Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session ZC22: Flow Instability: Interfacial and Thin Film III 
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Chair: Reid Prichard, Liberty University Room: 147B 
Tuesday, November 21, 2023 12:50PM  1:03PM 
ZC22.00001: Wetting transition and fluid trapping in a microfluidic fracture Ruben Juanes, Yu Qiu, Ke Xu, Amir Pahlavan Immiscible fluid–fluid displacement in confined geometries is a fundamental process occurring in many natural phenomena and technological applications, from geological CO2 sequestration to microfluidics. Due to the interactions between the fluids and the solid walls, fluid invasion undergoes a wetting transition from complete displacement at low displacement rates to leaving a film of the defending fluid on the confining surfaces at high displacement rates. While most real surfaces are rough, fundamental questions remain about the type of fluid–fluid displacement that can emerge in a confined, rough geometry. Here, we study immiscible displacement in a microfluidic device with a precisely controlled structured surface as an analogue for a rough fracture. We analyze the influence of the degree of surface roughness on the wetting transition and the formation of thin films of the defending liquid. We show experimentally, and rationalize theoretically, that roughness affects both the stability and dewetting dynamics of thin films, leading to distinct latetime morphologies of the undisplaced (trapped) fluid. Finally, we discuss the implications of our observations for geologic and technological applications. 
Tuesday, November 21, 2023 1:03PM  1:16PM 
ZC22.00002: Linear stability analysis of viscous multilayer shear flows with interfacial slip Anna Katsiavria, Demetrios T Papageorgiou The stability of two superposed viscous, incompressible, immiscible fluid layers sheared in a plane Couette flow configuration is considered when slip is present at the deforming liquidliquid interface. Guided by experiments and molecular dynamics simulations in the literature, slippage is modelled by employing a Navierslip boundary condition at the liquidliquid interface, and the arising novel instabilities are studied in detail. The linear stability of the system is addressed asymptotically for long and shortwaves as well as with a combination of analytical and numerical calculations for arbitrary wavenumbers and other parameter values. Slip is found to be capable of destabilising perturbations of all wavelengths due to the presence of a velocity jump at the interface, a phenomenon that appears to be a viscous analogue of classical KelvinHelmholtz instabilities. In regimes where the flow is stable to perturbations of all wavelengths when slip is absent, the presence of slip and a favorable combination of the physical parameters, induces a Turingtype instability by destabilisation of a small band of finite wavenumber perturbations. In the case where the underlying layer is asymptotically thin, the results are found to agree with the linear properties of a weakly nonlinear asymptotic model. 
Tuesday, November 21, 2023 1:16PM  1:29PM 
ZC22.00003: Effect of lightactuated photosurfactants on the stability of a viscous thread Michael D Mayer, Demetrios T Papageorgiou, Toby L Kirk This talk investigates the effects of a lightactuated photosurfactant on the canonical problem of the stability of a viscous thread supported by a liquid of negligible viscosity. A model consisting of the NavierStokes equations and a set of molar concentration equations is presented that capture lightinduced switching between two stable surfacant isomer states, trans and cis. These two states display significantly different interfacial properties, allowing for some external control of the stability behaviour of the thread via incident light. Details on the impact of this light on the linear stability of the thread are discussed. Furthermore, to validate our solution method, we compare our solutions with analytical solutions of increasing complexity, while on the way providing a holistic discussion of the effect of surfactants in general on the stability of a liquid thread. 
Tuesday, November 21, 2023 1:29PM  1:42PM 
ZC22.00004: Instabilities of thinfilm flow over a spinning disk Laura Milne, Alexander W Wray, Omar K Matar, Marc Pradas, Stephen K Wilson We study the dynamics of a thin, axisymmetric film of Newtonian fluid on a uniformly rotating disk with topography. The system is modelled via a thinfilm approximation together with the Method of Weighted Residuals up to second order. The resulting model is a closed initialvalue problem for the film thickness and the radial and azimuthal fluxes, including effects of inertia, viscosity, centrifugation and capillarity. We find the spatial stability depends on the position relative to the inlet: close to the inlet the flow is convectively unstable while far from it the flow is absolutely unstable. We investigate the temporal stability in the far field and find there exist three distinct regions that exhibit different behaviors: no growth or decay, conditionally stable and unconditionally stable. We study a family of topographies with parameters controlling the asymmetry, smoothness, amplitude and frequency of the topography. The effect of topography on the flow is determined using an integral measure of the interfacial waviness. In particular, we find that the presence of topography can cause additional interfacial waves that increase the surface area of the film. 
