Hele-Shaw Cell Research Articles

Fall and breakup of miscible magnetic fluid drops in a Hele–Shaw cell

The fall and breakup of a miscible drop of magnetic fluid in a vertical Hele–Shaw cell, taking into account the dependence of the physical properties of the fluid (density, viscosity, diffusion coefficient, and magnetization) on the volume concentration of magnetic particles is studied in the paper numerically and experimentally. There are four governing dimensionless parameters: the Archimedes number Ar, the magnetic Archimedes number Arm, the relative width of the gap between the cell walls δ, and the dimensionless initial half-width of the diffusion front w. As a result of numerical simulation, five types of droplets fall and breakup were found: single drop, pair decay, trident, symmetric breakup, and cascade breakup. In the experiment performed, the correspondence to the data of the numerical analysis is confirmed in the absence of a magnetic field and in the vertical magnetic field.

3D Visualization of Viscous Fingering in Miscible Fluids Flow in Porous Materials

Viscous fingering is a type of flow instability that occurs when a less viscous fluid displaces a more viscous fluid, causing instability at the displacement front. Owing to the opaque nature of porous media, experimental studies on the structure of viscous fingering and its development over time have been mostly limited to 2D porous media or Hele–Shaw cells. In this study, we used a micro-focused X-ray computed tomography scanner to investigate the 3D characteristics of viscous fingering in porous media. A low-viscosity iodine brine solution was injected in 3D-printed porous samples initially saturated by a high-viscosity syrup solution. The resulting miscible invasion was monitored by a sequence of X-ray tomography. Seven experiments were conducted to explore a large range of Péclet number and viscosity ratio. It allowed to identify the 3D morphology of fingering patterns and to quantitatively evaluate changes in physical properties such as iodine concentration in miscible fluids. As already identified in 2D experiments, characteristic events such as tip splitting, shielding, and coalescence were observed in 3D viscous fingering. At relatively low Péclet numbers, the fingering of the brine phase was more prone to breakthrough at certain points, forming a slender finger structure. As the Péclet number increased, the instability of the brine phase flow increased, making it easier to form multiple finger structures, and the tips were more prone to splitting into small finger structures. When the viscosity ratio decreased, the brine phase flow became more unstable. After halving the viscosity ratio of the miscible solution, multiple finger structures were formed at lower Péclet numbers, with small finger structures continuously splitting at the tips.

On the exact solutions of Darcy–Brinkman model in rectangular Hele–Shaw channels under no-slip and slip boundary conditions

This study demonstrates the effectiveness of Darcy–Brinkman model to derive exact solutions for laminar flow in rectangular microchannels, presenting a robust alternative to traditional methods that rely on complex Fourier series expansions for velocity distributions. Derived here are analytical solutions for two specific cases: the classical Hele–Shaw configuration with no-slip boundaries and a slip-induced configuration featuring a permeable lateral wall with a square array of cubic elements. For both cases, the Darcy–Brinkman model effectively captures flow behavior including boundary layer effects and central plug flow, and the results are validated using micro-Particle Image Velocimetry measurements. For channels with high width-to-height ratios (w/h>4), the model perfectly aligns with established permeability formulations, with a mean relative error consistently remaining below 5%. In the slip-induced configuration, an effective slip length (Ls) is introduced, correlated with porosity and velocity ratios, to reflect the properties of the porous material. This slip length is expressed as a function of the Hele–Shaw cell height and porosity, modeled using an inverse error function, and demonstrates excellent agreement with experimental results, with a mean relative error below 3.5%. This study highlights the potential of Darcy–Brinkman model for exact solutions in microfluidic systems.

Faraday instability of a three-layer fluid system in a Hele-Shaw cell: Transition from zigzag mode to B-interface instability mode

Faraday instability of a three-layer fluid system in a Hele-Shaw cell: Transition from zigzag mode to B-interface instability mode

Dewetting Fingering Instability in Capillary Suspensions: Role of Particles and Liquid Bridges.

This study investigates the fingering instability that forms during the stretching of capillary suspensions with and without added nanoparticles. The dewetting process is observed using a transparent lifted Hele-Shaw cell. The liquid bridge is stretched under constant acceleration, and the resulting instability patterns are recorded using two high-speed cameras. Finger-like structures, characteristic of the Saffman-Taylor instability, are observed. The total length of the dendrites and the intersecting number of branches are quantified. We reveal the roles of microparticles, nanoparticles, and the secondary liquid during the fingering instability. The addition of microparticles to pure liquid enhanced finger length due to increased particle interactions and nucleation sites for bubbles. The addition of secondary fluid reduces fingering length by forming a strong interparticle network. Incorporation of nanoparticles induces an early onset of cavitation and enhances fingering instability. However, nanoparticles make the capillary suspensions' overall microstructure more homogeneous, reduce the sample variation in fingering patterns, and promote the even distribution of gel on both slides during splitting. These findings highlight the complex interactions governing dewetting in capillary (nano)suspensions. This knowledge has potential applications in microfluidics, 3D printing, and thin-film coatings, where controlling dewetting is crucial.

