Hele-Shaw Cell Research Articles

Binder-jet 3D printing of pea-based snacks with modulated texture

This paper demonstrates, for the very first time, 3D printing of pea-based snacks with tunable texture using the binder jetting (BJT) method, pea flour as the print powder, and an aqueous binder solution. The binding mechanism was studied by performing both Hele-Shaw cell experiments and confocal microscopy on the printed samples. As the pea flour was exposed to an aqueous binder, the starch granules swelled. These granules remained swollen but were further joined by a network of protein-rich bridges as the sample dried. Inclusion of sugar and post-printing baking tended to strengthen the as-printed samples, and the resultant mechanical properties were on par with commercial snacks that are not 3D printed. By controlling the amount of aqueous binder dispensed from the inkjet print heads, more than one order of magnitude differences in compressive strength and modulus were achieved, demonstrating the exciting potential of using 3D printing for texture modulation of plant-based snacks.

Dynamics of the surface growth resulted from sedimentation of spheres in a Hele–Shaw cell containing a low-viscosity fluid

In this paper, we investigate the dynamics of surface growth resulting from sedimentation of spherical granular particles in a fluid environment, using experiments and simulations. In the experimental part, spherical polystyrene particles are poured down from the top of a vertical Hele–Shaw cell and form a 1 + 1-dimensional growing surface. The surface roughness is obtained from the images, and the growth and roughness exponents are measured. In the numerical simulation part, the surface growth process is simulated using the discrete element method, considering the interactions between the grains, and the exponents are calculated. In this method, unlike conventional simulation models, instead of a discrete deposition law, the dynamics of the individual particles throughout the process are obtained, considering different forces acting on the particles. Finally, the simulation results are compared with the experiment, and we see a very good agreement between them. We find different values for the exponents using different methods, indicating that the system is multi-affine and does not obey the scaling laws of affine models.

Experimental study of the dynamics and mass transfer of single CO2 bubble accompanied by reactions in Hele-Shaw cell

The reduction of carbon emissions has become a critical global issue, and the use of monoethanolamine (MEA) solution for CO2 absorption is prevalent in industry. To elucidate the mass transfer mechanisms in reactive multiphase flow, we employed high-speed photography and digital image processing to examine the dynamics and mass transfer behavior of CO2 bubbles in a Hele-Shaw cell. The results indicate that as the MEA solution concentration increases, oscillations during bubble ascent diminish, and the terminal velocity decreases. Based on changes in the mass transfer coefficient, the reaction process can be segmented into a phase of intensified mass transfer, marked by a rapid decrease in bubble equivalent diameter, and a phase of deteriorating mass transfer, where the diameter stabilizes. Additionally, we introduced a dimensionless mathematical model for the Sherwood number based on experimental findings, and its reliability was confirmed.

Periodic Precipitation in a Confined Liquid Layer.

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Study of Thermal Instability in Magneto-Convection Nanoliquid Confined within Hele-Shaw Cell Under Three Types of Thermal/Gravity Modulation

In the present paper, we investigate a thermal instability of magneto-convection in an electrically conducting nanoliquid confined within Hele-Shaw cell, subjected to an applied time-periodic boundary thermal (ATBT) or gravitational modulation (ATGM), and surrounded by a constant vertical magnetic field. A steady portion and a time-dependent oscillatory portion constitute the temperature gradient seen between liquid layer’s walls in the context of ATBT. In this scenario, both walls’ temperatures are modulated. The liquid layer oscillation can be used to realise the externally applied time periodic component of the gravity field that is present in the ATGM problem. The perturbation is described in terms of the power series of the assumed-small convective amplitude. The impact of modulations on heat/mass transfer are examined utilising Ginzburg-Landau (GBL) approach. The impact of different parameters on the transportation of mass and heat is also explored. Additionally, we observe that gravitational modulation is very much effective than thermal modulation. Lewis-number, modified-diffusivity ratio and concentration Rayleigh-number increase heat and mass transport in the system.

