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Pouplard A, Tsai PA. Controlling viscous fingering instabilities of complex fluids. Sci Rep 2024; 14:2338. [PMID: 38282007 PMCID: PMC10822875 DOI: 10.1038/s41598-024-52218-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 01/16/2024] [Indexed: 01/30/2024] Open
Abstract
Despite their aesthetic elegance, wavy or fingering patterns emerge when a fluid of low viscosity pushes another immiscible fluid of high viscosity in a porous medium, producing an incomplete sweep and hampering several crucial technologies. Some examples include chromatography, printing, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enhanced oil recovery. Controlling such fingering instabilities is notoriously challenging and unresolved for complex fluids of varying viscosity because the fluids' mobility contrast is often predetermined and yet the predominant drive in determining a stable, flat or unstable, wavy interface. Here we show, experimentally and theoretically, how to suppress or control the primary viscous fingering patterns of a common type of complex fluids (of shear-thinning with a low yield stress) using a radially tapered cell of linearly varying gap thickness, h(r). Experimentally, we displace a complex viscous (PAA) solution with gas under a constant flow rate (Q), varied between 0.02 and 2 slpm (standard liter per minute), in a radially converging cell with a constant gap-thickness gradient, [Formula: see text]. A stable, uniform interface emerges at low Q and in a steeper cell (i.e., greater [Formula: see text]) for the complex fluids, whereas unstable fingering pattern at high Q and smaller [Formula: see text]. Our theoretical predictions with a simplified linear stability analysis show an agreeable stability criterion with experimental data, quantitatively offering strategies to control complex fluid-fluid patterns and displacements in microfluidics and porous media.
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Affiliation(s)
- Alban Pouplard
- Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada
| | - Peichun Amy Tsai
- Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada.
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Coutinho ÍM, Anjos PHA, Oliveira RM, Miranda JA. Fingering stabilization and adhesion force in the lifting flow with a fluid annulus. Phys Rev E 2024; 109:015104. [PMID: 38366430 DOI: 10.1103/physreve.109.015104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 01/04/2024] [Indexed: 02/18/2024]
Abstract
The lifting Hele-Shaw cell flow commonly involves the stretching of a viscous oil droplet surrounded by air, in the confined space between two parallel plates. As the upper plate is lifted, viscous fingering instabilities emerge at the air-oil interface. Such an interfacial instability phenomenon is widely observed in numerous technological and industrial applications, being quite difficult to control. Motivated by the recent interest in controlling and stabilizing the Saffman-Taylor instability in lifting Hele-Shaw flows, we propose an alternative way to restrain the development of interfacial disturbances in this gap-variable system. Our method modifies the traditional plate-lifting flow arrangement by introducing a finite fluid annulus layer encircling the central oil droplet, and separating it from the air. A second-order, perturbative mode-coupling approach is employed to analyze morphological and stability behaviors in this three-fluid, two-interface, doubly connected system. Our findings indicate that the intermediate fluid ring can significantly stabilize the interface of the central oil droplet. We show that the effectiveness of this stabilization protocol relies on the appropriate choice of the ring's viscosity and thickness. Furthermore, we calculate the adhesion force required to detach the plates, and find that it does not change significantly with the addition of the fluid envelope as long as it is sufficiently thin. Finally, we detect no distinction in the adhesion force computed for stable or unstable annular interfaces, indicating that the presence of fingering at the ring's boundaries has a negligible effect on the adhesion force.
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Affiliation(s)
- Írio M Coutinho
- Departamento de Física, Universidade Federal de Pernambuco, CCEN, Recife, Pernambuco 50670-901, Brazil
| | - Pedro H A Anjos
- Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
| | - Rafael M Oliveira
- Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, CCEN, Recife, Pernambuco 50670-901, Brazil
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Karnal P, Wang Y, Jha A, Gryska S, Barrios C, Frechette J. Interface Stabilization in Adhesion Caused by Elastohydrodynamic Deformation. PHYSICAL REVIEW LETTERS 2023; 131:138201. [PMID: 37831986 DOI: 10.1103/physrevlett.131.138201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2023] [Accepted: 08/22/2023] [Indexed: 10/15/2023]
Abstract
Interfacial instabilities are common phenomena observed during adhesion measurements involving viscoelastic polymers or fluids. Typical probe-tack adhesion measurements with soft adhesives are conducted with rigid probes. However, in many settings, such as for medical applications, adhesives make and break contact from soft surfaces such as skin. Here we study how detachment from soft probes alters the debonding mechanism of a model viscoelastic polymer film. We demonstrate that detachment from a soft probe suppresses Saffman-Taylor instabilities commonly encountered in adhesion. We suggest the mechanism for interface stabilization is elastohydrodynamic deformation of the probe and propose a scaling for the onset of stabilization.
