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de Oliveira Pereira VH, Barros W. Detachment forces during parallel-plate gap separation mediated by a simple yield-stress fluid. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:7. [PMID: 38261239 DOI: 10.1140/epje/s10189-023-00397-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 12/14/2023] [Indexed: 01/24/2024]
Abstract
In this work we have monitored the multiple stages of the normal traction force response of a yield-stress fluid confined between two circular parallel plates that are separated at constant velocity. At narrow initial gaps, the air-fluid interface suffers from the Saffman-Taylor instability, confirmed by visual inspection of fingering patterns imprinted on the fluid. At larger initial gaps, the fluid preserves the initially imposed circular symmetry of the confining plates, indicating the absence of instability. Due to the system characteristics and experimental environment, the multiple traction force contributions occurred in cascade, permitting us to isolate the adhesion responses associated with viscosity, capillarity, and yield stress. Employing a standard Herschel-Bulkley model, we assessed the scaling of the traction force in multiple regimes-specifically, evaluating the dependencies of the fingering to yield-stress transitions.
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Affiliation(s)
- Vítor Hugo de Oliveira Pereira
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Cidade Universitária, 50670-901, Recife, Pernambuco, Brazil
| | - Wilson Barros
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Cidade Universitária, 50670-901, Recife, Pernambuco, Brazil.
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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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Coutinho ÍM, Miranda JA. Role of interfacial rheology on fingering instabilities in lifting Hele-Shaw flows. Phys Rev E 2023; 108:025104. [PMID: 37723719 DOI: 10.1103/physreve.108.025104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 08/06/2023] [Indexed: 09/20/2023]
Abstract
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.
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Affiliation(s)
- Írio M Coutinho
- Departamento de Física, Universidade Federal de Pernambuco, CCEN, Recife, Pernambuco 50670-901, Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, CCEN, Recife, Pernambuco 50670-901, Brazil
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Anjos PHA, Rocha FM, Dias EO. Controlling fluid adhesion force with electric fields. Phys Rev E 2022; 106:055109. [PMID: 36559446 DOI: 10.1103/physreve.106.055109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2022] [Accepted: 10/29/2022] [Indexed: 06/17/2023]
Abstract
Developing adhesives whose bond strength can be externally manipulated is a topic of considerable interest for practical and scientific purposes. In this work, we propose a method of controlling the adhesion force of a regular fluid, such as water and/or glycerol, confined between two parallel plates by applying an external electric field. Our results show the possibility of enhancing or diminishing the bond strength of the liquid sample by appropriately tuning the intensity and direction of the electric current generated by the applied electric field. Furthermore, we verify that, for a given direction of the electric current, the adhesion force can be reduced enough for the fluid to lose its adhesive properties and begin exerting a force to move apart the confining plates. In these circumstances, we obtain an analytical expression for the minimum electric current required to detach the plates without requiring the action of an external force.
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Affiliation(s)
- Pedro H A Anjos
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | | | - Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
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Wang Y, Hensel R, Arzt E. Attachment of bioinspired microfibrils in fluids: transition from a hydrodynamic to hydrostatic mechanism. J R Soc Interface 2022; 19:20220050. [PMID: 35382580 PMCID: PMC8984370 DOI: 10.1098/rsif.2022.0050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Reversible and switchable adhesion of elastomeric microstructures has attracted significant interest in the development of grippers for object manipulation. Their applications, however, have often been limited to dry conditions and adhesion of such deformable microfibrils in the fluid environment is less understood. In the present study, we performed adhesion tests in silicone oil using single cylindrical microfibrils of a flat-punch shape with a radius of 80 µm. Stiff fibrils were created using three-dimensional printing of an elastomeric resin with an elastic modulus of 500 MPa, and soft fibrils, with a modulus of 3.3 MPa, were moulded in polyurethane. Our results suggest that adhesion is dominated by hydrodynamic forces, which can be maximized by stiff materials and high retraction velocities, in line with theoretical predictions. The maximum pull-off stress of stiff cylindrical fibrils is 0.6 MPa, limited by cavitation and viscous fingering, occurring at retraction velocities greater than 2 µm s-1. Next, we add a mushroom cap to the microfibrils, which, in the case of the softer material, deforms upon retraction and leads to a transition to a hydrostatic suction regime with higher pull-off stresses ranging from 0.7 to 0.9 MPa. The effects of elastic modulus, fibril size and viscosity for underwater applications are illustrated in a mechanism map to provide guidance for design optimization.
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Affiliation(s)
- Yue Wang
- INM - Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany
| | - René Hensel
- INM - Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany
| | - Eduard Arzt
- INM - Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany.,Department of Materials Science and Engineering, Saarland University, Campus D2 2, 66123 Saarbrücken, Germany
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Coutinho ÍM, Rocha FM, Miranda JA. Viscous normal stresses and fingertip tripling in radial Hele-Shaw flows. Phys Rev E 2021; 104:045106. [PMID: 34781440 DOI: 10.1103/physreve.104.045106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 10/12/2021] [Indexed: 11/07/2022]
Abstract
Viscous fingering in radial Hele-Shaw cells is markedly characterized by the occurrence of fingertip splitting, where growing fingered structures bifurcate at their tips, via a tip-doubling process. A much less studied pattern-forming phenomenon, which is also detected in experiments, is the development of fingertip tripling, where a finger divides into three. We investigate the problem theoretically, and employ a third-order perturbative mode-coupling scheme seeking to detect the onset of tip-tripling instabilities. Contrary to most existing theoretical studies of the viscous fingering instability, our theoretical description accounts for the effects of viscous normal stresses at the fluid-fluid interface. We show that accounting for such stresses allows one to capture the emergence of tip-tripling events at weakly nonlinear stages of the flow. Sensitivity of fingertip-tripling events to changes in the capillary number and in the viscosity contrast is also examined.
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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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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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