Mass transfer of solute in an oscillating flow in a two-dimensional channel

The effective diffusion of a solute in a rectangular two-dimensional channel is experimentally studied. We experimentally examine the effective diffusion of Rhodamine B dissolved in water oscillating in a rectangular Hele–Shaw cell. The concentration of Rhodamine B in water is measured by the intensity of its fluorescence emission. In particular, we consider two problems: (i) effective diffusion of solute in water oscillating in a two-dimensional rectangular channel (Hele–Shaw cell) and (ii) effective diffusion of solute in pores between monosized hard spheres randomly packed in a rectangular Hele–Shaw cell. It is revealed that the rate of solute mass transfer exceeds the molecular diffusion rate in both cases. It has been demonstrated that when water oscillates between parallel walls, diffusion is accelerated by Taylor dispersion with the effective diffusion coefficient Deff exceeding the molecular diffusion coefficient Dm by 1–2 orders of magnitude. The effective diffusion coefficient Deff depends only on the relative amplitude but not on the frequency of the fluid oscillations in the studied range of frequencies and amplitudes. When the fluid oscillates in the pores of the porous medium, solute transport is faster than in the case of Taylor dispersion. Here, the effective diffusion coefficient depends on both the frequency and amplitude of oscillations. The analysis shows that the experimental data obtained at various frequencies and amplitudes of oscillations are consistent with the relation Deff/Dm∼Pe2 (Pe is the Peclet number). We suggest that the enhanced solute mass transfer is associated with the time-averaged fluid flows that arise due to spatial heterogeneity of the amplitude of water oscillations in the pores between randomly packed hard spheres.

Nonlinear Thermal Instability in Nanoliquid Under Magnetic-Field Modulation Within Hele-Shaw Cell

In a nanoliquid-confined Hele-Shaw cell, the effect of magnetic-modulation is investigated. The goal of this study is to conclude the work described in Rai et al. [45] for oscillatory convection. The existence of the CGLE42, 43 model is constrained by the condition ω2 > 0 and determined transfer analysis. The magnetic fluxes in Heleshaw cells are governed by CGLE and magnetic modulation limitations. Changes in magnetic modulation can affect heat and mass transfer in terms of modulation frequency and amplitude. In addition, the findings of earlier research on heat and mass transport indicate that oscillatory mode is preferable than stationary mode. Further, the transport analysis is compared to previous research and shown to have improved results.

Experimental study for visualizing CO2-dissolved water plume migration under hydraulic gradient conditions and implication for field monitoring data

Investigating the possible direction of a CO2-dissolved water plume migration near the potential CO2 leakage area is a significant task because it helps estimate the spatial and temporal monitoring scale to detect the signal of released CO2 from the storage. Accordingly, the Korea CO2 Storage Environmental Management (K-COSEM) research center tried to develop an intensive monitoring system and applied it to the artificial CO2 release test in the actual field. Monitoring data from the field tests depicted the horizontal movement of the CO2-dissolved water plume along the direction of the groundwater flow. However, it remains unclear how the CO2-dissolved water plume migrates vertically and how gas accumulation occurs near the capillary zone. The present study simulated the CO2 release test with a visual expression method utilizing a Hele-Shaw cell with hydraulic gradient conditions (i = 0, 0.1, and 0.01) and tried to estimate the significant influences on a diffusive-advective transport of the dissolved gas plume with the shallow aquifer condition. The visualization experiment results were intuitively verified to determine whether the theoretical principles of action related to plume flow applied in this context. The results suggest that a CO2-dissolved water plume is distributed by hydraulic gradients and density-driven CO2 convective flow. The plume shape, center, and area were analyzed using an image analyzer program; the results demonstrated that the plume characteristic evolved depending on the significant effects on the plume. When the plume was mainly affected by the hydraulic gradient, it rapidly moved from the injection point to the last boundary; in contrast, when it was influenced primarily by density-driven CO2 convective flow, it flowed diagonally downward in the shape of varied branches. The numerical model calculated the migration of the CO2-dissolved water plume affected by both factors. The laboratory experiment and numerical simulation results suggest that the migration of a CO2-dissolved water plume may be affected by the hydraulic gradient and density-driven CO2 convective transport. As such, these factors should be considered when designing and analyzing CO2 monitoring signals to detect CO2 leaks from shallow aquifer systems.

The stability analysis based on viscous theory of Faraday waves in Hele–Shaw cells

The linear instability of Faraday waves in Hele–Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of contact angle. A new hydrodynamic model is thus derived and solved semi-analytically. The contribution of viscosity to critical acceleration amplitude is slight compared to other factors associated with dissipation, and the potential flow theory is sufficient to describe onset based on the present study, but the rotational component of velocity can change the timing of onset largely, which paradoxically comes from the viscosity. The model degenerates into a novel damped Mathieu equation if the viscosity is dropped with two damping terms referring to the gap-averaged damping and dissipation from dynamic contact angle, respectively. The former increases when the gap size decreases, and the latter grows as frequency rises. When it comes to the dispersion relation of Faraday waves, an unusual detuning emerges due to the imaginary part of the gap-averaged damping.