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Affiliation(s)
- Preetika Karnal
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
- Department of Chemical and Biomolecular Engineering, Lehigh University, 124 East Morton Street, Building 205, Bethlehem, Pennsylvania 18015, USA
| | - Yumo Wang
- College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China
| | - Anushka Jha
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - Stefan Gryska
- 3M Center, 3M Company, Building 201-4N-01, St. Paul, Minnesota 55144-1000, USA
| | - Carlos Barrios
- Adaptive3D, 608 Development Drive, Plano, Texas 75074, USA
| | - Joelle Frechette
- Department of Chemical and Biomolecular Engineering, University of California Berkeley, Berkeley, California 94720, USA
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Conrado H, Dias EO, Miranda JA. Impact of interfacial rheology on finger tip splitting. Phys Rev E 2023; 107:015103. [PMID: 36797856 DOI: 10.1103/physreve.107.015103] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Fluid-fluid interfaces, laden with polymers, surfactants, lipid bilayers, proteins, solid particles, or other surface-active agents, often exhibit a rheologically complex response to deformations. Despite its academic and practical relevance to fluid dynamics and various other fields of research, the role of interfacial rheology in viscous fingering remains fairly underexplored. A noteworthy exception is the work by Li and Manikantan [Phys. Rev. Fluids 6, 074001 (2021)2469-990X10.1103/PhysRevFluids.6.074001], who used linear stability analysis to show that surface rheological stresses act to stabilize the development of radial viscous fingering at the linear regime. In this paper, we perform a perturbative, second-order mode-coupling analysis of the system and investigate the influence of interfacial rheology on the morphology of the fingering structures at early nonlinear stages of the dynamics. In particular, we focus on understanding how interfacial rheology impacts the emblematic finger tip-widening and finger tip-splitting phenomena that take place in radial viscous fingering in Hele-Shaw cells. We describe the viscous Newtonian fluid-fluid interface by using a Boussinesq-Scriven model, and derive a generalized Young-Laplace pressure jump condition at the fluid-fluid interface. In this framing, we go beyond the purely linear description and use Darcy's law to obtain a perturbative mode-coupling differential equation which describes the time evolution of the perturbation amplitudes, accurate to second order. Our early nonlinear mode-coupling results indicate that regardless of their stabilizing action at the linear regime, interfacial rheology effects favor finger tip widening, leading to the occurrence of enhanced finger tip-splitting events.
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Affiliation(s)
- Habakuk Conrado
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
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Effect of Hele–Shaw cell gap on radial viscous fingering. Sci Rep 2022; 12:18967. [DOI: 10.1038/s41598-022-22769-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 10/19/2022] [Indexed: 11/11/2022] Open
Abstract
AbstractThe flow through a Hele–Shaw cell is an experimental prototype to study the flow through a porous medium as well as the flow in microfluidic devices. In context with porous medium flows, it is used to visualize and understand hydrodynamic instabilities like viscous fingering (VF). The gap between the plates of the cell is an important parameter affecting the flow dynamics. However, the effect of the gap on the Hele–Shaw cell flows has been minimally explored. We perform experiments to understand the effect of the gap on VF dynamics. It is observed that a minimum gap is required to observe rigorous fingering instability. The onset time of instability, as well as the width of the fingers, increases with an increment in the gap due to a decrease in the convection. The instability increases with an increase in Péclet number, but the effect of gap width on fingering patterns is evident with broader fingers observed for larger b. The results are validated by performing numerical simulations. It is further shown that the gap-averaged three-dimensional simulations using the Stokes law approach and the two-dimensional Darcy’s law result in a small gap Hele–Shaw cell.
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Ho THM, Yang J, Tsai PA. Microfluidic mass transfer of CO 2 at elevated pressures: implications for carbon storage in deep saline aquifers. LAB ON A CHIP 2021; 21:3942-3951. [PMID: 34636830 DOI: 10.1039/d1lc00106j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Carbon capture and sequestration (CCS) in a deep saline aquifer is one of the most promising technologies to mitigate anthropologically emitted carbon dioxide. Accurately quantifying the mass transport of CO2 at pore-scales is crucial but challenging for successful CCS deployment. Here, we conduct high-pressure microfluidic experiments, mimicking reservoir conditions up to 9.5 MPa and 35 °C, to elucidate the microfluidic mass transfer process of CO2 at three different states (i.e., gas, liquid, and supercritical phase) into water. We measure the size change of CO2 micro-bubbles/droplets generated using a microfluidic T-junction to estimate the volumetric mass transfer coefficient (kLa), quantifying the rate change of CO2 concentration under the driving force of concentration gradient. The results show that bubbles/droplets under high-pressure conditions reach a steady state faster than low pressure. The measured volumetric mass transfer coefficient increases with the Reynolds number (based on the liquid slug) and is nearly independent of the injection pressure for both the gas and liquid phases. In addition, kLa significantly enlarges with increasing high pressure at the supercritical state. Compared with various chemical engineering applications using millimeter-sized capillaries (with typical kLa measured ranging from ≈0.005 to 0.8 s-1), the microfluidic results show a significant increase in the volumetric mass transfer of CO2 into water by two to three orders of magnitude, O (102-103), with decreasing hydrodynamic diameter (of ≈50 μm).
