Lifting Hele-Shaw Cell Research Articles

Stability Transition in Gap Expansion-Driven Interfacial Flow.

We investigate interfacial instability in a lifting Hele-Shaw cell by experiments and theory. We characterize the unexplored transition from stable to unstable patterns under a wide range of controlling parameters. Surprisingly, we find that the perturbation growth rate-based criterion for the onset of instability from linear stability theory is too strict by over 3 orders of magnitude. To reconcile this striking discrepancy, we propose a new criterion based on perturbation amplitude, which is in excellent agreement with the experimental results. We further show that the fingering pattern evolves to produce a hierarchical fluid structure and derive a theoretical equation to predict the fingering evolution.

Role of interfacial rheology on fingering instabilities in lifting Hele-Shaw flows.

The lifting Hele-Shaw cell setup is a popular modification of the classic, fixed-gap, radial viscous fingering problem. In the lifting cell configuration, the upper cell plate is lifted such that a more viscous inner fluid is invaded by an inward-moving outer fluid. As the fluid-fluid interface contracts, one observes the rising of distinctive patterns in which penetrating fingers having rounded tips compete among themselves, reaching different lengths. Despite the scholarly and practical relevance of this confined lifting flow problem, the impact of interfacial rheology effects on its pattern-forming dynamics has been overlooked. Authors of recent studies on the traditional injection-induced radial Hele-Shaw flow and its centrifugally driven variant have shown that, if the fluid-fluid interface is structured (i.e., laden with surfactants, particles, proteins, or other surface-active entities), surface rheological stresses start to act, influencing the development of the viscous fingering patterns. In this paper, we investigate how interfacial rheology affects the stability as well as the shape of the emerging fingered structures in lifting Hele-Shaw flows, at linear and early nonlinear dynamic stages. We tackle the problem by utilizing the Boussinesq-Scriven model to describe the interface and by employing a perturbative mode-coupling scheme. Our linear stability results show that interfacial rheology effects destabilize the interface. Furthermore, our second-order findings indicate that interfacial rheology significantly alters intrinsically nonlinear morphological features of the shrinking interface, inducing the formation of narrow sharp-tip penetrating fingers and favoring enhanced competition among them.

Inertia-induced dendriticlike patterns in lifting Hele-Shaw flows

A theoretical analysis of inertial effects in viscous fingering instabilities in a lifting Hele-Shaw cell provides a physical explanation for the dendriticlike patterns observed in experiments where large lifting speeds are used. A generalized Darcy's law description and a perturbative mode-coupling theory are used to properly account for inertial effects, verifying that inertia induces a mechanism for finger side-branching formation and favors the intensification of finger competition events.

Elastic fingering patterns in confined lifting flows.

The elastic fingering phenomenon occurs when two confined fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes elastic. We study elastic fingering pattern formation in Newtonian fluids flowing in a lifting (time-dependent gap) Hele-Shaw cell. Using a mode-coupling approach, nonlinear effects induced by the interplay between viscous and elastic forces are investigated and the weakly nonlinear behavior of the fluid-fluid interfacial patterns is analyzed. Our results indicate that the existence of the elastic interface allows the development of unexpected morphological behaviors in such Newtonian fluid flow systems. More specifically, we show that depending on the values of the governing physical parameters, the observed elastic fingering structures are characterized by the occurrence of either finger tip splitting or side branching. The impact of the elastic interface on finger-competition events is also discussed.

Controlling Viscous Fingering Using Time-Dependent Strategies.

Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. We report theoretical and experimental results on a time-dependent control strategy by manipulating the gap thickness b(t) in a lifting Hele-Shaw cell in the power-law form b(t)=b(1)t(1/7). Experimental results show good quantitative agreement with the predictions of linear stability analysis. By choosing the value of a single time-independent control parameter, we can either totally suppress the viscous fingering instability or maintain a series of nonsplitting viscous fingers during the fluid displacement process. In addition to the gap thickness of a Hele-Shaw cell, time-dependent control strategies can, in principle, also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tension between the two fluids.

Influence of wetting on fingering patterns in lifting Hele-Shaw flows.

We study the pattern formation dynamics related to the displacement of a viscous wetting fluid by a less viscous nonwetting fluid in a lifting Hele-Shaw cell. A perturbative weakly nonlinear analysis of the problem is presented. We focus on examining how wetting effects influence the morphology of the emerging interfacial patterns at the early nonlinear regime. Our analytical results indicate that wettability has a significant impact on the resulting nonlinear patterns. It restrains finger length variability while inducing the development of structures presenting short, blunt penetrating fingers of the nonwetting fluid, alternated by short, sharp fingers of the wetting fluid. The basic mode-coupling mechanisms leading to such behavior are discussed.

Determining the number of fingers in the lifting Hele-Shaw problem

The lifting Hele-Shaw cell flow is a variation of the celebrated radial viscous fingering problem for which the upper cell plate is lifted uniformly at a specified rate. This procedure causes the formation of intricate interfacial patterns. Most theoretical studies determine the total number of emerging fingers by maximizing the linear growth rate, but this generates discrepancies between theory and experiments. In this work, we tackle the number of fingers selection problem in the lifting Hele-Shaw cell by employing the recently proposed maximum-amplitude criterion [Dias and Miranda, Phys. Rev. E 88, 013016 (2013)]. Our linear stability analysis accounts for the action of capillary, viscous normal stresses, and wetting effects, as well as the cell confinement. The comparison of our results with very precise laboratory measurements for the total number of fingers shows a significantly improved agreement between theoretical predictions and experimental data.

