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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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2
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Coutinho ÍM, Miranda JA. Field-controlled flow and shape of a magnetorheological fluid annulus. Phys Rev E 2022; 106:025105. [PMID: 36109920 DOI: 10.1103/physreve.106.025105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Accepted: 08/05/2022] [Indexed: 06/15/2023]
Abstract
We investigate the behavior of a magnetorheological (MR) fluid annulus, bounded by a nonmagnetic fluid and confined in a Hele-Shaw cell, under the simultaneous effect of in-plane, external radial and azimuthal magnetic fields. A second-order mode-coupling theory is used to study the early nonlinear stage of the pattern-forming dynamics. We examine changes in the morphology of the MR fluid annular structure as a function of its magnetic-field-tunable rheological properties, as well as the combined magnetic field's intensities, and thickness of the ring. Our weakly nonlinear perturbative results show that, depending on the system control parameters, the MR fluid annulus adopts various stationary shapes. These equilibrium annular structures present slightly bent, asymmetric fingered protrusions which may emerge on the inner, outer, or even on both boundaries of the magnetic fluid ring. On top of these morphological changes, we find that the resulting permanent shape patterns rotate with a well defined angular velocity. We focus on analyzing how the overall shape of the fingered patterns, in particular their sharpness and asymmetric form, as well as the number of resulting fingers are impacted by the magnetic-field-dependent yield stress of the MR fluid annulus. The influence of the magnetically controlled rheological properties of the MR fluid on the angular velocity of the rotating annulus is also scrutinized.
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Affiliation(s)
- Írio M Coutinho
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil
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Fontana JV, Miranda JA. Elastic fingering patterns in confined lifting flows. Phys Rev E 2016; 94:033110. [PMID: 27739751 DOI: 10.1103/physreve.94.033110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2016] [Indexed: 11/07/2022]
Abstract
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.
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Affiliation(s)
- João V Fontana
- 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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Dias EO, Lira SA, Miranda JA. Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023003. [PMID: 26382499 DOI: 10.1103/physreve.92.023003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Indexed: 06/05/2023]
Abstract
Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.
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Affiliation(s)
- Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - Sérgio A Lira
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-900 Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
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Anjos PHA, Dias EO, Dias L, Miranda JA. Adhesion force in fluids: effects of fingering, wetting, and viscous normal stresses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:013003. [PMID: 25679704 DOI: 10.1103/physreve.91.013003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Indexed: 06/04/2023]
Abstract
Probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. This is done by recording the adhesion force that is required to lift the upper plate, while the lower plate is kept at rest. During the lifting process, it is known that the interface separating the confined fluids is deformed, causing the emergence of intricate interfacial fingering structures. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, causing a decrease in intensity. In this work, we propose an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting and viscous normal stresses. The role played by the system's spatial confinement is also considered. We show that the incorporation of all these physical ingredients is necessary to provide a better agreement between theoretical predictions and experiments.
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Affiliation(s)
- Pedro H A Anjos
- 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
| | - Laércio 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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Dias EO, Miranda JA. Determining the number of fingers in the lifting Hele-Shaw problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:043002. [PMID: 24229271 DOI: 10.1103/physreve.88.043002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2013] [Indexed: 06/02/2023]
Abstract
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.
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Affiliation(s)
- Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil
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Dias EO, Miranda JA. Taper-induced control of viscous fingering in variable-gap Hele-Shaw flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:053015. [PMID: 23767628 DOI: 10.1103/physreve.87.053015] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2013] [Indexed: 06/02/2023]
Abstract
Variable-gap Hele-Shaw flows consider viscous fluid displacements resulting from the lifting or squeezing of the upper cell plate, while the lower plate remains at rest. Conventionally, researchers focus on the situation in which the cell plates are perfectly parallel. We study a slightly different version of the problem, where the upper plate is gently inclined so that the plates are no longer parallel. Within this tapered Hele-Shaw cell context we examine how the presence of such a small gap gradient affects the stability properties of the fluid-fluid interface. Linear stability analysis indicates that the existence of the taper offers a simple geometric way to control the development of interfacial fingering instabilities under both lifting and squeeze flow circumstances.