Wall effect on single bubble rising in a Hele–Shaw cell

Single air bubble rising near vertical wall in a Hele–Shaw cell was investigated experimentally. Bubbles with a large range of size from 4.46 mm to 21.68 mm were generated. A vertical wall was introduced in the cell, and the initial distance between the wall and the bubble releasing position was varied systematically to study the wall effect on the rising dynamics. Rising trajectory, bubble morphology, and rising characteristics were analyzed. Bubble will migrates away from the wall, and the trajectory transits from rectilinear path to zigzag. Two mechanisms of zigzag were revealed as “rigid zigzag” for the small bubble and “contracting zigzag” for the large bubble. It is always easier to zigzag for a more rounded bubble, and migration is always stronger with a smaller normalized initial distance.

Disorder-induced non-linear growth of fingers in immiscible two-phase flow in porous media

Immiscible two-phase flow in porous media produces different types of patterns depending on the capillary number Ca and viscosity ratio M. At high Ca, viscous instability of the fluid–fluid interface occurs when the displaced fluid is the more viscous, and leads to viscous fingering, which is believed to exhibit the same growth behavior as the viscously-unstable fingers observed in Hele–Shaw cells by Saffman and Taylor [“The penetration of a fluid into a porous medium or Hele–Shaw cell containing a more viscous liquid,” Proc. R. Soc. London 245, 312 (1958)], or as diffusion-limited aggregates (DLA). In such Laplacian growth processes, the interface velocity depends linearly on the local gradient of the physical field that drives the growth process (for two-phase flow, the pressure field). However, a non-linear power-law dependence between the flow rate and the global pressure drop, reminiscent of what has also been observed for steady-state two-phase flow in porous media, was evidenced experimentally for the growth of viscously-unstable drainage fingers in two-dimensional porous media, 20 years ago. Here, we revisit this flow regime using dynamic pore-network modeling and explore the non-linearity in the growth properties. We characterize the previously unstudied dependencies of the statistical finger width and non-linear growth law's exponent on Ca, and discuss quantitatively, based on theoretical arguments, how disorder in the capillary barriers controls the growth process' non-linearity, and why the flow regime crosses over to Laplacian growth at sufficiently high Ca. In addition, the statistical properties of the fingering patterns are compared to those of Saffman–Taylor fingers, DLA growth patterns, and the results from the aforementioned previous experimental study.

Immiscible invasion of granular suspension by high-viscosity liquid

We investigate the morphology and dynamics of the pattern of immiscible invasion by injecting a high-viscosity liquid into a granular suspension consisting of movable solid grains in a low-viscosity liquid. Laboratory experiments conducted in a Hele–Shaw cell shed light on how the frictional forces of the grains and the viscous forces of the liquids affect the instability of the liquid–liquid interface and the formation of viscous fingers. The frictional force increases with an increase in either the volume fraction or the size of the grains, leading to higher resistance to the invading pattern. Upon changing the grain shape from spherical to irregular, both the frictional force and the rotational energy of the grains increase, resulting in more numerous but narrower fingers. Increasing either the injection rate or the viscosity of the injected liquid increases the viscous pressure within the fingers, promoting the splitting of the pattern. Although the defending liquid always has a lower viscosity than the invading liquid in this study, the former's viscous force becomes non-negligible as the viscosity ratio of the invading liquid to the defending liquid decreases to near unity, which destabilizes the fluid–fluid interface and causes a transition to an asymmetric pattern.

