1
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Chan CW, Yang Z, Gan Z, Zhang R. Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets. J Chem Phys 2024; 161:014904. [PMID: 38953449 DOI: 10.1063/5.0207355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 05/31/2024] [Indexed: 07/04/2024] Open
Abstract
In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.
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Affiliation(s)
- Chung Wing Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
| | - Zheng Yang
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
- Interdisciplinary Programs Office, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Zecheng Gan
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
- Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Rui Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
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2
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Zero EN, Crespi VH. Emergence of inertia in the low-Reynolds regime of self-diffusiophoretic motion. Phys Rev E 2024; 109:054602. [PMID: 38907454 DOI: 10.1103/physreve.109.054602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 11/06/2023] [Indexed: 06/24/2024]
Abstract
For isotropic swimming particles driven by self-diffusiophoresis at zero Reynolds number (where particle velocity responds instantaneously to applied force), the diffusive timescale of emitted solute can produce an emergent quasi-inertial behavior. These particles can orbit in a central potential and reorient under second-order dynamics, not the first-order dynamics of classical zero-Reynolds motion. They are described by a simple effective model that embeds their history-dependent behavior as an effective inertia, this being the most primitive expression of memory. The system can be parameterized with dynamic quantities such as particle size and swimming speed, without detailed knowledge of the diffusiophoretic mechanism.
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Affiliation(s)
- Emmy N Zero
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Vincent H Crespi
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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3
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Yang Q, Jiang M, Picano F, Zhu L. Shaping active matter from crystalline solids to active turbulence. Nat Commun 2024; 15:2874. [PMID: 38570495 DOI: 10.1038/s41467-024-46520-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 02/27/2024] [Indexed: 04/05/2024] Open
Abstract
Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.
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Affiliation(s)
- Qianhong Yang
- Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore
| | - Maoqiang Jiang
- School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan, Hubei, PR China
| | - Francesco Picano
- Department of Industrial Engineering and CISAS "G. Colombo", University of Padova, Padova, Italy
| | - Lailai Zhu
- Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore.
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4
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Wang Y, Zheng L, Li G. Self-propulsion of a droplet induced by combined diffusiophoresis and Marangoni effects. Electrophoresis 2024. [PMID: 38528332 DOI: 10.1002/elps.202400005] [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: 01/08/2024] [Revised: 02/22/2024] [Accepted: 03/12/2024] [Indexed: 03/27/2024]
Abstract
Chemically active droplets display complex self-propulsion behavior in homogeneous surfactant solutions, often influenced by the interplay between diffusiophoresis and Marangoni effects. Previous studies have primarily considered these effects separately or assumed axisymmetric motion. To understand the full hydrodynamics, we investigate the motion of a two-dimensional active droplet under their combined influences using weakly nonlinear analysis and numerical simulations. The impact of two key factors, the Péclet number (P e $Pe$ ) and the mobility ratio between diffusiophoretic and Marangoni effects ( m $m$ ), on droplet motion is explored. We establish a phase diagram in theP e - m $Pe-m$ space, categorizing the boundaries between four types of droplet states: stationary, steady motion, periodic/quasi-periodic motion, and chaotic motion. We find that the mobility ratio does not affect the criticalP e $Pe$ for the onset of self-propulsion, but it significantly influences the stability of high-wavenumber modes as well as the droplet's velocity and trajectory. Scaling analysis reveals that in the highP e $Pe$ regime, the Marangoni and diffusiophoresis effects lead to distinct velocity scaling laws:U ∼ P e - 1 / 2 $U\sim Pe^{-1/2}$ andU ∼ P e - 1 / 3 $U\sim Pe^{-1/3}$ , respectively. When these effects are combined, the velocity scaling depends on the sign of the mobility ratio. In cases with a positive mobility ratio, the Marangoni effect dominates the scaling, whereas the negative diffusiophoretic effect leads to an increased thickness of the concentration boundary layer and a flattened scaling of the droplet velocity.
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Affiliation(s)
- Yuhang Wang
- School of Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, China
| | - Longtao Zheng
- School of Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, China
| | - Gaojin Li
- School of Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, China
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5
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Feng K, Chen L, Zhang X, Gong J, Qu J, Niu R. Collective Behaviors of Isotropic Micromotors: From Assembly to Reconstruction and Motion Control under External Fields. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2900. [PMID: 37947744 PMCID: PMC10650937 DOI: 10.3390/nano13212900] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Revised: 10/27/2023] [Accepted: 10/30/2023] [Indexed: 11/12/2023]
Abstract
Swarms of self-propelled micromotors can mimic the processes of natural systems and construct artificial intelligent materials to perform complex collective behaviors. Compared to self-propelled Janus micromotors, the isotropic colloid motors, also called micromotors or microswimmers, have advantages in self-assembly to form micromotor swarms, which are efficient in resistance to external disturbance and the delivery of large quantity of cargos. In this minireview, we summarize the fundamental principles and interactions for the assembly of isotropic active particles to generate micromotor swarms. Recent discoveries based on either catalytic or external physical field-stimulated micromotor swarms are also presented. Then, the strategy for the reconstruction and motion control of micromotor swarms in complex environments, including narrow channels, maze, raised obstacles, and high steps/low gaps, is summarized. Finally, we outline the future directions of micromotor swarms and the remaining challenges and opportunities.
