Session A14: Non-Newtonian Flows: Rheology

Viscosity measurements of glycerol reveal the misalignment in parallel-plate rheometers

We consider the viscosity measurement of pure glycerol in a parallel-plate rheometer over time. Due to the hygroscopic nature of glycerol, it spontaneously absorbs water vapor from the atmosphere through the outer edge of the rheometer, leading to a transient decrease in the measured viscosity. A combination of diffusion and advection drive the transport of the dissolved water through the rheometer, resulting in regions of less-viscous fluid. The measured viscosity then represents an integration of the shear stresses on the plate device. We find that the rate of decrease of the measured viscosity is a complex function of the gap thickness and angular velocity, as well as the vapor flux at the outer edge. The decrease in viscosity is a nonlinear function of the angular velocity. For small angular velocities the dynamics are diffusive, and the water only slowly proceeds inward from the outer edge of the glycerol, resulting in high concentrations in the outermost region. Because this low viscosity fluid is confined to a relatively small region, the decrease in measured viscosity is slow for this case. For cases with modest angular velocities, the recirculating advection acts to pull some of the water inwards from the outer boundary, steepening the gradient of concentration at the outer edge and increasing the flux of water vapor into the system, leading to a faster decrease in viscosity up to a point. For very fast angular velocities, much of the water is pulled all the way to the center of the rheometer, where the effect on the measured viscosity is relatively less (since the majority of the torque develops at the outer edge). Nevertheless, we see a deviation from these behaviors for very small gap heights (which should be purely diffusive), in which the measured viscosity drops much faster than expected. We propose that this is due to plate misalignment of the rheometer, and we use computational fluid dynamics simulations to support this hypothesis.   

Multi-fidelity modeling to predict the rheological properties of fiber suspensions

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications like biofuel production. The 3D numerical simulations of the suspension of fibers are often computationally expensive and time-consuming. Machine learning methods such as neural networks can simplify the prediction of rheological behavior; however, they require a relatively large training data set. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified physical equations, can lead to optimized predictions. Here, we focus on a neural network with two levels of fidelity, i.e., high and low fidelity networks. To produce high-fidelity data, we perform direct numerical simulations to model the fibers as one-dimensional inextensible slender bodies that obey the Euler- Bernoulli beam equation. The Navier-Stokes equations govern the suspended fluid, and an immersed boundary method is used to couple the fluid and solid motion. The low-fidelity data is produced by using constitutive equations. Noticeable improvements have been observed in the accuracy of predicting the rheological behavior when a multi-fidelity network is used compared to the single-fidelity network.    

Investigating the applicability of physics-based machine learning algorithms to meta-modeling of complex fluids

We briefly present three types of physics-based machine learning frameworks, to model, describe, and predict the behavior of complex fluids. In the area of data-driven constitutive meta-modeling, we present Rheology-Informed Neural Networks (RhINNs) and Multi-Fidelity Neural Network (MFNN), in which the physical intuition is being included explicitly and implicitly, respectively. We used RhINNs as an alternative solver for systems of Ordinary Differential Equations (ODEs) in a direct approach, and to learn the model/material parameters using a series of limited experimental data in an inverse platform. MFNN is also used as a data-driven constitutive meta-modeling of complex fluids and compares its rheological predictions with those of a simple Deep NN and experimental measurements. Generation of the low-fidelity data points is done using the underlying rheological constitutive models, while the high-fidelity network is trained on a limited number of experimentally measured data. We will discuss the MFNN predictions of a set of flow curves for a multi-component colloidal and wormlike micelle solution with respect to temperature, salinity, and aging of the mixture. With regards to complex fluid flow modeling, non-Newtonian physics-informed neural network (nn-PINNs) is introduced for solving systems of coupled PDEs. nn-PINNs are then employed to solve the constitutive models in conjunction with conservation of momentum while avoiding the mesh generation step, followed by validating for a number of different complex fluids with various constitutive models. These include a range of Generalized Newtonian Fluids empirical constitutive models and some phenomenological models with memory effects and thixotropic timescales, and for several flow protocols. We finally discuss the outlook and opportunities, and more importantly the limitations of science-based ML platforms in rheology and non-Newtonian fluid mechanics.   

Lagrangian and Eulerian signatures of inertio-elastic instabilities and turbulence in polymer jets

We report on the spatiotemporal evolution of flow structures in a jet of dilute polymer solution entering a quiescent bath of Newtonian fluid. High-speed digital Schlieren imaging and laser Doppler velocimetry are used to study the Lagrangian and Eulerian signatures of the onset of inertio-elastic instabilities and the subsequent transition to a turbulent flow state. Applying Dynamic Mode Decomposition to the Schlieren images reveals the dominant inertio-elastic instability modes and their dependence on elasticity number and polymer extensibility. The advective growth of these inertio-elastic modes results in the jet transitioning to a state of elasto-inertial turbulence (EIT). Velocity measurements at fixed Eulerian locations along the center line of the jet show that EIT is characterized by a dramatic decrease in turbulence intensity with a distinctly different power-law spectrum as compared to a turbulent Newtonian jet.    

