Rheological effects on purely-elastic flow asymmetries in the cross-slot geometry.

Viscoelastic flows in the cross-slot geometry can undergo a transition from a steady symmetric to a steady asymmetric flow state, ostensibly due to purely-elastic effects arising beyond a critical flow rate, or Weissenberg number Wi. However, some reports suggest that shear thinning of the fluid's viscosity may also play an important role in this transition. We employ a series of polymer solutions of varying rheological properties to investigate in detail how the interplay between fluid elasticity and shear thinning affects the onset and development of asymmetric flows in the cross-slot. Flow velocimetry is performed on each of the polymer solutions, and is used to assess the degree of flow asymmetry I in the cross-slot as a function of both Wi and a dimensionless parameter S quantifying the flow-rate-dependent extent of shear thinning. Typically, the flow field breaks symmetry as Wi is increased beyond a critical value, but the magnitude of I is found to also be dependent on S. For a few specific polymer solutions, the flow field recovers symmetry above a second, higher critical Wi as S becomes small. The experimental results are summarized in a flow state diagram in Wi-S space, showing the relationship between flow asymmetry and fluid rheology. Finally, to gain a deeper understanding of the effects of shear thinning, numerical simulations are performed using the linear simplified Phan-Thien-Tanner model. We demonstrate that the degree of both shear thinning and elasticity of the fluid, and their interplay, are important factors controlling elastic instabilities in the cross-slot geometry.

Edge fracture of thixotropic elastoviscoplastic liquid bridges.

It has recently been shown that torsion can break liquid bridges of viscoelastic fluids, with potential application to their clean and rapid dispensing. However, many commonplace fluids (paints, adhesives, pastes, and foodstuffs like chocolate) have more complex thixotropic elastoviscoplastic (TEVP) properties that depend on the imposed stress and the timescale of deformation. Using a commercial thermal paste, we show that liquid bridges of TEVP fluids can also be broken by torsion, demonstrating the applicability of the technique for improved dispensing of real industrial fluids. The liquid bridge breaking mechanism is an elastic instability known as "edge fracture." Dimensional analysis predicts that the effects of thixotropy and plasticity can be neglected during edge fracture. Simulation using a nonlinear, phenomenological TEVP constitutive model confirms such a prediction. Our work yields new insight into the free-surface flows of TEVP fluids, which may be important to processes such as electronic packaging, additive manufacturing, and food engineering.

Alignment of Colloidal Rods in Crowded Environments.

Understanding the hydrodynamic alignment of colloidal rods in polymer solutions is pivotal for manufacturing structurally ordered materials. How polymer crowding influences the flow-induced alignment of suspended colloidal rods remains unclear when rods and polymers share similar length scales. We tackle this problem by analyzing the alignment of colloidal rods suspended in crowded polymer solutions and comparing that to the case where crowding is provided by additional colloidal rods in a pure solvent. We find that the polymer dynamics govern the onset of shear-induced alignment of colloidal rods suspended in polymer solutions, and the control parameter for the alignment of rods is the Weissenberg number, quantifying the elastic response of the polymer to an imposed flow. Moreover, we show that the increasing colloidal alignment with the shear rate follows a universal trend that is independent of the surrounding crowding environment. Our results indicate that colloidal rod alignment in polymer solutions can be predicted on the basis of the critical shear rate at which polymer coils are deformed by the flow, aiding the synthesis and design of anisotropic materials.

Torsional instability of constant viscosity elastic liquid bridges.

By experiment and simulation, we report that viscoelastic liquid bridges made of constant viscosity elastic liquids, a.k.a. Boger fluids, can be effectively destabilized by torsion. Under torsion, the deformation of the liquid bridge depends on the competition between elastocapillarity and torsion-induced normal stress effects. When the elastocapillary effect dominates, the liquid bridge undergoes elastocapillary instability and thins into a cylindrical thread, whose length increases and whose radius decays exponentially over time. When the torsion-induced normal stress effect dominates, the liquid bridge deforms in a way similar to edge fracture, a flow instability characterized by the sudden indentation of the fluid's free surface when a viscoelastic fluid is sheared at above a critical deformation rate. The vertical component of the normal stress causes the upper and lower portions of the liquid bridge to approach each other, and the radial component of the normal stress results in the liquid bridge thinning more quickly than under elastocapillarity. Whether such quick thinning continues until the bridge breaks depends on both the liquid bridge configuration and the level of torsion applied.

Bifurcations in flows of complex fluids around microfluidic cylinders.