Numerical modeling of fluid displacement in Hele-Shaw cells: a gap-averaged approach for power-law and Newtonian fluids

Abstract This work presents a physics-based two-dimensional model for simulating displacement flows of power-law fluids in Hele-Shaw cells. The model is derived by approximating fully developed velocity profiles across the gap-wise direction and averaging the mass and momentum conservation equations, resulting in a two-dimensional formulation that efficiently captures complex fluid dynamics. Implemented in OpenFOAM, this approach achieves computational speeds over 200 times faster than comparable 3D simulations, while preserving the accuracy of displacement dynamics. Validated against 3D DNS results and experimental data, this 2D model accurately replicates observed flow phenomena. Simulations of over 70 cases examined the effect of the ratio of friction pressure gradients (RFG) between fluid pairs on interface stability. Results show that RFGs below unity maintain a flat interface, while higher values induce viscous fingering. In cases with RFG closer to unity, a longer duct or extended displacement time is required for significant finger growth.

Polymer flooding characteristics in modified Hele–Shaw cells

In this study, numerical simulations are employed to investigate the displacement flow of oil by viscoelastic polymer solutions inside modified Hele–Shaw cells (HSCs). The flooding characteristics within converging and diverging geometrical configurations and various flow injection rates are explored by utilizing the White–Metzner model to capture the viscoelastic behavior of hydrolyzed polyacrylamide solutions at different concentrations. The simulations are conducted in OpenFOAM using the volume of fluid method to model the multiphase interface. Results demonstrate that higher elasticity numbers (El) and lower modified capillary numbers (Ca′) enhance the oil recovery to over 75% in terms of swept volume due to improved flow stability and reduced finger branching. Additionally, the diverging HSCs positively influence the flow patterns and facilitate an extra increase in sweeping efficiency (SE) by more than 12% via favorably alleviating the stability threshold in terms of Ca′–El relationship. In contrast, the opposite holds for the converging channel, decreasing SE by 16% and narrowing down the stability region. The findings indicate that adjusting polymer concentration and cell configuration can mitigate the adverse effects of finger instability, thereby improving the overall success of oil displacement processes. Moreover, a supervised machine learning study was carried out to predict the sweep efficiency based on the flow dimensionless numbers, where the multi-layered artificial neural network was exhibited as a high-accuracy model with an R2 value of 94.46%.

Features of Hydrogen-Enriched Methane–Air Flames Propagating in Hele-Shaw Channels

Mixtures of hydrogen with common hydrocarbon fuels are considered viable for reducing carbon footprint in modern industry, power production, and transportation. The addition of hydrogen alters the kinetics and thermophysical properties of the mixtures, as well as the composition and properties of combustion products, requiring detailed research into the features of flame propagation in hydrogen-enriched hydrocarbon–air mixtures. Of particular interest are also the safety aspects of such fuels. In this paper, experimental results are presented on the premixed laminar flame propagation in channels formed by two closely spaced plates (Hele-Shaw cell), with the internal straight walls forming a diverging (diffuser) channel with the opening angles between 5 and 25 degrees. Methane–hydrogen–air mixtures with the hydrogen relative contents of 0%, 25%, and 50% and global equivalence ratio of unity were ignited by a spark near the closed narrow end of the channel. Experiments were performed with the gap width of 3.5 mm; video recordings were processed in order to determine the quantitative features of the flame front propagation (leading and trailing point coordinate, coordinates of the cusps, cell sizes and shapes). The main features of flame propagation (fast initial expansion, development of cellular flame, self-induced longitudinal oscillations) are obtained and compared to clarify the effect of hydrogen contents in the fuel and channel geometry (gap width, opening angle).

Fracturing behaviour of a shear-thinning fluid in a lubricated Hele-Shaw cell

We undertake an experimental investigation into the instabilities that emerge when a shear-thinning fluid intrudes a less viscous Newtonian fluid axisymmetrically in a lubricated Hele-Shaw cell. Pre-formed lubrication layers of Newtonian fluid that separate the shear-thinning fluid from the cell walls are incorporated into the experimental design. Provided the lubrication layers remain effective at reducing shear stress, so that extensional stresses dominate the flow of the intruding fluid, the instabilities evolve to form branch-like structures, which exhibit fracturing or tearing behaviour at their troughs. Thicker lubrication layers enable the branches to propagate radially outwards, whilst thinner, less effective ones hinder their development and progression. In the absence of lubrication layers, the shear-thinning fluid spreads radially and remains axisymmetric. For lubricated flows, we show that the number of branches is dependent primarily on the strain rate at the radial distance where they first emerge, and that the number of branches decreases with increasing strain rate.

