Non-Newtonian Flow: Interfacial and Bulk Phenomena

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge. Full article

Surface rheology becomes important for droplets with adsorbed proteins, solid particulates, lipids, or polymers, and understanding how surface rheology alters basic droplet processes like coalescence provides insight into the processing of dispersions in industrial and biological systems. In this work, we model the approach of two equal-size deformable droplets under an axisymmetric, biaxial extensional flow in the Stokes flow limit. We explore how the viscosity contrast between the drop and suspending fluid alters the film drainage behaviour when interfacial viscosity is present. For a clean droplet at a fixed capillary number, the drainage time is observed to be independent of the viscosity ratio ($\lambda$) for $\lambda \le \mathcal{O}\left(1\right)$, while the drainage increases linearly with the viscosity ratio for $\lambda \ge \mathcal{O}\left(1\right)$. Surface viscosity increases the drainage time by causing the thin film between the droplets to flatten and widen, and shifts the viscosity ratio at which the aforementioned scaling behaviour changes to larger values. The drainage time is increased more significantly at lower viscosity ratio values than higher values. In the second half of the paper, we examine how surface viscosity alters film drainage when the surfactant can be soluble. We examine the kinetically controlled adsorption/desorption limit. We find that surfactant solubility abolishes surface tension gradients and increases the prominence of surface viscosity effects, the effects of which are quantified for Boussinesq numbers $Bq\sim \mathcal{O}\left(0.1\right)$. Full article

In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations ρ of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate $\dot{\gamma }$ values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed $P\prime$ parameter, equal to ${Re}_{EI}/{Re}^{0.22}$, which collapse into a single distribution over the range of $P\prime$ values considered which range from 0 to about 182. Such characteristics indicate that the $P\prime$ parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for $Re$ additionally gives $P\prime$ values which are dominated by ${Re}_{EI}$ values when the Weissenberg number Wi is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s⁻¹. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with H = 5 mm are generally the highest values measured, with magnitudes that steadily increase with $\dot{\gamma }$. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence. Full article