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Bureau L, Coupier G, Salez T. Lift at low Reynolds number. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:111. [PMID: 37957450 DOI: 10.1140/epje/s10189-023-00369-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 10/19/2023] [Indexed: 11/15/2023]
Abstract
Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.
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Affiliation(s)
- Lionel Bureau
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000, Grenoble, France.
| | | | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France.
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Binysh J, Chakraborty I, Chubynsky MV, Melian VLD, Waitukaitis SR, Sprittles JE, Souslov A. Modeling Leidenfrost Levitation of Soft Elastic Solids. PHYSICAL REVIEW LETTERS 2023; 131:168201. [PMID: 37925690 DOI: 10.1103/physrevlett.131.168201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 07/14/2023] [Accepted: 09/05/2023] [Indexed: 11/07/2023]
Abstract
The elastic Leidenfrost effect occurs when a vaporizable soft solid is lowered onto a hot surface. Evaporative flow couples to elastic deformation, giving spontaneous bouncing or steady-state floating. The effect embodies an unexplored interplay between thermodynamics, elasticity, and lubrication: despite being observed, its basic theoretical description remains a challenge. Here, we provide a theory of elastic Leidenfrost floating. As weight increases, a rigid solid sits closer to the hot surface. By contrast, we discover an elasticity-dominated regime where the heavier the solid, the higher it floats. This geometry-governed behavior is reminiscent of the dynamics of large liquid Leidenfrost drops. We show that this elastic regime is characterized by Hertzian behavior of the solid's underbelly and derive how the float height scales with materials parameters. Introducing a dimensionless elastic Leidenfrost number, we capture the crossover between rigid and Hertzian behavior. Our results provide theoretical underpinning for recent experiments, and point to the design of novel soft machines.
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Affiliation(s)
- Jack Binysh
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
| | | | - Mykyta V Chubynsky
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Vicente Luis Díaz Melian
- Institute of Science and Technology Austria (ISTA), Lab Building West, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Scott R Waitukaitis
- Institute of Science and Technology Austria (ISTA), Lab Building West, Am Campus 1, 3400 Klosterneuburg, Austria
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Anton Souslov
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
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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: 1] [Impact Index Per Article: 1.0] [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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Gao Y, Sprinkle B, Springer E, Marr DW, Wu N. Rolling of soft microbots with tunable traction. SCIENCE ADVANCES 2023; 9:eadg0919. [PMID: 37083533 PMCID: PMC10121164 DOI: 10.1126/sciadv.adg0919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Microbot (μbot)-based targeted drug delivery has attracted increasing attention due to its potential for avoiding side effects associated with systemic delivery. To date, most μbots are rigid. When rolling on surfaces, they exhibit substantial slip due to the liquid lubrication layer. Here, we introduce magnetically controlled soft rollers based on Pickering emulsions that, because of their intrinsic deformability, fundamentally change the nature of the lubrication layer and roll like deflated tires. With a large contact area between μbot and wall, soft μbots exhibit tractions higher than their rigid counterparts, results that we support with both theory and simulation. Upon changing the external field, surface particles can be reconfigured, strongly influencing both the translation speed and traction. These μbots can also be destabilized upon pH changes and used to deliver their contents to a desired location, overcoming the limitations of low translation efficiency and drug loading capacity associated with rigid structures.
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Affiliation(s)
- Yan Gao
- Materials Science and Engineering Program, Colorado School of Mines, Golden, CO, USA
| | - Brennan Sprinkle
- Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, USA
| | - Ela Springer
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO, USA
| | - David W. M. Marr
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO, USA
- Corresponding author. (D.W.M.M.); (N.W.)
| | - Ning Wu
- Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO, USA
- Corresponding author. (D.W.M.M.); (N.W.)
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Kopecz-Muller C, Bertin V, Raphaël E, McGraw JD, Salez T. Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology. Proc Math Phys Eng Sci 2023. [DOI: 10.1098/rspa.2022.0832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/10/2023] Open
Abstract
When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which further complexifies the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.
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Affiliation(s)
- Caroline Kopecz-Muller
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
- Gulliver, CNRS UMR 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- Institut Pierre-Gilles de Gennes, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Vincent Bertin
- Physics of Fluids, Faculty of Sciences and Technology, University of Twente, 7500AE Enschede, The Netherlands
| | - Elie Raphaël
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
| | - Joshua D. McGraw
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
- Gulliver, CNRS UMR 7083, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Thomas Salez
- Institut Pierre-Gilles de Gennes, ESPCI Paris, Université PSL, 75005 Paris, France
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Kargar-Estahbanati A, Rallabandi B. Rotation-translation coupling of soft objects in lubricated contact. SOFT MATTER 2022; 18:4887-4896. [PMID: 35707981 DOI: 10.1039/d2sm00434h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We study the coupling between rotation and translation of a submerged cylinder in lubricated contact with a soft elastic substrate. Using numerical solutions and asymptotic theory, we analyze the elastohydrodynamic problem over the entire range of substrate deformations relative to the thickness of the intervening fluid film. We find a strong coupling between the rotation and translation of the cylinder when the surface deformation of the substrate is comparable to the thickness of the lubricating fluid layer. In the limit of large deformations, we show that the bodies are in near-Hertzian contact and cylinder rolls without slip, reminiscent of dry frictional contact. When the surface deformation is small relative to the separation between the surfaces, the coupling persists but is weaker, and the rotation rate scales with the translation speed to the one-third power. We then show how the external application of a torque modifies these behaviors by generating different combinations of rotational and translational motions, including back-spinning and top-spinning states. We demonstrate that these behaviors are robust regardless of whether the elastic substrate is thick or thin relative to the length scales of the flow.
