Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session P07: Non-Newtonian Flows: General |
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Chair: Gwynn Elfring, Univeristy of British Columbia Room: North 122 C |
Monday, November 22, 2021 4:05PM - 4:18PM |
P07.00001: Flow rate-pressure drop relation for viscoelastic fluids in narrow geometries Evgeniy Boyko, Howard A Stone Pressure-driven flows of viscoelastic polymer solutions in narrow non-uniform geometries are ubiquitous in nature and various applications. For such flows, one of the key interests is understanding the relationship between the flow rate and pressure drop, which, to date, is studied primarily using numerical simulations. Here, we provide a theoretical framework for calculating the flow rate-pressure drop relation for viscoelastic flows in arbitrarily shaped, narrow channels. We apply lubrication theory and derive analytical expressions for the flow rate-pressure drop relation for the Oldroyd-B model in the weakly viscoelastic limit. Furthermore, we apply the Lorentz reciprocal theorem and show that the flow rate-pressure drop at higher orders can be determined only using the velocity and stress fields at the previous orders. We compare our analytical results with numerical simulations and find excellent agreement. Given the inability of numerical simulations using the Oldroyd-B and FENE-CR models to predict the experimental flow rate-pressure drop behavior of viscoelastic fluids in some cases, we believe that our approach may be important in providing insight into the cause of this disagreement and in resolving it by accounting for additional microscopic features of polymer flows. |
Monday, November 22, 2021 4:18PM - 4:31PM Not Participating |
P07.00002: Numerical investigation of acoustic streaming flows induced by an oscillating cylinder in non-Newtonian fluids Md Rifat Hassan, Jie Zhang, Beijia Yao, Joontaek Park, Cheng Wang Steady streaming is the time averaged flow of an oscillating flow, which can be induced by vibrating bodies, such as an acoustic bubble or an oscillating solid body. Microscale, steady streaming flows have demonstrated broad use in mixing enhancement, cell sorting, cell trapping and gene transfer. Non-Newtonian biological fluids are often used in lab-on-a-chip systems; however, the steady streaming in these fluids is less studied and understood. This work presents numerical investigation of microscale steady streaming induced by an oscillating cylinder in non-Newtonian fluids, including viscoelastic fluids (FENE-P model), and power-Law fluids in the small amplitude regime. The numerical results show that the edge to vortex center distances of Newtonian, FENE-P and power law fluids are very similar to each other for a wide range of oscillating frequency, while the flow patterns show subtle differences due to the non-Newtonian nature. |
Monday, November 22, 2021 4:31PM - 4:44PM |
P07.00003: Intrusion of yield-stress fluid beneath an elastic membrane Torstein Sæter, Blandine F. P. Feneuil, Olivier Galland, Andreas Carlson We investigate a yield-stress fluid intrusion beneath an elastic membrane by deploying experiments and in numerical simulations. Our results show that the dynamics of the intrusion is clearly influenced by the yield-stress property of the fluid, as both the time evolution of the height and radius of the rising fluid blister follow different power-laws in the elastic regime, as a function of the fluid's yield-stress threshold. A higher yield-stress leads to bumps with steeper shapes and slower radial expansion, consistent with conservation of mass. As expected, for smaller yield-stress the dynamics become closer to when the intruding liquid is Newtonian. In the elastic regime, the inner region of the blister takes the same quasi-static shape independent of the fluid's yield-stress threshold. Thus, we expect the changing power-laws to be controlled by local effects at the propagating front, steered by the non-Newtonian properties. The findings from studying the viscoplastic intrusion can provide valuable new insights in the geoscientifical context of magmatic intrusions into the earth's crust and land formation. |
Monday, November 22, 2021 4:44PM - 4:57PM |
P07.00004: Transition to the viscoelastic regime in the thinning of polymer solutions Sreeram Rajesh, Virgile Thiévenaz, Alban Sauret When a dilute polymer solution is extruded through a nozzle, the initial thinning of the liquid shows a Newtonian behavior, where the time evolution of the neck diameter can be fitted with a power-law. The presence of polymer, however, inhibits the singularity expected in Newtonian fluids and the fluid transitions to a viscoelastic regime, where a long and slender cylindrical filament is formed and thins exponentially. The time scale of thinning of the filament is associated with the relaxation time of the dilute polymer. The present study focuses on the intermediate regime where the fluid undergoes a dynamic transition from the Newtonian to the viscoelastic behavior. The short time scales associated with the transitional regime require high-resolution imaging at large frame rates. We characterize here the influence of the polymer concentration, solvent viscosity and molecular weight on the length scale and timescale associated with the transition. We report a self-similar behavior for the instantaneous strain rate at the neck, where the critical strain rate is the relevant scale that allows us to rescale the experimental data. Such an approach is a useful tool to predict the thinning and drop formation of a non-Newtonian liquid, from the initial Newtonian thinning to the viscoelastic behavior. |
Monday, November 22, 2021 4:57PM - 5:10PM |
P07.00005: Modeling and Simulation of Transient Poiseuille Blood Flow in Microfluidic Tubes Soham Jariwala, Norman J Wagner, Antony N Beris Last year we discussed the development of an efficient methodology for numerical simulation of viscoelastic and thixotropic flows in tubular geometries using a pseudo-spectral method based on Chebyshev orthogonal polynomial approximations. This method has been validated showing that it produces results that follow with high fidelity the analytical solution of Newtonian and upper-convected Maxwell fluids in oscillatory Poiseuille flows. |
Monday, November 22, 2021 5:10PM - 5:23PM |