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Affiliation(s)
- Tsai-Hsing Martin Ho
- Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9 Canada.
| | - Junyi Yang
- Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9 Canada.
| | - Peichun Amy Tsai
- Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9 Canada.
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Malekian S, Ahmadlouydarab M, Najjar R. Effects of zero-shear rate viscosity and interfacial tension on immiscible Newtonian-Non-Newtonian fluids morphology in radial displacement inside the Hele-Shaw cell. J Taiwan Inst Chem Eng 2021. [DOI: 10.1016/j.jtice.2021.07.042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Anjos PHA, Zhao M, Lowengrub J, Bao W, Li S. Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects. Phys Rev E 2021; 103:063105. [PMID: 34271714 DOI: 10.1103/physreve.103.063105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 05/29/2021] [Indexed: 11/07/2022]
Abstract
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically affects the pressure drop at the fluid-fluid interface by introducing a nonlinear dependence on the interfacial velocity. In this framework, two cases of interest are analyzed: The injection-driven flow (expanding evolution), and the lifting plate flow (shrinking evolution). In particular, we investigate the possibility of controlling the development of fingering instabilities in these two different Hele-Shaw setups when wetting effects are taken into account. By employing linear stability theory, we find the proper time-dependent injection rate Q(t) and the time-dependent lifting speed b[over ̇](t) required to control the number of emerging fingers during the expanding and shrinking evolution, respectively. Our results indicate that the consideration of wetting leads to an increase in the magnitude of Q(t) [and b[over ̇](t)] in comparison to the nonwetting strategy. Moreover, a spectrally accurate boundary integral approach is utilized to examine the validity and effectiveness of the controlling protocols at the fully nonlinear regime of the dynamics and confirms that the proposed injection and lifting schemes are feasible strategies to prescribe the morphologies of the resulting patterns in the presence of the wetting film.
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Affiliation(s)
- Pedro H A Anjos
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Meng Zhao
- Department of Mathematics, University of California Irvine, Irvine, California 92697, USA
| | - John Lowengrub
- Department of Mathematics, University of California Irvine, Irvine, California 92697, USA
| | - Weizhu Bao
- Department of Mathematics, National University of Singapore, Singapore 119067
| | - Shuwang Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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Coutinho ÍM, Miranda JA. Control of viscous fingering through variable injection rates and time-dependent viscosity fluids: Beyond the linear regime. Phys Rev E 2021; 102:063102. [PMID: 33466051 DOI: 10.1103/physreve.102.063102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 11/25/2020] [Indexed: 11/07/2022]
Abstract
During the past few years, researchers have been proposing time-dependent injection strategies for stabilizing or manipulating the development of viscous fingering instabilities in radial Hele-Shaw cells. Most of these studies investigate the displacement of Newtonian fluids and are entirely based on linear stability analyses. In this work, linear stability theory and variational calculus are used to determine closed-form expressions for the proper time-dependent injection rates Q(t) required to either minimize the interface disturbances or to control the number of emerging fingers. However, this is done by considering that the displacing fluid is non-Newtonian and has a time-varying viscosity. Moreover, a perturbative third-order mode-coupling approach is employed to examine the validity and effectiveness of the controlling protocols dictated by these Q(t) beyond the linear regime and at the onset of nonlinearities.
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Affiliation(s)
- Írio M Coutinho
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
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Eslami A, Basak R, Taghavi SM. Multiphase Viscoplastic Flows in a Nonuniform Hele-Shaw Cell: A Fluidic Device to Control Interfacial Patterns. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.9b06064] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ali Eslami
- Department of Chemical Engineering, Université Laval, Québec, Canada
| | - Raunak Basak
- Department of Chemical Engineering, Université Laval, Québec, Canada
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Computational Analysis of Interfacial Dynamics in Angled Hele-Shaw Cells: Instability Regimes. Transp Porous Media 2019. [DOI: 10.1007/s11242-019-01371-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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