Session Q18: Drops: Complex Fluids

Thinning and pinch-off of viscoelastic particulate suspensions

Dispensing liquid through dripping or spraying requires its breakup into droplets, each of which ultimately involving the pinching of a liquid neck. This situation is, for instance, found in additive manufacturing or during the dispersal of drops when one sneezes or speaks. For a Newtonian fluid, as the liquid neck becomes thinner, its thickness follows a power-law with time until the breakup in a finite-time singularity. However, a small quantity of polymer dissolved in the liquid removes this singularity: the neck stretches into a long, slender filament whose thickness decays exponentially. On the other hand, solid particles suspended in a Newtonian liquid are known to speed up the thinning process. Although these two separate mechanisms have been thoroughly studied, their combination remains widely unexplored. We investigate here the pinch-off of drops of a viscoelastic suspension, i.e., non-Brownian spherical particles dispersed in a dilute polymer solution. Our experiments reveal that particles primarily affect the initial Newtonian regime through a higher effective viscosity. In a second time, the viscoelastic regime remains dominated by the sole polymer with no effect of the particles. However, the interplay between particles and polymer chains affects the transition between the two regimes where the coil-stretch transition of the polymer is strongly affected by the particle content.   

Entanglement attenuates the entrained air film underneath polymeric droplets

Recent studies have revealed that droplets tend to rebound from the surface when the ambient air sufficiently decelerates the droplet, where an interstitial air layer prevents contact. While this air cushioning effect has been studied under Newtonian liquid droplets, the air entrainment mechanism underneath polymeric droplets is lacking in the literature. In this study, we demonstrate that for Weber numbers, We∽Ο(1-10), the spatiotemporal evolution of the air films is either enhanced or attenuated by the viscoelastic properties of the aqueous polymeric droplets. A submicron air layer is visualized during droplet impact of aqueous poly(ethylene oxide) and xanthan gum solutions from the dilute to the concentrated regimes with a high-speed total internal reflection microscopy (TIRM) technique. We observe that the slope of the air film is attenuated in the semi-dilute regime yet enhanced in the dilute and entangled regimes. Additionally, the air dimple inversion induced by the strong capillary wave upon impact is suppressed in the entangled regime for polymeric droplets with poly(ethylene oxide) and xanthan gum additives.   

Drying Colloidal Suspensions: Simple Patterns and Complex Flows

Sessile drops of colloidal suspensions display a diverse range of phenomena when they dry, from the ubiquitous coffee ring to a wide variety and scale of cracks. There are numerous factors that influence the final drop pattern such as surface chemistry, evaporation kinetics, colloidal interactions, as well as particle anisotropy and size. Much of the previous work on this problem has been focused on suspensions where the volume fraction of particles is at most 1%. Here, we present a broad experimental study of drying suspension droplets with volume fractions ranging from 0.1% to 45%. We work with highly monodisperse silica colloids made in-house via the Stöber process and examine both the final pattern morphology and the dynamics of crack formation in the drying droplet. In the limit of high concentration, we see intriguing structures emerging: a single dimple appears near the center of the droplet that then connects to growing radial fractures. Analysis of these features seems to suggest that they result from a transition from a Stokes-dominant flow at lower volume fractions to a "Darcy-like" flow at higher volume fractions.   

Drop impact of colloidal suspensions: effect of particle anisotropy

Dense suspension flows are ubiquitous in many industrial and agricultural processes, and drop impact provides a unique method to study these flows at very high shear rates, above the range easily accessible using conventional rheometry.  These extreme shear rates have been recently shown to lead to the appearance of a wide range of elastic behaviors upon impact, from localized jamming to complete solidification.  Here, we present an experimental study of how anisotropy influences impact and spreading dynamics in a dense suspension.  Using highly monodisperse silica rods, we explore how increasing particle aspect ratio influences impact-generated shear jamming.  Our observations suggest that impacting drops of rod-shaped suspensions show thickening and jamming at lower volume fractions as compared to sphere suspensions, in agreement with rheological measurements.  Furthermore, we observe that the extent of jamming behavior is more pronounced for higher impact velocities and higher particle aspect ratios.   

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent. These properties are utilized in bioprinting technologies for tissue engineering and drop deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving 1) the dispersion relationship for free oscillations, and 2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We illustrate the results for the classical cases of a Kelvin- Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We show how the frequency response of the droplet due to forced oscillation changes with viscoelasticity and how it can potentially be used to measure the rheology.   

Arbitrary Lagrangian-Eulerian simulations of interfacial dynamics between a hydrogel and a fluid

Hydrogels are crosslinked polymer networks swollen with an aqueous solvent, and play central roles in biomicrofluidic devices. In such appli-cations, the gel is often in contact with a flowing fluid, thus setting up a fluid-hydrogel two-phase system. Using a recently proposed model (Y.-N. Young et al., Phys. Rev. Fluids 4, 063601, 2019), we treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian viscous solvent, and develop a finite-element method for computing flows involving a fluid-hydrogel interface. The interface is tracked by using a fixed-mesh arbitrary Lagrangian-Eulerian method that maps the interface to a reference configuration. The interfacial deformation is coupled with the fluid and solid governing equations into a monolithic algorithm us- ing the finite-element library deal.II. The code is validated against available analytical solutions in several non-trivial flow problems: one-dimensional compression of a gel layer by a uniform flow, two-layer shear flow, and the deformation of a Darcy gel particle in a planar extensional flow. In all cases, the numerical solutions are in excellent agreement with the analytical solu- tions. Numerical tests show second-order convergence with respect to mesh refinement, and first-order convergence with respect to time-step refinement.   