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Affiliation(s)
- Arash Kargar-Estahbanati
- Department of Mechanical Engineering, University of California, Riverside, California, 92521, USA.
| | - Bhargav Rallabandi
- Department of Mechanical Engineering, University of California, Riverside, California, 92521, USA.
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Henkel C, Snoeijer JH, Thiele U. Gradient-dynamics model for liquid drops on elastic substrates. SOFT MATTER 2021; 17:10359-10375. [PMID: 34747426 DOI: 10.1039/d1sm01032h] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.
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Affiliation(s)
- Christopher Henkel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.
| | - Jacco H Snoeijer
- Physics of Fluids Group and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität, Corrensstr. 40, 48149 Münster, Germany
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Christov IC. Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:063001. [PMID: 34678790 DOI: 10.1088/1361-648x/ac327d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 10/22/2021] [Indexed: 06/13/2023]
Abstract
Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the flow forces and the inherently compliant conduits of such microfluidic devices requires careful consideration. While mechanical compliance was initially a side-effect of the manufacturing process and materials used, compliance has now become a paradigm, enabling new approaches to microrheological measurements, new modalities of micromixing, and improved sieving of micro- and nano-particles, to name a few applications. This topical review provides an introduction to the physics of these systems. Specifically, the goal of this review is to summarize the recent progress towards a mechanistic understanding of the interaction between non-Newtonian (complex) fluid flows and their deformable confining boundaries. In this context, key experimental results and relevant applications are also explored, hand-in-hand with the fundamental principles for their physics-based modeling. The key topics covered include shear-dependent viscosity of non-Newtonian fluids, hydrodynamic pressure gradients during flow, the elastic response (deformation and bulging) of soft conduits due to flow within, the effect of cross-sectional conduit geometry on the resulting fluid-structure interaction, and key dimensionless groups describing the coupled physics. Open problems and future directions in this nascent field of soft hydraulics, at the intersection of non-Newtonian fluid mechanics, soft matter physics, and microfluidics, are noted.
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Affiliation(s)
- Ivan C Christov
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, United States of America
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Hammond PS. Will we ever wash our hands of lubrication theory? PHYSICS OF FLUIDS (WOODBURY, N.Y. : 1994) 2021; 33:081908. [PMID: 34471336 PMCID: PMC8404380 DOI: 10.1063/5.0060307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 07/02/2021] [Indexed: 06/13/2023]
Abstract
Lubrication theory is used to investigate how weakly bound particles can be transported away from the vicinity of the wall when two spatially periodic rough surfaces are sheared relative to one another at constant velocity U while immersed in fluid. The aim is to model what could be an important process during decontamination of hands by washing and is motivated by Mittal et al. ["The flow physics of COVID-19," J. Fluid Mech. 894, F2 (2020)] who remark "Amazingly, despite the 170+ year history of hand washing in medical hygiene, we were unable to find a single published research article on the flow physics of hand washing." Under the assumption that the roughness wavelength 2 π / k is large compared with the spacing of the surfaces, a, the lubrication approximation permits closed-form expressions to be found for the time-varying velocity components. These are used to track the motion of a particle that is initially trapped in a potential well close to one of the surfaces, and experiences a drag force proportional to the difference between its velocity and that of the surrounding fluid. Complications such as particle-wall hydrodynamic interactions, finite size effects, and Brownian motion are ignored for now. Unsurprisingly, particles remain trapped unless the flow driven by the wall motion is strong compared to the depth of the trapping potential well. Perhaps less obvious is that for many starting positions the process of escape to large distances from the wall takes place over a large number of periods 2 π / k U , essentially because the no-slip boundary condition means that fluid velocities relative to the wall are small close to the wall, and thus the velocities of particles along or away from the wall are also small. With reasonable estimates for the various dimensional parameters, the escape times in these cases are found to be comparable in magnitude to the washing times recommended in hand washing guidelines.
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Affiliation(s)
- Paul S. Hammond
- Hammond Consulting Limited, 62 High Street, Bourn, Cambridge CB23 2TR, United Kingdom
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Chandler TGJ, Vella D. Validity of Winkler's mattress model for thin elastomeric layers: beyond Poisson's ratio. Proc Math Phys Eng Sci 2020; 476:20200551. [PMID: 33223950 DOI: 10.1098/rspa.2020.0551] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Accepted: 09/23/2020] [Indexed: 11/12/2022] Open
Abstract
Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point-indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness, which itself depends on the problem under consideration.
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Affiliation(s)
- Thomas G J Chandler
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
| | - Dominic Vella
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
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