Torsional fracture of viscoelastic liquid bridges

Short liquid bridges are stable under the action of surface ten- sion. In applications like electronic packaging, food engineering, and additive manufacturing, this poses challenges to the clean and fast dispensing of viscoelastic fluids. Here, we investigate how viscoelastic liquid bridges can be destabilized by torsion. By combining high-speed imaging and numerical simulation, we show that concave surfaces of liquid bridges can localize shear, in turn localizing normal stresses and making the surface more con- cave. Such positive feedback creates an indent, which propagates toward the center and leads to breakup of the liquid bridge. The indent formation mechanism closely resembles edge fracture, an often undesired viscoelastic flow instability characterized by the sudden indentation of the fluid's free surface when the fluid is subjected to shear. By applying torsion, even short, capillary sta- ble liquid bridges can be broken in the order of 1 s. This may lead to the development of dispensing protocols that reduce substrate contamination by the satellite droplets and long capillary tails formed by capillary retraction, which is the current mainstream industrial method for destabilizing viscoelastic liquid bridges.   

Coronavirus Pleomorphism and Rotational Diffusivity

The coronavirus is always idealized as a spherical capsid with radially protruding spikes. However, histologically, in the tissues of infected patients, capsids in cross section are elliptical, and only sometimes spherical. This capsid ellipticity implies that coronaviruses are oblate or prolate or both. We call this diversity of shapes, pleomorphism. Recently, the rotational diffusivity of the coronavirus in suspension was calculated, from first principles, using general rigid bead-rod theory [M.A. Kanso, Phys Fluids, 32, 113101 (2020)]. We did so by beading the capsid, and then also by replacing each of its bulbous spikes with a single bead. We use energy minimization for the spreading of the spikes, charged identically, over the oblate or prolate capsids. We use general rigid bead-rod theory to explore the role of coronavirus ellipticity on its rotational diffusivity, the transport property around which its cell attachment revolves. We learn that coronavirus ellipticity decreases its rotational diffusivity for both oblate and prolate ellipsoids. 

Experiments in non-Newtonian fluids: Saffman-Taylor instability

Viscous fingering instability can be controlled by adding polymers to either displacing or displaced fluid as polymers alter the fluid viscosity, the main cause of viscous fingering. Most of the polymeric solutions exhibit shear-rate dependent viscosity and elasticity, simultaneously. The fluid rheology can affect the growth of fingers due to the non-uniform viscosity distribution and the presence of normal stresses. To investigate the role of rheological properties on the instability, experiments are performed using Hele-Shaw cell when one of the fluids is polymeric fluid. The aqueous solutions of polyethylene oxide (PEO) of different concentrations and molecular weights are used. The evolution of the fingers shows that displacement of PEO solutions of high concentration or high molecular weight leads to more complex and fractal-like patterns involving tip-splitting and side-branching mechanisms. The displacement when the displaced fluid is PEO solution shows more intensified patterns than the displacing PEO solution for similar viscosity contrast and rheological properties. It is observed that the shear-thinning behavior always strengthens the shielding behavior whereas the fluid elasticity always leads to tip-spitting, irrespective of the flow arrangement.     

Spreading of complex fluids with a soft blade.

The spreading of complex fluids is a part of our everyday life: we spread jam, cosmetics, paint, etc. It is also central in industry, mostly to make paper or protective coatings. Here, we consider the spreading of polymer solutions with an elastic blade that is soft enough to deform during the spreading (similarly to a brush, a finger or rubber squeegees). We compare fluids with identical shear-thinning rheology, but which generates – or not – normal stresses when flowing. This allows us to disentangle the effects of viscosity, shear-thinning and normal stresses on the spreading process. We thus reveal two counter-intuitive results: first, shear-thinning does not significantly modify the film thickness compared with an equivalent Newtonian fluid, but increases the force that has to be applied to spread the liquid. In addition, the geometry of the experiment can make normal stresses negligible compared with the viscous forces even if they are dominant over the shear stress. We combine experiments, a numerical model and a scaling analysis to evidence and explain these observations.   

Experimental characterization of elasto-inertial turbulence

The addition of polymers in flows in pipes has been shown to delay the subcritical transition of Newtonian type turbulence (NTT) to higher Reynolds numbers (Re). Increasing the polymer concentration within the dilute regime causes a continuous transition to a novel state of turbulence dubbed Elasto-inertial turbulence (EIT). Recent studies have shown that by controlling the parameters of the flow, one can observe the salient features of EIT at Re far lower than that of classical transition to NTT, showing that the transition can happen even at Re of the order of 1. In the present study we show that the structural composition of EIT persists from Reynolds numbers of order one to the  maximum drag reduction limit. In particular we show that energy spectra across the entire EIT regime collapse and are distinct from the Kolmogrov scaling associated with NTT. We explore further the existence of the EIT flow structures at much higher Re far away from the transition regime, deeper into the Maximum Drag Reduction (MDR) range.