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Affiliation(s)
- Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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Dias EO, Miranda JA. Variational scheme towards an optimal lifting drive in fluid adhesion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:046322. [PMID: 23214692 DOI: 10.1103/physreve.86.046322] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Indexed: 06/01/2023]
Abstract
One way of determining the adhesive strength of liquids is provided by a probe-tack test, which measures the force or energy required to pull apart two parallel flat plates separated by a thin fluid film. The vast majority of the existing theoretical and experimental works in fluid adhesion use very viscous fluids, and consider a linear drive L(t)∼Vt with constant lifting plate velocity V. This implies a given energy cost and large lifting force magnitude. One challenging question in this field pertains to what would be the optimal time-dependent drive Lopt(t) for which the adhesion energy would be minimized. We use a variational scheme to systematically search for such Lopt(t). By employing an optimal lifting drive, in addition to saving energy, we verify a significant decrease in the adhesion force peak. The effectiveness of the proposed lifting procedure is checked for both Newtonian and power-law fluids.
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Affiliation(s)
- Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
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Dias EO, Miranda JA. Effect of fluid inertia on probe-tack adhesion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:016312. [PMID: 22400663 DOI: 10.1103/physreve.85.016312] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2011] [Revised: 12/14/2011] [Indexed: 05/31/2023]
Abstract
One way of determining the adhesive strength of liquids is provided by a probe-tack test, which involves measuring the force required to pull apart two parallel flat plates separated by a thin fluid film. The large majority of existing theoretical and experimental work on probe-tack adhesion use very viscous fluids and considers relatively low lifting plate velocities, so that effects due to fluid inertia can be neglected. However, the employment of low-viscosity fluids and the increase in operating speeds of modern lifting apparatus can modify this scenario. By dealing with a proper gap averaging of the Navier-Stokes equation, we obtain a modified Darcy-law-like description of the problem and derive an adhesion force which incorporates the effects of fluid inertia, fluid viscosity (for Newtonian and power law fluids), and the contribution of the compliance and inertia of the probe-tack apparatus. Our results indicate that fluid inertia may have a significant influence on the adhesion force profiles, inducing a considerable increase in the force peaks and producing oscillations in the force-displacement curves as the plate-plate separation is increased. The combined role of inertial and non-Newtonian fluid behaviors on the adhesion force response is also investigated.
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Affiliation(s)
- Eduardo O Dias
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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Lira SA, Miranda JA, Oliveira RM. Stationary shapes of confined rotating magnetic liquid droplets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:036318. [PMID: 21230182 DOI: 10.1103/physreve.82.036318] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2010] [Indexed: 05/30/2023]
Abstract
We study the family of steady shapes which arise when a magnetic liquid droplet is confined in a rotating Hele-Shaw cell and subjected to an azimuthal magnetic field. Two different scenarios are considered: first, the magnetic fluid is assumed to be a Newtonian ferrofluid, and then it is taken as a viscoelastic magnetorheological fluid. The influence of the distinct material properties of the fluids on the ultimate morphology of the emerging stationary patterns is investigated by using a vortex-sheet formalism. Some of these exact steady structures are similar to the advanced time patterns obtained by existing time-evolving numerical simulations of the problem. A weakly nonlinear approach is employed to examine this fact and to gain analytical insight about relevant aspects related to the stability of such exact stationary solutions.
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Affiliation(s)
- Sérgio A Lira
- Departamento de Física, LFTC, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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Lira SA, Miranda JA, Oliveira RM. Field-induced patterns in confined magnetorheological fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046303. [PMID: 20481823 DOI: 10.1103/physreve.81.046303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2009] [Indexed: 05/29/2023]
Abstract
We study the behavior of a magnetorheological fluid droplet confined to a Hele-Shaw cell in the presence of an applied radial magnetic field. Interfacial pattern formation is investigated by considering the competition among capillary, viscoelastic, and magnetic forces. The contribution of a magnetic field-dependent yield stress is taken into account. Linear stability analysis reveals the stabilizing role played by yield stress. On the other hand, a mode-coupling approach predicts that the resulting fingering structures should become less and less sharp as yield stress effects are increased. By employing a vortex-sheet formalism we have been able to identify a family of exact stationary solutions of the problem, unveiling the development of swollen polygonal patterns. A suggestive magnetically controlled shape transition in which the edges of the patterns change from convex to concave has been also identified.
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Affiliation(s)
- Sérgio A Lira
- Departamento de Física, LFTC, Universidade Federal de Pernambuco, Recife 50670-901, PE, Brazil
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