Primary bifurcation mechanism, heat transfer and bicriticality in time temperature-modulated Rayleigh–Bénard convection in a Hele–Shaw cell

In this paper, we perform a detailed numerical study of the linear dynamics of Rayleigh–Bénard convection in a fluid layer confined in a Hele–Shaw cell and subjected to a temperature gradient with a stationary and a periodic time-dependent component. Using Floquet theory for time and the spectral method for space, we show that the system exhibits three classes of time-dependent solutions, namely harmonic, sub-harmonic and quasi-periodic instabilities. These compete into the primary bifurcation driven by two different mechanisms depending on the modulation amplitude. Indeed, harmonic convective rolls, driven by the stationary thermal gradient, arise below critical modulation amplitudes beyond which the well-known parametric resonance mechanism is responsible for the development of convective rolls. In addition, it is revealed that the convective flow reversal could identify this exchange of instability mechanisms occurring via either bicritical states with codimension-two bifurcation points between harmonic and subharmonic modes or via displacement of Floquet multipliers in the Floquet-complex plane. This latter scenario sets in between subharmonic and quasiperiodic instability modes in the high frequency limit by varying the phase-lag between the temperatures of the lower and upper boundaries. Moreover, it is shown that the nature of the instability mechanism alters considerably the heat transfer dynamics of the system.

Air invasion into three-dimensional foam induces viscous fingering instabilities

We conducted an experimental investigation to examine the immiscible radial displacement flows of air invading three-dimensional foam in a Hele-Shaw cell. Our study successfully identified three distinct flow regimes. In the initial regime, characterized by relatively low fingertip velocities, the foam underwent a slow displacement through plug flow. During this process, the three-phase contact lines slipped at the cell walls. Notably, we discovered that the air injection pressure exhibited a proportional relationship with the power of the fingertip velocity. This relationship demonstrated excellent agreement with a power law, where the exponent was determined to be 2/3. Transitioning to the second regime, we observed relatively high velocities, resulting in the displacement of the foam as a plug within single layers of foam bubbles. The movement of these bubbles near the cell walls was notably slower. Similar to the first regime, the behavior in this regime also adhered to a power law. In the third regime, which manifested at higher air injection pressures, the development of air fingers occurred through narrow channels. These channels had the potential to isolate the air fingers as they underwent a process of "healing." Furthermore, our results unveiled a significant finding that the width of the air fingers exhibited a continuous scaling with the air injection pressure, irrespective of the flow regimes being observed.

Synthesis and Characterization of Magnetic Nanoparticles and its Study to Displace Oil from a Hele-Shaw Cell

Introduction:: Oil spill incidents caused by human activities can cause major habitat damage and pose serious threats to all living organisms living on and within sources of water and soil. Finding a solution for oil spills is necessary to protect ecosystems, the environment, and health. Nanotechnology seems to be an interesting tool in many applications, such as soil and water remediation and oil recovery. Nanoparticles are a good alternative since they are not as expensive as chemicals used to remove oil. Objective:: The prime purpose of this research work was the comparison of the additional displacement of sunflower oil from a single fracture using ferrofluids prepared with bare and novel covalent functionalized magnetic nanoparticles. Experiences were performed at constant nanoparticle concentration and variable flow rate and at constant flow rate and variable nanoparticle concentration. The novel ferrofluid stability and its recovery properties related to a low-cost process were explored. Methods:: Tests were carried out by image analysis. Stable ferrofluids were prepared using magnetic nanoparticles (MNPs) and novel covalent functionalized magnetic nanoparticles (MSMs). Their ability to displace the residual oil in a single fracture model previously invaded by an aqueous brine solution was tested. A flow channel of a single fracture by a typical transparent Hele-Shaw cell with 12% of its area covered by a random distribution of obstacles was modeled. Oil recovery was performed at three different flow rates: 0.36, 1.80, and 3.60 mL min-1, using relatively low ferrofluid concentrations (0.0125 wt%). Oil recovery was also carried out with MSM ferrofluid at a constant flow rate of 1.80 and 3.60 mL min-1 at different nanoparticle concentrations (0.00625, 0.0125, and 0.025 wt%). Results:: Ferrofluids prepared with MSMs were more effective for oil recovery than those prepared with bare nanoparticles due to their surfactant behavior for all flows studied here. A 7.86% extra percentage of oil was removed after brine flooding. Oil recovery using MSM ferrofluid at a constant flow rate of 1.80 and 3.60 mL min-1 increased linearly with nanoparticle concentration. Magnetic nanoparticles can be efficiently recovered and reused in at least three oil displacements for the fracture model used as covalent functionalization promotes ferrofluids' stability. Conclusion:: The characteristics of the MSM amphiphilic novel coating cause the nanoparticles to be attracted to both water and oil, enhancing oil displacement. These results indicate that this novel material, whose structure stability is related to the covalent bonding of organic coating, can be considered for remediation and oil recovery in fractured media

Extensive tip-splitting of injected organic liquid into an aqueous viscoelastic fluid

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele–Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process.

