresses and a high streamline curvature present in this flow system. The present thesis aims to investigate the complex flow dynamics of these viscoelastic fluids through various model porous systems, such as a straight microchannel with step expan sion and contraction or a microchannel with in-built obstacles, under both pressure and electrokinetically driven flow conditions. Extensive finite volume method (FVM) based computational fluid dynamics (CFD) simulations and limited microfluidic experiments comprising soft lithography and micro-particle image velocimetry (µ-PIV) techniques have been conducted to achieve the objectives of the present thesis. Additionally, the present dissertation performs a detailed rheological study of viscoelastic fluids and uses the data-driven reduced-order modeling technique to explain and understand the results in more detail. The chapter-wise abstract of the present thesis is written below. Chapter 4 discusses the rheological investigation of rhamnolipid, a well-known bac terial biosurfactant produced by the Pseudomonas aeruginosa bacteria. This chapter presents a thorough and complete investigation of this biosurfactant’s shear and exten sional rheological behaviours. While steady shear and small amplitude oscillatory shear (SAOS) measurements are conducted to investigate the shear rheological behaviour, the dripping-onto-substrate (DoS) extensional rheometry technique is used to understand its extensional rheological behaviour. A chemically derived surfactant (cetyltrimethyl am monium bromide (CTAB)) is also used in the analysis to show and discuss the qualitative and quantitative differences in their rheological behaviours. Along with the detailed rhe ological study, some studies on the physicochemical properties, such as surface tension, contact angle, particle size analysis, thermal stability, etc., are also conducted to com pare the two surfactants. Both surfactants show strong shear-thinning and extensional hardening behaviors in shear and extensional rheological flows, respectively. However, the zero-shear rate viscosity and extensional viscosity are higher for rhamnolipid surfac tant solutions than for CTAB. The corresponding shear and extensional relaxation times also follow the same trend. Furthermore, the surface tension is found to be less, and the contact angle is found to be more for rhamnolipid biosurfactant than for CTAB. Rham nolipid shows more excellent thermal stability, particularly at high temperatures, than CTAB. Therefore, the results and discussion presented in this chapter will help to choose the present rhamnolipid biosurfactant for any particular application, particularly where the knowledge of the rheological responses of a surfactant solution is essential. The flow of wormlike micellar solutions past a microfluidic cylinder confined in a channel is considered in chapter 5. Earlier experiments showed the existence of an elastic instability for the flow of a wormlike micellar solution in this model porous system after a critical value of the Weissenberg number in the creeping flow regime. This chapter presents a detailed numerical investigation of this elastic instability in this model porous system using the two-species VCM (Vasquez-Cook-McKinley) constitutive model for the wormlike micellar solution. In line with the experimental trends, we also observe a similar elastic instability in this flow system once the Weissenberg number exceeds a critical value. Wealso find that the breakage and reformation dynamics of the wormlike micelles greatly influence the elastic instability in this model geometry. In particular, the onset of such an elastic instability is delayed or even maybe suppressed entirely as the micelles become progressively easier to break. Furthermore, this elastic instability is associated with the elastic wave phenomena, which have been recently observed experimentally for polymer solutions. The present study reveals that the speed of such an elastic wave increases non-linearly with the Weissenberg number similar to that seen in polymer solutions. Chapter 6 presents an extensive numerical investigation of the flow characteristics of wormlike micellar solutions past a single and two vertically aligned microcylinders placed in a microchannel in the creeping flow regime. For the case of a single microcylinder, as the blockage ratio (ratio of the cylinder diameter to that of the channel height) is gradually varied, we find the existence of a flow bifurcation in the system and also a gradual transition for a range of flow states, for instance, steady and symmetric or Newtonian like, steady and asymmetric, unsteady periodic and asymmetric, unsteady quasi-periodic and asymmetric, and finally, unsteady quasi-periodic and symmetric. For the case of two microcylinders, we observe the presence of three distinct flow states in the system, namely, diverging (D), asymmetric-diverging (AD), and converging (C) states as the intercylinder spacing between the two cylinders is varied. Recent experiments dealing with wormlike micellar solutions also observe similar flow states. However, we show that either this transition from one flow state to another in the case of a single microcylinder or the occurrence of any flow state in the case of two microcylinders is strongly dependent upon the values of the Weissenberg number and the non-linear VCM model parameter ξ, which indicates how easy or hard it is to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we hope this study will facilitate the understanding behind the formation of preferential paths or lanes during the flow of viscoelastic fluids through a porous media, which was seen in many prior experiments in the creeping flow regime. Chapter 7 presents a detailed numerical investigation of the electrokinetic transport of both Newtonian and viscoelastic fluids in a model porous system consisting of a long micropore with step expansion and contraction. Over the whole range of conditions encompassed in this study, a steady and symmetric flow field is observed for a Newtonian f luid. However, for a viscoelastic fluid, we observe a transition in the flow field from steady and symmetric to unsteady and asymmetric once the Weissenberg number (ratio of the elastic to that of the viscous forces) exceeds a critical value. We show that this transition is caused due to the onset of an electro-elastic instability in the system. The critical value of this Weissenberg number (at which this transition occurs) depends on various factors. In particular, this value increases with the polymer viscosity ratio and expansion and contraction lengths of the micropore. At fixed values of the electric field strength, polymer viscosity ratio, contraction, and expansion lengths of the micropore, we observe the existence of different vortex dynamics within this model porous system as the Weissenberg number gradually increases, such as the emergence of the entrant and re-entrant lip vortices, oscillating lip vortices, multi vortices, etc. Therefore, the electrokinetic flow dynamics of viscoelastic fluids in a porous system are much more complex than that of simple Newtonian fluids. We hope this study for a model porous system will facilitate a better understanding of the electrokinetic transport phenomena of viscoelastic fluids in an actual porous media. Furthermore, we show how this model system of a long micropore with step expansion and contraction could also be successfully utilized for other practical applications, such as mixing two viscoelastic fluids. Chapter 8 investigates the electroosmotic flows of viscoelastic fluids through a mi crofluidic setup consisting of a straight microchannel with an in-built cylindrical obstacle present in it with the help of both numerical simulations and experiments. It has been found that the flow dynamics of viscoelastic fluids inside this microfluidic setup become unsteady and fluctuating as the applied electric field strength is gradually increased, even though the Reynolds number remains much lower than one. This is because of the origin of the electro-elastic instability (EEI) phenomenon, resulting from the interaction between the non-linear elastic stresses in viscoelastic fluids and streamline curvature present in the flow system. This instability ultimately leads to a flow-switching phenomenon inside the microfluidic setup, observed both in numerical simulations and experiments. The results and discussion of this chapter could facilitate a better understanding of the elec trokinetic flows of complex fluids through a porous media, which is encountered in many practical applications such as electro-chromatography, micro-pumping, chemical radia tion of contaminated soil, etc. Furthermore, this chapter shows that this flow-switching phenomenon could successfully mix viscoelastic fluids in this simple, easy-to-fabricate microfluidic setup. Additionally, the data-driven dynamic mode decomposition (DMD) analysis has been employed in this study to understand better the dynamical behaviour of various coherent flow structures that originated due to this flow-switching phenomenon and their subsequent influence on the mixing phenomenon.