Session X25: Flow Instability: Interfacial and Thin Film II

Direct Numerical Simulation for Flooding Behavior in Counter-current Gas/Liquid Flow Systems for Carbon Capture

Understanding incipient flooding is crucial for industrial systems that involve liquid-gas counter current flow. A biocatalytic textile-based gas-liquid contactor is one application that utilizes immobilized enzymes to accelerate CO₂ capture. A spiral-wound design of such structured packing is assembled by folding cheesecloth fabric over the long edge of a rectangular mesh reinforcement and rolling up the sandwich as a tube. Counter-current flow takes place between an aqueous K₂CO₃ solution and an N₂ and CO₂ gas mixture. Evaluating gas/liquid interactions using two-phase flow capabilities is a challenging problem. Owing to the complex geometry and flow, an investigation of interfacial waves is necessary to understand the local mechanisms initiating the transition to flooding. Identifying counter-current flow limitations (CCFL) are important as these inhibit the interaction of carbon-dioxide with biocatalytic surfaces. Direct numerical simulation (DNS) approach with PHASTA code is utilized to establish predictive metrics for identifying CCFL proposed in the biocatalytic reactor design. Strong influence of instantaneous flow parameters requires local mesh refinement for the resolution of interfaces. Simulations that evaluate the two-phase flow can lead to developing models that predict two-phase flow behavior from global parameters to benefit improved contactor design for efficient CO₂ capture.   

Rayleigh-Plateau Instability of a Viscoelastic Layer Coated on a Rigid Cylindrical Fibre.

The Rayleigh-Plateau (RP) instability driven by the surface tension is observed in day to day life such as water jet from a tap breaks into droplets. Surface tension can play an important role in soft solid materials like gels, elastomers and biological tissues. We study the RP instability of a viscoelastic solid layer coated on a rigid cylindrical fibre. We solve the governing equation for the deformation of soft solid and obtain the dispersion relation. We present the results of how the RP instability depends on the elastocapillary length, the viscoelastic time scale, the rigid fibre radius and the substrate frictional coefficient.   

Radiation Stress Links Faraday Waves to the Shrinkage of Holes in Capillary Surfaces

When subjecting a liquid film to vertical vibrations, a phenomenon known as Faraday instability can occur. Its characteristic waves become increasingly chaotic with stronger vibrations. In the absence of vibrations, stable holes in a bounded liquid film are described by the Young-Laplace equation. Combining both phenomena raises the question of how the waves affect the hole. We present a quantitative model that incorporates the underlying physics and describes the time-averaged size of the hole. Remarkably, we find that the experimentally obtained hole size can still be described by the Young-Laplace equation using an effective capillary length. We establish a relationship between this effective capillary length and the dynamic system by mapping it to the required wave radiation stress for the measured hole shrinkage. In addition, we determine the radiation stress by measuring the wave energy through spectral surface deformation measurements. Comparing these independent measurements of the radiation stress shows good quantitative agreement in the highly dynamic regime of chaotic Faraday waves. This agreement holds irrespective of the initial hole size and exciter frequency. Our results demonstrate the possibility of quantifying the radiation stress due to chaotic Faraday waves solely by observing the time-averaged shrinkage of a hole.   

Linear stability of a shear-imposed heated falling film

A linear stability analysis is carried out for a thin liquid film flowing down a uniformly heated inclined plate under the action of gravity. The free surface of the liquid film is subjected to a constant imposed shear stress. The long-wave approximation is used to capture the hydrodynamic H mode instability analytically. The imposed shear stress exerts a destabilizing effect on the hydrodynamic H mode instability. The Padé approximation predicts the temporal growth rate more accurately compared to that determined from the third order and fifth order long wave approximations. To capture the hydrodynamic shear mode and thermo-capillary S and P modes numerically, the Chebyshev spectral method is employed. Imposed shear is found to have a destabilizing effect on the S mode and shear mode instabilities, whereas it stabilizes the P mode instability. It has been observed that after a certain critical value of the imposed shear stress, the P mode instability disappears. The P mode instability gets destabilized with increasing spanwise wavenumber, whereas the shear mode, H mode and S mode instabilities get stabilized with increasing spanwise wavenumber. The Marangoni number exerts a destabilizing effect on all the instability modes, namely, H, S, P and shear mode.

