1
|
Farutin A, Misbah C. Singular bifurcations and regularization theory. Phys Rev E 2024; 109:064218. [PMID: 39021029 DOI: 10.1103/physreve.109.064218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2024] [Accepted: 06/06/2024] [Indexed: 07/20/2024]
Abstract
Nonlinear sciences are present today in almost all disciplines, ranging from physics to social sciences. A major task in nonlinear science is the classification of different types of bifurcations (e.g., pitchfork and saddle-node) from a given state to another. Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. We then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked.
Collapse
|
2
|
Singh K, Raman H, Tripathi S, Sharma H, Choudhary A, Mangal R. Pair Interactions of Self-Propelled SiO 2-Pt Janus Colloids: Chemically Mediated Encounters. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:7328-7343. [PMID: 38526954 DOI: 10.1021/acs.langmuir.3c03415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
Driven by the necessity to achieve a thorough comprehension of the bottom-up fabrication process of functional materials, this experimental study investigates the pairwise interactions or collisions between chemically active SiO2-Pt Janus colloids. These collisions are categorized based on the Janus colloids' orientations before and after they make physical contact. In addition to the hydrodynamic interactions, the Janus colloids are also known to affect each other's chemical field, resulting in chemophoretic interactions, which depend on the degree of surface anisotropy in reactivity of Janus colloid and the solute-surface interaction at play. Our study reveals that these interactions lead to a noticeable decrease in particle speed and changes in orientation that correlate with the contact duration and yield different collision types. Distinct configurations of contact during collisions were found, whose mechanisms and likelihood are found to be dependent primarily on the chemical interactions. Such estimates of collision and their characterization in dilute suspensions shall have a key impact in determining the arrangement and time scales of dynamical structures and assemblies of denser suspensions and potentially the functional materials of the future.
Collapse
Affiliation(s)
- Karnika Singh
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Harishwar Raman
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Shwetabh Tripathi
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Hrithik Sharma
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Akash Choudhary
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Rahul Mangal
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
| |
Collapse
|
3
|
Chen Y, Chong KL, Liu H, Verzicco R, Lohse D. Buoyancy-driven attraction of active droplets. JOURNAL OF FLUID MECHANICS 2024; 980:jfm.2024.18. [PMID: 38361591 PMCID: PMC7615645 DOI: 10.1017/jfm.2024.18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al. Eur. Phys. J. E, vol. 39, 2016, pp. 1-9). In this study, we numerically analyze the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by Péclet number Pe). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by Galileo number Ga, and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number Ra. We analyze how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters Pe, Ga, and Ra. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large Ra, even collisions between the droplets can take place. Our study on the effect of Ga further shows that with increasing Ga, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number Red, is proportional to Ra1/4/(ℓ/R), where ℓ/R is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number Rerep, which is proportional to PeRa-0.38. The balance of attractive and repulsive effect leads to Pe ~ Ra0.63, which agrees well with the transition curve between the regimes with and without collision.
Collapse
Affiliation(s)
- Yibo Chen
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Kai Leong Chong
- Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, PR China
| | - Haoran Liu
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Roberto Verzicco
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
- Gran Sasso Science Institute - Viale F. Crispi, 7 67100 L’Aquila, Italy
| | - Detlef Lohse
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Max Planck Institute for Dynamics and Self-Organisation, Am Fassberg 17, 37077 Göttingen, Germany
| |
Collapse
|
4
|
Théry A, Maaß CC, Lauga E. Hydrodynamic interactions between squirmers near walls: far-field dynamics and near-field cluster stability. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230223. [PMID: 37388310 PMCID: PMC10300678 DOI: 10.1098/rsos.230223] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 05/30/2023] [Indexed: 07/01/2023]
Abstract
Confinement increases contacts between microswimmers in dilute suspensions and affects their interactions. In particular, boundaries have been shown experimentally to lead to the formation of clusters that would not occur in bulk fluids. To what extent does hydrodynamics govern these boundary-driven encounters between microswimmers? We consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through far-field interaction of a pair of weak squirmers, as well as the lubrication interactions occurring after contact between two or more squirmers. In the far field, the orientation of microswimmers is controlled by the wall and the squirming parameter. The presence of a second swimmer influences the orientation of the original squirmer, but for weak squirmers, most of the interaction occurs after contact. We thus analyse next the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilize clusters of pullers, while the opposite is true for pushers; to be stable, clusters of pushers thus need to be governed by other interactions (e.g. phoretic). This simplified approach to the phenomenon of active clustering enables us to highlight the hydrodynamic contribution, which can be hard to isolate in experimental realizations.
Collapse
Affiliation(s)
- A. Théry
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
| | - C. C. Maaß
- Physics of Fluids, University of Twente, 7500AE Enschede, The Netherlands
| | - E. Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
| |
Collapse
|
5
|
|
6
|
Abstract
The out-of-equilibrium dynamics of chemotactic active matter—be it animate or inanimate—is closely coupled to the environment, a chemical landscape shaped by secretions from the motile agents, fuel uptake, or autochemotactic signaling. This gives rise to complex collective effects, which can be exploited by the agents for colony migration strategies or pattern formation. We study such effects using an idealized experimental system: self-propelled microdroplets that communicate via chemorepulsive trails. We present a comprehensive experimental analysis that involves direct probing of the diffusing chemical trails and the trail–droplet interactions and use it to construct a generic theoretical model. We connect these repulsive autochemotactic interactions to the collective dynamics in emulsions, demonstrating a state of dynamical arrest: chemotactic self-caging. A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent–trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other’s trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.
Collapse
|
7
|
Gouiller C, Ybert C, Cottin-Bizonne C, Raynal F, Bourgoin M, Volk R. Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization. Phys Rev E 2021; 104:064608. [PMID: 35030840 DOI: 10.1103/physreve.104.064608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 11/23/2021] [Indexed: 11/07/2022]
Abstract
We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.
Collapse
Affiliation(s)
- Clément Gouiller
- Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, CNRS, F-69622 Villeurbanne, France
| | - Christophe Ybert
- Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, CNRS, F-69622 Villeurbanne, France
| | - Cécile Cottin-Bizonne
- Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, CNRS, F-69622 Villeurbanne, France
| | - Florence Raynal
- Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, INSA Lyon, CNRS, F-69134 Écully, France
| | - Mickaël Bourgoin
- Laboratoire de Physique, Université de Lyon, École Normale Supérieure de Lyon, CNRS, F-69342 Lyon, France
| | - Romain Volk
- Laboratoire de Physique, Université de Lyon, École Normale Supérieure de Lyon, CNRS, F-69342 Lyon, France
| |
Collapse
|