Axisymmetric numerical simulations of drop formation in viscoelastic jets

Droplet formation of non-Newtonian fluids is of central importance to numerous industrial applications; these include spray-drying, atomisation, and paints, involving large interfacial deformations and complex spatio-temporal dynamics. We perform axisymmetric simulations of an impulsively-started viscoelastic jet exiting a nozzle and entering a stagnant gas phase using the open-source code Basilisk. This code allows for efficient computations through an adaptively-refined volume-of-fluid technique to capture the interface, and the log-conformation transformation, which provides a stable and accurate solution of the viscoelastic constitutive equation. For the first time, the entire jetting and breakup process of a viscoelastic fluid is simulated, including the flow through the nozzle which results in an initial radial stress distribution that affects the subsequent breakup dynamics. The velocity field and the shear stresses in the nozzle, and the early stages of the jet evolution, are validated against analytical solutions and linear stability predictions, respectively. We explore the effect of shear flow inside the nozzle on the thinning dynamics of the viscoelastic jet via analysis of the spatio-temporal evolution of the polymeric stresses. We also investigate systematically the dependence of the filament thinning rate and its breakup length on the axial momentum of the jet and the fluid relaxation time. Finally, we demonstrate the capacity of Basilisk to resolve the elasto-capillary regime of the breakup process, using mesh adaptivity, as a function of the finite extensibility of the polymeric chains.   

The role of surfactants in stabilizing liquid-liquid interfaces: their effect on interfacial tension and film drainage times

Liquid-liquid separation is important in different emulsion systems, such as oily bilgewater and water in fuel, and is mainly achieved by coalescence. Effective removal of the dispersed droplets requires understanding of the effect of surfactant presence in these emulsions on their stability. In this work, we highlight this using measurements done across a range of surfactant concentrations, viscosity ratios, and velocities. The first factor studied is the interfacial tension (IFT), where dynamic IFT measurements are performed at two length scales: a millimeter scale using pendant drop experiments and a microscale using microfluidic tensiometry, with systems of light and heavy mineral oil containing SPAN80 surfactant. It was found that the rate of IFT decay decreases with increasing viscosity ratio of the outer to the inner phase. The surfactant diffusivity and interfacial adsorption rates are extracted by fitting a surfactant diffusion equation and an equation of state to the IFT data. The second factor studied is the film drainage time between two coalescing water droplets in oil as well as fuel systems, which is found to increase with decreasing timescales to reach equilibrium IFT.    

Open-source finite volume solvers for the simulation of multiphase (n-phase) Newtonian/non-Newtonian fluid flows

We present two newly developed finite volume solvers based on OpenFOAM® suitable for the numerical prediction of n-phase flows involving Newtonian and non-Newtonian fluids. These solvers introduce crucial modifications into the original multiphaseInterFoam solver, provided by OpenFOAM, considerably enhancing its efficiency and, most importantly, its accuracy for flows dominated by surface tension. The non-Newtonian solver is able to account for a wide range of rheologically complex materials which may exhibit yield stress, viscoelastic, or elasto-viscoplastic effects. This is accomplished by incorporating the RheoTool toolbox that offers numerous constitutive equations for modelling fluids with complex rheology. The new solvers are verified for several two- and three-phase benchmark flows, including dam break with an obstacle, a floating lens, a levitating drop, and a bubble rising in an ambient fluid; flows involving Newtonian, viscoplastic, or viscoelastic liquids are considered. Comparisons are performed against analytical solutions and data available in the literature, indicating that our solvers can accurately simulate three-phase flows for simple and complex liquids with significant interfacial tension effects.   

Impact of a human blood drop on jean fabric: effect of the relative humidity and temperature.

After a bloody crime event, crime scene investigators find different evidence. By interpreting these later, they can reconstruct the crime scene. Blood drops are one of the most common crime scene evidence. To develop reliable models for crime scene reconstruction, it is important to understand all the phenomena related to their formation. 

We investigate the impact dynamics of a drop of whole human blood on jean fabric. The effect of relative humidity, temperature, and the space between the fabric and the substrate are considered by carrying out extensive experiments. For this purpose, we used human blood taken from the same donor. Blood drops had the same volume and the same initial temperature 37 °C. The impact dynamic of the blood drops is recorded through a high-speed camera. 

The results show that the final diameter is more important at low space between jean and substrate and is more important at high impact velocities. Also, with the same impact velocity, the increase in relative humidity leads to an increase in the final diameter. We will present our results by discussing its dynamics and the influence of all the parameters. Further, we will give a correction of an existing experimental model by taking the relative humidity and temperature into account.