Flow around a cylinder is a classical problem in fluid dynamics and also one of the benchmarks for testing viscoelastic flows. The problem is of wide relevance to understanding many microscale industrial and biological processes and applications, such as porous media and mucociliary flows. In recent years, we have developed model microfluidic geometries consisting of very slender cylinders fabricated in glass by selective laser-induced etching. The cylinder radius is small compared with the channel width, which allows the effects of the stagnation points in the flow to dominate over the effects of squeezing between the cylinder and the channel walls. Furthermore, the cylinders are contained in high aspect ratio microchannels that render the flow field approximately two-dimensional (2D) and therefore conveniently permit comparison between experiments and 2D numerical simulations. A number of different viscoelastic fluids including wormlike micellar and various polymer solutions have been tested in our devices. Of particular interest to us has been the occurrence of a striking, steady-in-time, flow asymmetry that occurs for certain non-Newtonian fluids when the dimensionless Weissenberg number (quantifying the importance of elastic over viscous forces in the flow) increases above a critical value. In this perspective review, we present a summary of our key findings related to this novel flow instability and present our current understanding of the mechanism for its onset and growth. We believe that the same fundamental mechanism may also underlie some important non-Newtonian phenomena observed in viscoelastic flows around particles, drops, and bubbles, or through geometries composed of multiple bifurcation points such as cylinder arrays and other porous media. Knowledge of the instability we discuss will be important to consider in the design of optimally functional lab-on-a-chip devices in which viscoelastic fluids are to be used.

Origin of the Sharkskin Instability: Nonlinear Dynamics.

The appearance of surface distortions on polymer melt extrudates, often referred to as sharkskin instability, is a long-standing problem. We report results of a simple physical model, which link the inception of surface defects with intense stretch of polymer chains and subsequent recoil at the region where the melt detaches from the solid wall of the die. The transition from smooth to wavy extrudate is attributed to a Hopf bifurcation, followed by a sequence of period doubling bifurcations, which eventually lead to elastic turbulence under creeping flow. The predicted flow profiles exhibit all the characteristics of the experimentally observed surface defects during polymer melt extrusion.

Structure-property relationship of a soft colloidal glass in simple and mixed flows.

HYPOTHESIS: Under specific conditions, rod-like cellulose nanocrystals (CNC) can assemble into structurally ordered soft glasses (SGs) with anisotropy that can be controlled by applying shear. However, to achieve full structural control of SGs in real industrial processes, their response to mixed shear and extensional kinematics needs to be determined. We hypothesise that by knowing the shear rheology of the CNC-based soft glass and adopting a suitable constitutive model, it is possible to predict the structure-property relationship of the SG under mixed flows. EXPERIMENTS: We use an aqueous suspension with 2 wt% CNC at 25 mM NaCl to form a structurally ordered SG composed of a CNC network containing nematic domains. We combine rheometry and microfluidic experiments with numerical simulations to study the flow properties of the SG in shear, extension, and mixed flow conditions. Extensional flow is investigated in the Optimised Shape Cross-slot Extensional Rheometer (OSCER), where the SG is exposed to shear-free planar elongation. Mixed flow kinematics are investigated in a benchmark microfluidic cylinder device (MCD) where the SG flows past a confined cylinder in a microchannel. FINDINGS: The SG in the MCD displays a velocity overshoot (negative wake) and a pronounced CNC alignment downstream of the cylinder. Simulations using the thixotropic elasto-visco-plastic (TEVP) model yield near quantitative agreement of the velocity profiles in simple and mixed flows and capture the structural fingerprint of the material. Our results provide a comprehensive link between the structural behaviour of a CNC-based SG and its mechanistic properties, laying foundations for the development of functional, built-to-order soft materials.

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Description of the Model and Rheological Predictions.

This work focuses on the advanced modeling of the thixotropic nature of blood, coupled with an elasto-visco-plastic formulation by invoking a consistent and validated model for TEVP materials. The proposed model has been verified for the adequate description of the rheological behavior of suspensions, introducing a scalar variable that describes dynamically the level of internal microstructure of rouleaux at any instance, capturing accurately the aggregation and disaggregation mechanisms of the RBCs. Also, a non-linear fitting is adopted for the definition of the model's parameters on limited available experimental data of steady and transient rheometric flows of blood samples. We present the predictability of the new model in various steady and transient rheometric flows, including startup shear, rectangular shear steps, shear cessation, triangular shear steps and LAOS tests. Our model provides predictions for the elasto-thixotropic mechanism in startup shear flows, demonstrating a non-monotonic relationship of the thixotropic index on the shear-rate. The intermittent shear step test reveals the dynamics of the structural reconstruction, which in turn is associated with the aggregation process. Moreover, our model offers robust predictions for less examined tests such as uniaxial elongation, in which normal stress was found to have considerable contribution. Apart from the integrated modeling of blood rheological complexity, our implementation is adequate for multi-dimensional simulations due to its tensorial formalism accomplished with a single time scale for the thixotropic effects, resulting in a low computational cost compared to other TEVP models.

Transition between solid and liquid state of yield-stress fluids under purely extensional deformations.

We report experimental microfluidic measurements and theoretical modeling of elastoviscoplastic materials under steady, planar elongation. Employing a theory that allows the solid state to deform, we predict the yielding and flow dynamics of such complex materials in pure extensional flows. We find a significant deviation of the ratio of the elongational to the shear yield stress from the standard value predicted by ideal viscoplastic theory, which is attributed to the normal stresses that develop in the solid state prior to yielding. Our results show that the yield strain of the material governs the transition dynamics from the solid state to the liquid state. Finally, given the difficulties of quantifying the stress field in such materials under elongational flow conditions, we identify a simple scaling law that enables the determination of the elongational yield stress from experimentally measured velocity fields.