P07.00006: Gravity-driven spreading of a solidifying melt Michela Geri Gravity-driven flows are ubiquitous in both nature and engineering applications and hence they have been widely studied both theoretically and experimentally. In many instances though, viscous spreading is coupled with cooling and solidification. Examples can be found in nature, e.g., lava flows and polythermal ice sheet dynamics, and in industrial applications, as in continuous casting. Several theoretical and a few experimental works have tried to study this phenomenon; however, in most cases the tested fluids do not capture the complex non-linear rheology that is expected in natural and industrial settings. In this talk we explore gravity-driven flows of a solidifying model melt composed of a paraffin-oil solution. Above the liquidus temperature this model melt is a simple Newtonian fluid, while below, it shows a continuous crystallization process that transforms the fluid to a visco-plastic suspension of crystals. We focus on fixed-volume release experiments over a flat surface and explore the effect of basal solidification on the flow dynamics. We record the spatial and temporal evolution of the advancing liquid and solid fronts and compare our results with a theoretical model of the underlying transport phenomena coupled with the rheology of the melt. |
Monday, November 22, 2021 5:23PM - 5:36PM |
P07.00007: The shape of yield stress filaments on a surface Maziyar Jalaal, Jesse van der Kolk A liquid filament spreads on a surface until it reaches equilibrium. In the case of yield stress (a.k.a. viscoplastic) fluids, the dynamics and the final static shape are determined by the surface tension, gravity, solid surface properties, and the liquid's rheological properties. We experimentally show how the yield stress dictates the final shape of gently deposited yield stress filaments on a surface. We also present a counterpart theory based on viscoplastic lubrication theory and compare the results with the experiments. |
Monday, November 22, 2021 5:36PM - 5:49PM |
P07.00008: Capillary rise of yield-stress fluids Neil J Balmforth The rise of a viscous fluid between two plates driven by capillary effects is a classical problem in fluid mechanics, giving rise to Jurin's law for the elevation attained. In this talk I will reconsider this problem for a yield-stress fluid modelled by the Herschel-Bulkley constitutive law. Theoretically, the problem can be simplifed for the geometry of a relatively narrow (Hele-Shaw) cell, the non-Newtonian properties of the fluid being captured by a viscoplastic generalization of Darcy's law. This formulation leads to an interesting mathematical problem for the height to which a yield-stress fluid can rise within a cell with varying gap thickness, a problem that can be solved using the method of characteristics. In the limit that the gap varies over a wider scale than the height to which the fluid can rise, the problem reduces to a much simpler problem equivalent to one-dimensional, viscoplastic capillary rise, the solution of which has been given previously and compared with experiments. More generaliiy, the dynamics is richer, with the capillary pressures causing fluid to first rise and then plug up parts of the cell. |
Monday, November 22, 2021 5:49PM - 6:02PM |
P07.00009: Viscoplastic corner eddies Jesse Taylor-West, Andrew J Hogg When viscously-dominated fluid in a corner is disturbed, eddies can form. Examples of this motion include flow through an abrupt contraction and over a cavity. Five decades ago, Moffatt (1964) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous “Moffatt eddies”. In this study, we examine corner flows of Viscoplastic materials, a class of non-Newtonian fluids which exhibit a yield-stress below which they are solid-like. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt (1964) can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-lagrangian method, and analytically, by employing a visco-plastic boundary-layer formulation and scaling arguments. We measure the depth of the static plug as a function of Bingham number (dimensionless yield-stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid above the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs. |
Monday, November 22, 2021 6:02PM - 6:15PM |
P07.00010: A thin-film equation for a viscoelastic fluid, and its application to the Landau-Levich problem Charu Datt, Minkush Kansal, Jacco H Snoeijer Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. We derive a thin-film equation for a second-order fluid, and use it to study the classical Landau-Levich dip-coating problem. We show how viscoelasticity of the fluid affects the thickness of the deposited film, and address some apparent discrepancies in the literature. |
Monday, November 22, 2021 6:15PM - 6:28PM Not Participating |
P07.00011: Viscoplastic Blisters Thomasina V Ball, Neil J Balmforth The spreading of a viscous fluid injected between a thin sheet and an underlying rigid plane has been well explored for the case of an elastic sheet. In this talk we modify this problem to consider viscous flow underneath a thin sheet of viscoplastic fluid described by a Herschel-Bulkley constitutive law. We assume a large effective viscosity contrast between the sheet and the underlying viscous fluid such that the sheet is described by the viscoplastic counterpart of the Föppl-von Kármán plate model of solid mechanics. The dynamics of the flow is controlled by a boundary layer at the fluid front whereby the sheet is lifted off the underlying plane by the advancing fluid. By imposing a pre-wetted film between the sheet and the underlying rigid plane, we explore solutions when the sheet has a Bingham rheology influenced by bending forces. These results provide insight into a number of industrial and geophysical problems. |
Monday, November 22, 2021 6:28PM - 6:41PM Not Participating |
P07.00012: Capillary Flow of Wormlike Micellar Gels Ronak R Gupta, Masoud Daneshi, Gwynn J Elfring, Ian Frigaard Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex rheological features. We study the capillary flow of these wormlike micellar gels to uncover rheological fingerprints on a canonical flow scenario and calculate shear viscosity at high shear rates. We quantify pressure drop for a range of flow rates to see if micelles undergo a structural transition that reflects on the viscosity vs shear rate scaling. We also use optical coherence tomography-based velocimetry to ascertain if there are flow rate-driven transitions in velocity profiles. Our experiments shed light on the fluid dynamics of wormlike micelles and other complex fluids in simple geometries. |
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