Vivaswan Chandrashekar

Even in creeping flow, elastic stresses modify how viscoelastic fluids negotiate constrictions and bifurcations in complex geometries (e.g. porous media), producing increased resistance, preferential pathways, and even instabilities. Pore‐scale analogues are widely used to model these flows; predominantly, however, in symmetric forms. In practice, asymmetries are ubiquitous and bias the division of flow at bifurcations. This thesis examines how geometric asymmetries interact with elasticity by introducing asymmetry into the canonical geometries of the confined cylinder and the T‐junction. To this end, finite‐volume simulations were combined with millifluidic experiments. Simulations covered several constitutive models for complex fluids that incorporated viscoelasticity. Experiments used shear‐thinning polymer solutions and asymmetrically confined cylinder geometries. The primary observed phenomenon is an enhancement of flow asymmetry at Weissenberg numbers (Wi) of order unity. When Wi≳1, the non‐preferred pathway becomes progressively deprived of flow, with the preferred path receiving the majority of the flow, even for small geometric asymmetries. The onset aligns with steep pressure gradients and curved streamlines at the entrance of the non‐preferred path, which steer the fluid away from it. We posit a simple mechanism to explain this, a ‘tug-of-war’: when the local residence time at the asymmetric zone of bifurcation falls below the effective relaxation time of the fluid in the zone, Wi > 1, the elastic stresses cannot relax, and the fluid is driven into the preferred path; for Wi < 1, it divides as an inelastic viscous fluid would. The effect is robust against geometric details in the asymmetrically confined cylinder; yet, it is sensitive to rheological properties such as shear‐thinning. Therefore, it can serve as a practical sieve for constitutive models. With this in mind, various constitutive models were tuned to the rheology of test fluids, and the flow asymmetry enhancement predicted by the models was compared with millifluidic experiments. We then developed a comprehensive framework to compare the simulations and experiments. Although several models account for standard rheological characterisation, only the White‐Metzner and Giesekus models quantitatively captured the enhancement in flow asymmetry reasonably well. In a T‐junction, the enhanced flow asymmetry phenomenon also depends on downstream conditions, especially on the length of the preferred path. When the preferred path is long enough for the flow to be fully developed, the standard inelastic viscous solution is recovered. It is demonstrated that the enhanced flow asymmetry phenomenon is a unique function of the entrance length relative to the length of the preferred path for any given Wi and other geometric details. This criterion implies that the spatial extent of influence on the flow of a given geometric feature, such as an asymmetric zone of bifurcation, coincides with the entrance length. Overall, the work establishes the enhanced flow asymmetry phenomenon as a purely elastic, Wi‐controlled effect in simple asymmetric geometries. It provides an experimentally validated framework for evaluating constitutive models. It links pore‐scale kinematics to network‐scale transport by presenting this phenomenon as a primary driver of preferential pathways in viscoelastic flows in porous media.