Optimal control of viscous fingering

The paper considers the problem of optimally filling a Hele-Shaw cell. The system is subject to viscous fingering effect. It is shown that, despite the threshold terms appearing on the right-hand side of the governing equations, the dynamics can be rewritten using several prime integrals. This allows reforming optimal control problems for the Fourier modes describing the fluid interface into smooth optimization problems, in the sense of Gâteaux derivative. Some numerical experiments illustrate the advantages of using the optimal solutions obtained using this reformulation instead of the currently known time-dependent injection rates.

Oscillatory nonlinear thermal instability in nanoliquid under gravity modulation within Hele-Shaw cell

Abstract The effect of gravity-field modulation is investigated in a nano liquid-confined Hele-Shaw cell. This study aims to finish the work described in (S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, “Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell,” Int. J. Heat Mass Transfer, vol. 145, no. 7, p. 072501, 2023) for oscillatory convection. The existence of the complex Ginzburg-Landau equation (CGLE) model is constrained by the requirement ω 2 > 0. The magnetic fluxes in the Hele-shaw cell are governed by CGLE with g-jitter. The quantity of heat-mass transfer is examined in the presence of a g-jitter. In addition, the findings of our research on transport analysis indicate that oscillatory mode is preferable to stationary mode. It is also found that the gravity-driven Hele-Shaw layer has lower transport properties. Further, the transport analysis is compared to previous research and shown to have improved results.

Capillary waves and dendritic instability on radial Hele–Shaw displacements

The displacement of a fluid by another less viscous one in isotropic quasi-two-dimensional Hele–Shaw cells typically leads to viscous fingering patterns characterized by repeated tip-splitting and side-branching. When anisotropy is present, the viscous fingering patterns are replaced by dendritic instability. In isotropic cells, Couder et al. [“Dendritic growth in the Saffman-Taylor experiment,” Europhys. Lett. 2, 437 (1986)] induced the growth of a dendritic finger by placing a small isolated bubble in contact with the tip of a finger. Moreover, in rectangular displacements, Kopf-Sill and Homsy [“Narrow fingers in a Hele–Shaw cell,” Phys. Fluids 30, 2607–2609 (1987)] observed for specific ranges of modified capillary numbers, Ca, that narrow fingers develop into dendritic patterns after carefully cleaning the Hele–Shaw cell with a soap solution. In the current work, by injecting air to radially displace a lubricant oil with strong adsorption properties, we observe for the first time the growth of dendritic instability in displacements confined in isotropic Hele–Shaw cells in the absence of air bubbles driving the fingertip. These structures are driven by the formation of capillary waves inside the finger adjacent to the Hele–Shaw surfaces. Furthermore, we compare displacements of different materials at similar high Ca values and obtain significantly different morphological results, indicating the pattern formation may not scale with this parameter in this range. Discrepancies are explained based on both wetting and inertia effects.

A comparative study of a viscous froth lens in two and three dimensions

The two-dimensional (2D) viscous froth model was initially designed to capture the dynamic behavior of dry foams within a Hele–Shaw cell, characterized by two parallel covering plates separated by a small gap. However, due to its inherent 2D nature, this model does not explicitly account for the dimension across the gap. To address this limitation, we have opted for a three-dimensional (3D) version of the viscous froth model. In this 3D model, the dynamic effect is introduced through the motion of the surface Plateau borders, while the configurations of films in bulk are determined via surface energy minimization subject to specified bubble volumes and surface Plateau border locations. We use this 3D model to simulate the motion of a viscous froth lens within a straight channel. The steady states of the viscous froth lens in 3D are primarily influenced by the driving velocity-to-gap size ratio, particularly at relatively small values of this ratio. By contrast, as the ratio becomes relatively large, the gap size begins to play a significant role in influencing the behavior of the viscous froth lens in 3D. Differences are observed in the steady-state configurations of the viscous froth lens in 3D when compared to those in 2D. However, the behavior of the viscous froth lens in 2D can be better aligned with the results in 3D by treating the drag coefficient required in the 2D viscous froth model as a fitting parameter. A further quantitative analysis indicates that the drag coefficient needed in the 2D viscous froth model may not serve as a uniform parameter for the entire foam structure. Instead, it may depend on the specific location along the evolving foam films over time.