Diffusive Transfer between a Droplet and an Immiscible Oscillating Liquid in a Radial Hele-Shaw Cell

Diffusive Transfer between a Droplet and an Immiscible Oscillating Liquid in a Radial Hele-Shaw Cell

Non-Newtonian fluids, viscosity and fractal dimensions

The aim of the paper is to propose a laboratory task for high school students, which would enable them to investigate the properties of non-Newtonian fluids. The key problem is that the concept of viscosity which is important to characterize non-Newtonian fluids, is not part of the high school curricula. Basic information about the idea of viscosity is presented. Viscosity was measured using the Höppler viscometer. The following liquids were measured: flower honey, shower gel, soap, paint color, engine oil, propylene glycol, oil, and solution propylene glycol. The outcomes of our measurement of viscosity and the creation of fractals in a Hele-Shaw cell are described. The fractal dimensions of the shapes in the Hele-Shaw cell are determined using the “Box counting” method and the software Fractalyse. The process of finding the dependence of the fractal dimension on the viscosity ratio of the given liquids is discussed. The findings are presented in tables and figures. The activity is suitable for high school learners and first-year university students. The necessary experimental equipment is a viscometer, Hele-Shaw cell, liquids, syringes, and computer. The needed software is free to download.

Motion and deformation of a bubble in a Hele-Shaw cell

Motion and deformation of a bubble in a Hele-Shaw cell

Characteristic Features of Modeling Multiphase Flows in the Hele-Shaw Cell

Characteristic Features of Modeling Multiphase Flows in the Hele-Shaw Cell

A three-layer Hele-Shaw problem driven by a sink

In this paper, we investigate a sink-driven three-layer flow in a radial Hele-Shaw cell. The three fluids are of different viscosities, with one fluid occupying an annulus-like domain, forming two interfaces with the other two fluids. Using a boundary integral method and a semi-implicit time stepping scheme, we alleviate the numerical stiffness in updating the interfaces and achieve spectral accuracy in space. The interaction between the two interfaces introduces novel dynamics leading to rich pattern formation phenomena, manifested by two typical events: either one of the two interfaces reaches the sink faster than the other (forming cusp-like morphology), or they come very close to each other (suggesting a possibility of interface merging). In particular, the inner interface can be wrapped by the other to have both scenarios. We find that multiple parameters contribute to the dynamics, including the width of the annular region, the location of the sink, and the mobilities of the fluids.

Surface wave damping by a Robin boundary condition at a permeable seabed

Surface wave damping by a Robin boundary condition at a permeable seabed

CO2 foam structure and displacement dynamics in a Hele–Shaw cell

CO2 foam structure and displacement dynamics in a Hele–Shaw cell

Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

Flow manipulation of a nematic liquid crystal in a Hele-Shaw cell with an electrically controlled viscous obstruction

The flow of a nematic liquid crystal in a Hele-Shaw cell with an electrically controlled viscous obstruction is investigated using both a theoretical model and physical experiments. The viscous obstruction is created by temporarily electrically altering the viscosity of the nematic in a region of the cell across which an electric field is applied. The theoretical model is validated experimentally for a circular cylindrical obstruction, demonstrating user-controlled flow manipulation of an anisotropic liquid within a heterogeneous single-phase microfluidic device.

Decay of a hydrogen-air flame front to cup-like cells in a narrow horizontal gap

Decay of a hydrogen-air flame front to cup-like cells in a narrow horizontal gap

Convection induced by centrifugal and Coriolis buoyancy in a rotating Hele-Shaw reactor

The study of heat and mass transfer in a Hele-Shaw cell rotating around a perpendicular axis has various advanced technological applications. These include the design of microfluidic devices and continuous-flow chemical microreactors, to name a couple. In this setup configuration, the quasi-two-dimensional design allows for recording the density field using optical methods, and the rotation enables control of this field through spatially distributed inertial forces. As is known, in the limit of an infinitely thin layer, the Coriolis force vanishes within a standard mathematical model. However, experimental observations of fluid flow in a rotating Hele-Shaw cell indicate the opposite. In this paper, we show that the correct derivation of the equation of motion under the Hele-Shaw approximation leads to the appearance of a Boussinesq-type term for the Coriolis force. To study the effect of the Coriolis buoyancy, we consider the problem of fluid stability during the internal generation of a transfer component, which can be either the concentration of the dissolved substance or the temperature of the medium. The careful study of system dynamics involves linear stability analysis, weakly nonlinear analysis, and direct numerical simulation. The general properties of the disturbance spectrum are analyzed. The branching of solutions near the first bifurcation is studied using the technique of multiple time scales. A stationary convection is replaced by an oscillatory one under the action of the Coriolis force, as demonstrated by weakly nonlinear analysis. Finally, we investigate the nonlinear dynamics using direct numerical simulation.