Finger competition in lifting Hele-Shaw flows with a yield stress fluid

A weakly nonlinear approach is used to investigate interfacial pattern formation in a lifting Hele-Shaw cell containing a yield stress fluid surrounded by a fluid of negligible viscosity. By considering the onset of nonlinear effects and the regime in which viscous effects dominate over yield stress, we study how the system responds to changes in two controlling dimensionless parameters: (i) the geometric aspect ratio (ratio of the initially circular radius of the fluid-fluid interface to the initial Hele-Shaw cell plate spacing), and (ii) a yield stress parameter (relative measure of yield stress to viscous forces). Within this context, we discuss how these key factors influence interface stability and finger competition dynamics during early linear and intermediate stages of pattern evolution.

Computer simulation of viscous fingering in a lifting Hele-Shaw cell with grooved plates

We simulate viscous fingering generated by separating two plates with a constant force, in a lifting Hele-Shaw cell. Variation in the patterns for different fluid viscosity and lifting force is studied. Viscous fingering is strongly affected by anisotropy. We report a computer simulation study of fingering patterns, where circular or square grooves are etched on to the lower plate. Results are compared with experiments.

Fingering and pressure distribution in lifting Hele-Shaw cells with grooves: A computer simulation study

We report a computer simulation study of viscous fingering patterns in a lifting Hele-Shaw cell with grooves. Here circular or square grooves concentric to the plates are etched on the lower plate. Experiments show that the presence of such grooves affect formation of viscous fingers quite strongly. We report a simulated pressure map generated in such grooved cells, when the two plates are separated with a constant force and compare the patterns with experiments. Variation in the simulated patterns for different fluid viscosity and lifting force is also studied.

Adhesion and fingering in the lifting Hele-Shaw cell: Role of the substrate

The lifting Hele-Shaw cell (LHSC) is used to study adhesion as well as viscous fingering. In the present paper we report a series of observations of development of the interface for different viscous fluids, both Newtonian and non-Newtonian, in a LHSC operated at a constant lifting force. Glass and perspex are used as the plates in two different sets of experiments. The objectives are 1) to measure the time required to separate the plates as a function of the lifting force and 2) to note the force above which viscous fingering appears. We find that for the Newtonian fluids, the plate separation time follows a universal power law with the lifting force, irrespective of fluid and substrate. The non-Newtonian fluids too, with proper scaling obey the same power law. The appearance of fingering, however, depends on the properties of the fluid as well as the substrate. We suggest a modified form of the capillary number which controls the onset of fingering; this new quantity, termed the "fingering parameter" involves the dielectric constants of the substrate and fluid in addition to the viscosity and surface tension.

Fingering instabilities in adhesive failure

We study the fingering instabilities that occur in the debonding of model adhesives. We perform a linear analysis of the instability in the lifting Hele-Shaw cell, relevant for the failure of soft adhesives. The analysis is done for a Newtonian fluid but can be extended to shear-thinning fluids without any problem. When compared to experiment, significant differences are found between the linear theory and the experimental results. We therefore, discuss three-dimensional effects, that are found to improve the agreement; nevertheless significant differences between theory and experiment persist.

Radially interrupted viscous fingers in a lifting Hele-Shaw cell

Viscous fingers have been produced in the lifting Hele-Shaw cell (LHSC), with concentric circular grooves etched onto the lower plate. The invading fluid (air) enters the defending newtonian fluid-olive oil, as fingers proceeding radially inwards towards the centre. The fingers are interrupted at the circular groove, and reform as secondary fingers. The effect of the grooves is to speed up the fingering process considerably and the fingers now reach the centre much faster. We explain this by comparing the variation with time, in velocity of the fingers in the normal LHSC and the grooved cells. In the normal lifting HS cell the fingers move fastest on initial formation and slow down later. Since in case of the grooved plate, the fingers reform and receive a boost in their speed each time they encounter a groove, the fingers proceed to the centre faster.

Finger velocities in the lifting Hele–Shaw cell

Velocities of viscous fingers growing in a lifting Hele–Shaw cell are studied. The plates are separated by a pneumatic cylinder arrangement exerting a constant force. It is observed that with air invading a non-Newtonian oil-paint, finger velocities show an anomalous behaviour, with a rapid growth towards the end of the process. The correlation coefficient between neighbouring fingers shows the dominant modes selected as the pattern develops.

Discrete scale invariance in viscous fingering patterns

We study viscous fingering patterns in a lifting Hele-Shaw cell, where a non-Newtonian fluid (oil paint) is displaced by air. The lengths of the air fingers are measured and their cumulative distribution is seen to follow a power law with log-periodic oscillations indicating the presence of discrete scale invariance.

Air viscous fingers in isotropic fluid and liquid crystals obtained in lifting hele-shaw cell geometry

The air viscous fingers in glycerol, nematic and smectic liquid crystals are studied using the so-called lifting Hele-Shaw cell geometry. It is shown experimentally that in this case a critical velocity of lifting exists, below which the viscous fingers do not grow. The dependences of this velocity and critical wavelength upon various parameters are measured. The obtained experimental data in the case of small lifting angles are in satisfactory agreement with the phenomenological estimations for linear Hele-Shaw cells.