Tuesday, November 21, 2023 1:42PM  1:55PM 
ZC22.00005: A continuum model for patterns and flow in frictional fluid dynamics Liam Morrow, Chris W MacMinn, Oliver Paulin, Duncan R Hewitt, Matthew Hennessy The injection of nonwetting gas into a liquidfilled HeleShaw cell is a classical problem in a HeleShaw cell. This problem has received significant attention because of the distinct interfacial patterns, often referred to as viscous fingers, that form due to hydraulic instabilities. A somewhat popular modification on this problem involves the air injection into a confined granular suspension such that the liquid phase is mixed with densitymatched beads. However, if these beads are left to settle on the bottom of the geometry, frictional forces between both adjacent beads as well as the walls of the geometry are introduced. The addition of these grains leads to a class of socalled ``multiphase frictional flows’’, which have implications in a variety of natural and engineering scenarios. Despite their ubiquity and importance, these frictional flows remain relatively understood, particularly from a theoretical perspective. Here, we present a reduced order continuum model for the capillary bulldozing of a sedimented granular material. The model involves three phases – gas, liquid, and solid – here the granular pile and the overlying fluid layer evolves as coupled thin films. By performing a numerical investigation of our model, we present a unified description of the emerging patterns whose morphology varies as the dynamics transition from a frictiondominated to a viscousdominated regime. 
Tuesday, November 21, 2023 1:55PM  2:08PM 
ZC22.00006: Abstract Withdrawn

Tuesday, November 21, 2023 2:08PM  2:21PM 
ZC22.00007: Retraction and breakup of a thin liquid sheet in a rotating field Toshan lal sahu, Ujjwal Chetan, Jagannath Mahato, Prabir Kumar Kar, Saurabh Dhopeshwar, Prasanta Kumar Das, Rajaram Lakkaraju

Tuesday, November 21, 2023 2:21PM  2:34PM 
ZC22.00008: Pressuredriven displacement of gasfluidgas plugs in a capillary tube Sravya Sasetty, Thomas Ward This talk focuses on the study of pressuredriven displacement of gasliquidgas plugs in a capillary tube using theory and experiments. Several researchers have shown that in the limit of low Re, when a right circular cylindrical plug is displaced at a constant flow rate in a confined cylindrical geometry, an analytical solution can be found by solving the 4thorder stream function equation E^{2}(E^{2} ψ) = 0. Here, we attempt to understand the instabilities that occur in a pressuredriven displacement of a liquid plug by using perturbation analysis. We utilize the general solution to the 4thorder stream function PDE, and apply boundary conditions appropriate to the pressuredriven flow, to derive an analytical solution that is a leadingorder solution of the perturbed system. This leadingorder solution depicts a right circular cylindrical plug, i.e., no deformation. In this study, experiments were also performed in a capillary tube (diameter ≈ 800 μm) by displacing liquid plugs containing aqueous glycerol solution using pressurized air with a range of 0.02 psig < P < 1 psig. We study the leadingorder solution at a zero capillary number to compare with lowpressure experiments. 
Tuesday, November 21, 2023 2:34PM  2:47PM 
ZC22.00009: Experimental demonstration on suppression of viscous fingering in a partially miscible system Ryuta X Suzuki, Kaori Iwasaki, Takahiko Ban, Jun Iijima, Manoranjan Mishra, Yuichiro Nagatsu Phase separation is ubiquitous in nature and technology. So far, the focus has primarily been on phase separation occurring in the bulk phase. Recently, phase separation taking place in interfacial areas has attracted more attention – in particular, a combination of interfacial phase separation and hydrodynamics. Studies on this combination have been conducted intensively in this past decade; however, the detailed dynamics remain unclear. Here, we perform fluid displacement experiments, where a less viscous solution displaces a more viscous one in a radially confined geometry and phase separation occurs at the interfacial region. We demonstrate that a fingerlike pattern, due to the viscosity contrast during the displacement, can be suppressed by the phase separation. We also claim that the direction of a body force, the socalled Korteweg force, which appears during the phase separation and induces convection, determines whether the fingering pattern is suppressed or changed to a droplet pattern. The change of the fingering pattern to the droplet pattern is enhanced by the Korteweg force directed from the less viscous solution to the more viscous one, whereas the fingering is suppressed by the force directed in the opposite direction. 
Tuesday, November 21, 2023 2:47PM  3:00PM 
ZC22.00010: Timeperiodic viscous fingering Jack Lawless, Anne Juel, Andrew Hazel Pattern formation due to viscous fingering exhibits a fascinating range of complex dynamics. For example, when air displaces a viscous liquid in the narrow gap between two parallel plates  a HeleShaw channel  the resulting steadily propagating finger of air can undergo a relatively abrupt transition to disordered front propagation. This motivates an exploration of the system's nonlinear dynamics. In this talk, we demonstrate that this system naturally supports a host of timeperiodic states, which are a fundamental buildingblock of disordered dynamics. The introduction of a bubble downstream is used to provide a sustained perturbation to the finger's tip and this can lead to its splitting and the subsequent advection of the tipdisturbance. The finger's continued propagation provides an inbuilt restoring mechanism because it broadens in order to reattain its preferred width set by the balance of viscous and capillary forces. The interplay between these two effects leads to a timeperiodic tip instability and the finger deposits a spatially periodic pattern as it propagates. We show that this mechanism generalises to a range of sustained perturbations to the finger's front. 
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