  

Numerical simulation of radial viscous fingering in a partially miscible system

When a displacing fluid is less viscous, the interface of two fluids gives a finger-like pattern in porous media. This phenomenon is called Saffman-Taylor instability or viscous fingering (VF). In addition to the importance of viscosity differences, fluid-fluid miscibility plays an important role in the VF dynamics. Miscibility has been traditionally classified into two types: fully miscible and immiscible systems. Recently a partially miscible system, in which two fluids mixed and the composition of solutions is finally different from that of initial solutions, has newly studied. It has been reported that diffusion and phase separation affect the VF dynamics in this case, and the partially miscible VF shows multiple droplets formation which cannot be explained by only hydrodynamic instability. Until now, the partially miscible cases have been studied with rectilinear numerical simulation and radial experiments. These two results show multiple droplets formation and the trend of changing the interface are consistent qualitatively. However, there is a clear difference between the displacement velocity between the rectilinear and radial geometries, and it is necessary to simulate partially miscible flows in a radial geometry. In this study, we simulate radial flows in partially miscible cases. We compare the results with the previous studies qualitatively and quantitatively, and investigate the effect of velocity in radial and rectilinear displacements in the partially miscible systems.   

Modelling film flows down the inner surface of a nonuniformly heated rotating fibre

The study of the flow thin liquid films has gained a good momentum for years because of the rich dynamics that they exhibit and various industrial applications. In this work, we investigate the behavior of a falling liquid film inside a non-uniform heated, rotating, vertical cylinder. The interplay between gravity-driven film flow, cylinder rotation, and non-uniform heating introduces complex fluid dynamics and heat transfer phenomena. The study aims to elucidate the impact of rotation and non-uniform heating on the film's thickness and stability. Numerical simulations and theoretical analysis are employed to understand the intricate dynamics and heat transfer characteristics of this system. The findings provide valuable insights into the behavior of falling films in similar configurations, aiding in the optimization of various industrial applications involving heat and mass transfer processes. Stability analysis and numerical simulation agree well with the theoretical observations.   

Adhesion instability of thin liquid films

We are interested in the dynamics of propagation of an adhesion front between two solid surfaces. A recent study has shown how putting in contact of two glass plates both covered with a viscous liquid film results into a fingering instability distinct from classical Saffman-Taylor viscous fingering. In this configuration, the instability mechanism involves a depletion of the viscous film ahead of the propagation front.

In numerous practical applications, only one surface is coated with an adhesive layer, which brings fundamental questions on contact line dynamics. Experiments on coated/non-coated configuration exhibit a front instability with different morphologies. Fingers are also observed, but in the transverse direction. These patterns rely on an original cascading nucleation mechanism.

In practice, most surfaces display roughness of finite amplitude. We finally present model experiments with grooved surfaces obtained by micro-machining. In the explored configuration, the rough surface is coated with a thick viscous layer while the facing one is smooth. Surprisingly fingers are also observed in a direction perpendicular to the grooves.   

Suppressing the Plateau–Rayleigh instability between fibers

A falling liquid thread readily destabilizes due to the capillary-driven Plateau–Rayleigh instability. If the thread envelops a vertical fiber the well-studied “bead-on-fiber” pattern emerges. In many cases, these patterns can be leveraged for novel heat and mass transfer applications; however, other applications, such as fiber coating, require a uniform coating. To this end, we explore how thin fibers stabilize falling threads by suppressing the Plateau–Rayleigh instability. We perform experiments on liquid flow down two vertical fibers over an extensive range of flowrate Q, inter-fiber spacing w, viscosity µ, and fiber radius R. When the thread envelops the fibers, they elongate its profile. The elongated thread resists capillary instability for low Q, and the flattened thread flows uniformly down the fibers. As Q increases and the cylindrical profile is recovered, the Plateau–Rayleigh instability resurfaces. We characterize the thread profile using its minimum and maximum width as Q is increased. Furthermore, we report the variable ranges associated with Plateau–Rayleigh suppression.   

Electric Field Mediated Instabilities of a Thin Viscoelastic-Porous Confined Bilayer

The polymeric-porous media interfaces' instabilities directly impacts several contemporary applications, such as organ-on-a-chips, microplastic depositions, emulating biofluid flows through arteries, and the performance of electrochemical storage devices. We have considered a model prototype of the abovementioned systems to uncover the interfacial characteristics in the presence of an external electric field. A confined system of thin solid viscoelastic polymeric film and deformable porous layer under the application of an external electric field is explored with the help of General Linear Stability Analysis (GLSA). The modified Kelvin-Voigt-Darcy-Brinkman model is used to represent the polymer displacement through the porous media, whereas zero-frequency solid linear viscoelastic constitutive relation is used to represent the polymeric film. The theoretical analysis unveils two distinct pathways of instabilities, (i) critical mode and (ii) dominant mode. The simulation results revealed that increasing electric-field potential reduces the length scale of instability in the dominant mode, which leads to pattern miniaturization. However, the porous layer's presence significantly alters the instability's time scale. The self-organized mesoscale patterns developed at the porous media interface with tunable length and time scales over a large area can be exploited to fabricate high-efficiency miniaturised smart devices for energy storage and biomedical applications.   

