Nonlinear Dynamics Of Complex Fluids In Fragmentation And Fracture

The fragmentation and breakup of complex fluids are fundamental elements of many industrial and biological processes. The fracture of food gels, atomization of paints, combustion of fuels containing anti-misting agents and application of pharmaceutical and agricultural sprays, as well as involuntary physiological processes such as sneezing, are common examples in which the atomized/fractured material contains synthetic or biological macromolecules that result in viscoelastic fluid characteristics. For many of these processes the effects of varying the rheological properties on the dynamics of fragmentation or fracture are still poorly understood. In this thesis, we investigate some of the underlying complexities associated with varying the rheology of such materials in both shear and elongation. The complex nonlinear rheology of these complex fluids under representative conditions of large strain and deformation rate is difficult to quantify experimentally and is a known challenge for existing constitutive models. The contribution of this thesis is therefore to develop and exploit several new experimental tools that enable precise rheological measurements under appropriate test conditions. A better experimental understanding of the dynamics of fragmentation/fracture in complex fluids will also help guide the development of new theoretical models that can quantitatively predict the mechanical response of complex fluids in such flows. Two distinct classes of model fluids/gels are studied in this thesis. First, a series of model viscoelastic solutions composed of a flexible homopolymer, poly(ethylene oxide) or PEO, dissolved in a water/glycerol mixture. These dilute solutions are known to behave very similarly to their Newtonian solvent in shearing deformations but exhibit markedly different extensional rheological properties due to the onset of a coil-stretch transition in the solvated microstructure at high elongation rates. Secondly we also consider a family of biopolymer networks: acid-induced casein gels. These canonical protein gels display a multiscale microstructure that is responsible for their gel-like viscoelastic properties. Upon external deformation, these soft viscoelastic solids exhibit a generic power-law rheological response followed by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. We study the dynamics of fragmentation for the dilute PEO solutions in different canonical flows: air-assisted atomization, drop impact on a small target, jet impact atomization and rotary spraying. We also study the fracture of the casein protein gels under conditions of both constant applied stress and constant applied shear rate. Through quantitative study of these high strain and high deformation rate phenomena, we reach several conclusions about how the rheological properties of these materials can affect their mechanical behavior in fragmentation/fracture. First, for dilute viscoelastic solutions, the breakup and atomization of these fluids is markedly different than the analogous processes in a simple Newtonian fluid. The average droplet diameter shows a monotonic increase with added viscoelasticity, which is precisely monitored by accurate measurements of elongational relaxation times through a novel characterization method we have developed; Rayleigh Ohnesorge Jet Elongational Rheometry (ROJER). Based on our measurements of the material relaxation time scale a new theoretical model for the evolution in the average droplet diameter is developed for viscoelastic sprays. Second, the size distributions measured in each viscoelastic fragmentation process show a systematic broadening from the Newtonian solvent. In each case the droplet sizes are well described by Gamma distributions that correspond to an underlying fragmentation/coalescence scenario. We show that this broadening results from the pronounced change in the corrugated shape of viscoelastic ligaments as they separate from the liquid core. These corrugations saturate in amplitude and the measured distributions for viscoelastic liquids in each process are given by a universal probability density function, corresponding to a Gamma distribution with nmin = 4. The breadth of this size distribution for viscoelastic filaments is shown to be constrained by a geometrical limit, which can not be exceeded in ligament-mediated fragmentation phenomena. Third, in the fracture of the model acid-induced protein gels, we show that the fractal network of the underlying microstructure leads to a very broad power-law behavior in their linear viscoelastic response that can be precisely modeled by a simple model based on fractional calculus. We show that specific geometric properties of the microstructure set the value of the parameters that are used in the fractional model. The nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' that enables quantitative prediction of the gel mechanical response up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation - built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response - we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress and strain for failure of the gel, and show how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels across a range of different deformation histories. Results from this work are of relevance to many processes that involve breakup and rupture of complex fluids such as failure of viscoelastic gels, emulsification, spray painting and even biological processes such as pathogen transfer resulting from violent expiration. By investigating the linear and nonlinear behavior of two distinct classes of soft matter that lie on two ends of the viscoelasticity spectrum, one close to Newtonian liquids and one close to elastic solids, we provide key physical insights that can be generalized to broad classes of different complex fluids that undergo fracture and fragmentation processes.