On the rheology of particle suspensions in viscoelastic fluids

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here, we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕ_alumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τ_min). Increasing ϕ_alumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τ_min. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕ_PVP = 0.005-0.050) to suspensions with constant ϕ_alumina = 0.550. DST was observed in all cases and increasing ϕ_PVP increased the viscosity and yield stress. Interestingly, increasing ϕ_PVP also increased τ_min. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τ_min.

Experimental and theoretical studies of cross-stream migration of non-spherical particles in a quadratic flow of a viscoelastic fluid

We experimentally investigate the cross-stream migration of spherical, prolate, and oblate particles in a circular tube flow of a weakly viscoelastic fluid (De = O(10^-2)) with negligible inertia (Re ≈ 0). From our previous theoretical studies, we developed mathematical models based on a second order fluid (i.e., retarded expansion for De ≪ 1) to characterize the migration trajectory of the particles in the absence of wall effects. The theory shows that the particle migration speed is proportional to the length the particle spans in the shear gradient direction (L_sg), and furthermore quantifies how particle shape alters the migration timescale. For particles with identical volume, spherical particles show the fastest migration speed among all the particles. The distinctive orientation behavior of prolate and oblate spheroids leads to a faster migration speed for an oblate particle compared to a prolate particle of the same aspect ratio. In this work, we verify our theory with microfluidic flow experiments using a model suspension of polystyrene (PS) micro-particles in a density-matched polyvinylpyrrolidone (PVP) solution (a Boger fluid). The experimental results show good qualitative and quantitative agreement with the theoretically predicted particle migration speed, indicating that the theory is able to provide reasonable predictions for real microfluidic systems.

Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells

We developed a biomechanics-informed online learning framework to learn the dynamics with ground truth generated with multiscale modeling simulation. It was built on Summit-like supercomputers, which were also used to benchmark and validate our framework on one physiologically significant modeling of deformable biological cells. We generalized the century-old equation of Jeffery orbits to a new equation of motion with additional parameters to account for the flow conditions and the cell deformability. Using simulation data at particle-based resolutions for flowing cells and the learned parameters from our framework, we validated the new equation by the motions, mostly rotations, of a human platelet in shear blood flow at various shear stresses and platelet deformability. Our online framework, which surrogates redundant computations in the conventional multiscale modeling by solutions of our learned equation, accelerates the conventional modeling by three orders of magnitude without visible loss of accuracy.

Bacterial streamers as colloidal systems: Five grand challenges

Bacteria can thrive in biofilms, which are intricately organized communities with cells encased in a self-secreted matrix of extracellular polymeric substances (EPS). Imposed hydrodynamic stresses can transform this active colloidal dispersion of bacteria and EPS into slender thread-like entities called streamers. In this perspective article, the reader is introduced to the world of such deformable 'bacteria-EPS' composites that are a subclass of the generic flow-induced colloidal structures. While bacterial streamers have been shown to form in a variety of hydrodynamic conditions (turbulent and creeping flows), its abiotic analogues have only been demonstrated in low Reynolds number (Re < 1) particle-laden polymeric flows. Streamers are relevant to a variety of situations ranging from natural formations in caves and river beds to clogging of biomedical devices and filtration membranes. A critical review of the relevant biophysical aspects of streamer formation phenomena and unique attributes of its material behavior are distilled to unveil five grand scientific challenges. The coupling between colloidal hydrodynamics, device geometry and streamer formation are highlighted.

Dynamics and extensional rheology of polymer-surfactant association complexes

Understanding and characterizing the influence of polymers and surfactants on rheology, application, and processing is critical for designing complex fluid formulations for enhanced oil recovery, pharmaceuticals, cosmetics, foods, inks, agricultural sprays, and coatings. It is well-established that the addition of anionic surfactant like sodium dodecyl sulfate (SDS) to an aqueous solution of an oppositely-charged or uncharged polymer like poly(ethylene oxide) (PEO) can result in the formation of the polymer-surfactant association complexes (P0S-ACs) and a non-monotonic concentration-dependent variation in zero shear viscosity. However, the extensional rheology response of polymer-surfactant mixtures remains relatively poorly understood, partially due to characterization challenges that arise for low viscosity, low elasticity fluids, even though the response to strong extensional flows impacts drop formation and many processing operations. In this article, we use the recently developed dripping-onto-substrate (DoS) rheometry protocols to characterize the pinching dynamics and extensional rheology response of aqueous P0S- solutions formulated with PEO (P0) and SDS (S-), respectively. We find the PEO-SDS mixtures display a significantly weaker concentration-dependent variation in the extensional relaxation time, filament lifespan, and extensional viscosity values than anticipated by the measured shear viscosity.

The rheologically-complex fluid beauty of nail lacquer formulations

Nail lacquer formulations are multi-ingredient complex fluids with additives that affect color, smell, texture, evaporation rate, viscosity, stability, leveling behavior, consumer's sensory experience, and dried coating's decorative and wear performance. Optimizing and characterizing the formulation rheology is critical for achieving longer shelf-life, better control over the nail painting process and adhesion, continuous manufacturing of large product volumes, and increasing overall consumer satisfaction. Dispensing, bottle filling, brush application, and dripping, as well as perceived tackiness of nail polishes, all involve capillarity-driven pinching flows associated with strong extensional deformation fields. However, a significant lack of characterization of pinching dynamics and extensional rheology response of multicomponent formulations, especially particle suspensions in viscoelastic solutions, motivates this study. Here, we characterize the shear rheology response of twelve commercial nail lacquer formulations using torsional rheometry and characterize pinching dynamics and extensional rheology response using dripping-onto-substrate (DoS) rheometry protocols we developed. We visualize and analyze brush loading, nail coating, dripping from brush, sagging, and lacquer application on a nail to outline the challenges posed by free-surface flows and non-Newtonian rheology. We find that the radius evolution over time obtained using DoS rheometry displays power law exponents distinct from those exhibited in shear thinning. Both shear and extensional viscosity decrease with deformation rate. However, the extensional viscosity appears to be rate-independent at the highest rates and displays nearly an order of magnitude larger values than the high shear rate viscosity. We envision that the findings and protocols described here will help and motivate industrial scientists to design better multicomponent formulations through a better characterization and understanding of the influence of ingredients like particles and polymers on rheology, processing, and applications.

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids

The prediction of the viscosity of suspensions is of fundamental importance in several fields. Most of the available studies have been focused on particles with simple shapes, for example, spheres or spheroids. In this work, we study the viscosity of a dilute suspension of fractal-shape aggregates suspended in a shear-thinning fluid by direct numerical simulations. The suspending fluid is modeled by the power-law constitutive equation. For each morphology, a map of particle angular velocities is obtained by solving the governing equations for several particle orientations. The map is used to integrate the kinematic equation for the orientation vectors and reconstruct the aggregate orientational dynamics. The intrinsic viscosity is computed by a homogenization procedure along the particle orbits. In agreement with previous results on Newtonian suspensions, the intrinsic viscosity, averaged over different initial orientations and aggregate morphologies characterized by the same fractal parameters, decreases by increasing the fractal dimension, that is, from rod-like to spherical-like aggregates. Shear-thinning further reduces the intrinsic viscosity showing a linear dependence with the flow index in the investigated range. The intrinsic viscosity can be properly scaled with respect to the number of primary particles and the flow index to obtain a single curve as a function of the fractal dimension.