The effect of parametric forcing on the supercritical Marangoni instability

This study investigates the behavior of a liquid-passive fluid bilayer heated from the liquid side, in the absence of gravity, and subject to parametric forcing. In large confinements without parametric forcing, a long-wave Marangoni instability and subsequent dry-out occur when the temperature difference exceeds a specific threshold. The primary objective is to explore mechanisms to prevent dry-out through mechanical parametric forcing. The results obtained using linear stability analysis and computations with a WRIBL-based nonlinear reduced-order model show that the liquid film can be rendered stable with a flat free surface within a specific range of forcing amplitudes. Beyond this range, the flow becomes unstable, leading to either Marangoni instability with dry spot formation at lower amplitudes or Faraday instability with large free surface oscillations at higher amplitudes. Beyond a critical value of the parametric frequency, stabilization to quiescent conditions cannot be achieved. Instead, we proceed directly from a Marangoni-dominated flow characterized by long-wavelengths to a short-wavelength resonance-dominated flow, again avoiding dry-out. The study identifies two critical factors for the occurrence of a critical parametric frequency: the finiteness of the container width and the presence of "resonant tongues," characterizing the threshold amplitude for Faraday instability.   

Stress field visualization of Saffman-Taylor instability in Hele-Shaw cell

When a less viscous fluid displaces a more viscous one in small space, such as porous media or Hele-Shaw cells, the interface forms a finger-like pattern due to hydrodynamic instability caused by the viscosity difference. This is known as Saffman-Taylor instability or viscous fingering (VF). Understanding of VF is important because it is related to the various applications such as enhanced oil recovery and chromatography. The previous theoretical, experimental, and numerical approaches pointed out that the three-dimensional structure inside the gap of Hele-Shaw cell plays an important role in the onset and suppression of VF. In this study, the photoelastic measurement of VF in a Hele-Shaw cell was performed to visualize stress field including three-dimensional effects. The interpretation of the experimental results were discussed by comparing of results in radial Hele-Shaw flow with numerical results. We will provide the effective explanation of the flow during fluid displacements in the Hele-Shaw cell by using the measurement results of the stress field.   

Origin of filaments in finite-time in Newtonian and non-Newtonian thin-films

The sticky fluids found in pitcher plant leaf vessels can leave fractal-like filaments behind when dewetting from a substrate. To understand the origin of these filaments, we investigate the dynamics of a retreating thin-film of aqueous polyethylene oxide (PEO) solutions which partially wet polydimethyl siloxane (PDMS) substrates. Under certain conditions the retreating film generates regularly-spaced liquid filaments. The early-stage thin-film dynamics of dewetting are investigated to identify a theoretical criterion for liquid filament formation. Starting with a linear stability analysis of a Newtonian or simple non-Newtonian (power-law) thin-film, a critical film thickness is identified which depends on the Hamaker constant for the fluid-substrate pair and the surface tension of the fluid. When the measured film thickness is smaller than this value, the film is unstable and forms filaments as a result of van der Waals forces dominating its behaviour. This critical film-height is compared with experimental measurements of film thickness obtained for receding films of Newtonian (glycerol-water mixtures) and non-Newtonian (PEO) solutions generated on substrates inclined at angles $0^{circ}$, $30^{circ}$, and $60^{circ}$ to the vertical. The observations of filament and its absence show good agreement with the theory. Further analysis of the former case, involving a stability analysis of the contact line, yields a prediction of the spacing (wavelength) $hat{lambda_{f}}$ between filaments as $hat{lambda} extsubscript{f}hat{eta}/hat{gamma} propto Ca$, where $hat{Ca}$ is the capillary number for contact line motion: our experiments yield $hat{lambda} extsubscript{f}hat{eta}/hat{gamma} propto Ca^{1.08}$ and earlier studies in the literature reported $hat{lambda} extsubscript{f}hat{eta}/hat{gamma} propto Ca^{0.945}$. The evolution of the thin-film shape is modelled numerically to show that the formation of filaments arises because the thin-film equation features a singular solution after a finite-time, hence termed a ``finite-time singularity''.