The linear and nonlinear rheology of multiscale complex fluids

Abstract

The microstructures of many complex fluids are typically characterized by a broad distribution of internal length scales. Examples of such multiscale materials include physically and chemically cross-linked gels, emulsions, soft colloidal glasses and concentrated suspensions. Due to the complex microstructure, these materials exhibit multiscale power law relaxation under externally imposed deformation. Compact constitutive frameworks that can accurately describe and predict both the linear as well as the nonlinear rheology of such complex fluids have remained elusive. Moreover, the rheological behavior of these materials under extensional deformations, which is important in applications such as spraying and fiber spinning, is relatively poorly understood. The primary contribution of this thesis is the development of a compact constitutive modeling framework to quantitatively describe the rheology of multiscale complex fluids. In the linear limit of small deformations, fractional constitutive equations in conjunction with the concept of quasi-properties have been shown to provide accurate physical descriptions of the broad power law relaxation dynamics exhibited by multiscale materials. In this thesis we very generally show how fractional constitutive equations enable the prediction of the rheological response of multiscale fluids under complex deformation profiles. As a specific example, we analyze the damped inertio-elastic oscillations exhibited at early times by viscoelastic interfacial layers upon the imposition of a constant stress, and the subsequent long time power law creep. We also analyze the small strain lubrication flow regime of a typical tack experiment performed on a crosslinked power law gel, where the extensional deformation of the complex material plays an important role. We extend these models to the large strain nonlinear regime using an integral K-BKZ framework coupled with a strain damping function. We demonstrate in a general manner that nonlinear rheological responses such as shear-thinning and positive first normal stress coefficients can be predicted a priori from linear viscoelastic data and a single additional nonlinear parameter introduced through the damping function. We also demonstrate that well-known empirical rheological models utilized to describe nonlinear behavior such as the Herschel-Bulkley, Cross and Carreau models can be derived using the K-BKZ framework by selecting a suitable fractional relaxation kernel and an appropriate damping function. Additionally, we derive expressions for linear viscometric functions as well as the first normal stress coefficient for materials that exhibit steady shear flow behavior predicted by the above empirical models. Our approach also quantifies the applicability of widely known empirical rheological rules for nonlinear rheology such as the Cox-Merz rule. The second contribution of this thesis is in increasing the understanding of the rheological behavior of multiscale complex fluids in extensional flow fields. For this purpose we utilize a variety of experimental extensional rheology techniques such as Capillary Breakup Extensional Rheometry (CaBER), Filament Stretching Extensional Rheometry (FiSER) and an Optimized Shape Cross-slot Extensional Rheometer (OSCER). Due to their ubiquity in industrial applications as well as in biologically relevant complex fluids, we primarily study aqueous polysaccharide systems (for example Mamaku gum). With the help of these detailed experiments, we investigate and quantify the strength of hydrogen-bonding interactions in this multiscale physically associated gel. We also investigate the extensional rheology of Hyaluronic acid, which has been shown to be an important factor in proper synovial fluid function. The findings of this thesis are widely applicable given the widespread use of multiscale complex fluids in industrial, and biological applications. The fractional constitutive framework derived here overcomes the limitations of current modeling approaches that invoke a large number of empirical constitutive parameters. Our simple models will be useful for quantitative material diagnostics and quality control comparisons as well as for computational simulations. Moreover, the experimental findings on the extensional rheology of multiscale polysaccharide systems will help in the formulation of biologically relevant complex fluids for the treatment of physiological conditions such as osteoarthritis and dysphagia.