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Affiliation(s)
- Kai Feng
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
| | - Ling Chen
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
| | - Xinle Zhang
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
| | - Jiang Gong
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
| | - Jinping Qu
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
- Key Laboratory of Polymer Processing Engineering, Ministry of Education, Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing, National Engineering Research Center of Novel Equipment for Polymer Processing, School of Mechanical and Automotive Engineering, South China University of Technology, Ministry of Education, Guangzhou 510641, China
| | - Ran Niu
- Key Laboratory of Material Chemistry for Energy Conversion and Storage, Ministry of Education, Hubei Key Laboratory of Material Chemistry and Service Failure, Hubei Engineering Research Center for Biomaterials and Medical Protective Materials, Semiconductor Chemistry Center, School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Ministry of Education, Wuhan 430074, China; (K.F.); (L.C.); (X.Z.); (J.Q.)
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6
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Kailasham R, Khair AS. Effect of speed fluctuations on the collective dynamics of active disks. SOFT MATTER 2023; 19:7764-7774. [PMID: 37791487 DOI: 10.1039/d3sm00665d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate β. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of β, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.
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Affiliation(s)
- R Kailasham
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
| | - Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
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7
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Feng K, Ureña Marcos JC, Mukhopadhyay AK, Niu R, Zhao Q, Qu J, Liebchen B. Self-Solidifying Active Droplets Showing Memory-Induced Chirality. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2300866. [PMID: 37526332 PMCID: PMC10520641 DOI: 10.1002/advs.202300866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 05/20/2023] [Indexed: 08/02/2023]
Abstract
Most synthetic microswimmers do not reach the autonomy of their biological counterparts in terms of energy supply and diversity of motions. Here, this work reports the first all-aqueous droplet swimmer powered by self-generated polyelectrolyte gradients, which shows memory-induced chirality while self-solidifying. An aqueous solution of surface tension-lowering polyelectrolytes self-solidifies on the surface of acidic water, during which polyelectrolytes are gradually emitted into the surrounding water and induce linear self-propulsion via spontaneous symmetry breaking. The low diffusion coefficient of the polyelectrolytes leads to long-lived chemical trails which cause memory effects that drive a transition from linear to chiral motion without requiring any imposed symmetry breaking. The droplet swimmer is capable of highly efficient removal (up to 85%) of uranium from aqueous solutions within 90 min, benefiting from self-propulsion and flow-induced mixing. These results provide a route to fueling self-propelled agents which can autonomously perform chiral motion and collect toxins.
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Affiliation(s)
- Kai Feng
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | | | - Aritra K. Mukhopadhyay
- Institut für Physik Kondensierter MaterieTechnische Universität Darmstadt64289DarmstadtGermany
| | - Ran Niu
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Qiang Zhao
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Jinping Qu
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Benno Liebchen
- Institut für Physik Kondensierter MaterieTechnische Universität Darmstadt64289DarmstadtGermany
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8
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Ray S, Roy A. Simple model for self-propulsion of microdroplets in surfactant solution. Phys Rev E 2023; 108:035102. [PMID: 37849129 DOI: 10.1103/physreve.108.035102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 08/23/2023] [Indexed: 10/19/2023]
Abstract
We propose a simple active hydrodynamic model for the self-propulsion of a liquid droplet suspended in micellar solutions. The self-propulsion of the droplet occurs by spontaneous breaking of isotropic symmetry and is studied using both analytical and numerical methods. The emergence of self-propulsion arises from the slow dissolution of the inner fluid into the outer micellar solution as filled micelles. We propose that the surface generation of filled micelles is the dominant reason for the self-propulsion of the droplet. The flow instability is due to the Marangoni stress generated by the nonuniform distribution of the surfactant molecules on the droplet interface. In our model, the driving parameter of the instability is the excess surfactant concentration above the critical micellar concentration, which directly correlates with the experimental observations. We consider various low-order modes of flow instability and show that the first mode becomes unstable through a supercritical bifurcation and is the only mode contributing to the swimming of the droplet. The flow fields around the droplet for these modes and their combined effects are also discussed.
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Affiliation(s)
- Swarnak Ray
- Soft Condensed Matter Group, Raman Research Institute, Bangalore 560080, India
| | - Arun Roy
- Soft Condensed Matter Group, Raman Research Institute, Bangalore 560080, India
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9
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Sumino Y, Yamashita R, Miyaji K, Ishikawa H, Otani M, Yamamoto D, Okita E, Okamoto Y, Krafft MP, Yoshikawa K, Shioi A. Droplet duos on water display pairing, autonomous motion, and periodic eruption. Sci Rep 2023; 13:12377. [PMID: 37524759 PMCID: PMC10390526 DOI: 10.1038/s41598-023-39094-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Accepted: 07/20/2023] [Indexed: 08/02/2023] Open
Abstract
Under non-equilibrium conditions, liquid droplets dynamically couple with their milieu through the continuous flux of matter and energy, forming active systems capable of self-organizing functions reminiscent of those of living organisms. Among the various dynamic behaviors demonstrated by cells, the pairing of heterogeneous cell units is necessary to enable collective activity and cell fusion (to reprogram somatic cells). Furthermore, the cyclic occurrence of eruptive events such as necroptosis or explosive cell lysis is necessary to maintain cell functions. However, unlike the self-propulsion behavior of cells, cyclic cellular behavior involving pairing and eruption has not been successfully modeled using artificial systems. Here, we show that a simple droplet system based on quasi-immiscible hydrophobic oils (perfluorodecalin and decane) deposited on water, mimics such complex cellular dynamics. Perfluorodecalin and decane droplet duos form autonomously moving Janus or coaxial structures, depending on their volumes. Notably, the system with a coaxial structure demonstrates cyclic behavior, alternating between autonomous motion and eruption. Despite their complexity, the dynamic behaviors of the system are consistently explained in terms of the spreading properties of perfluorodecalin/decane duplex interfacial films.
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Affiliation(s)
- Yutaka Sumino
- Department of Applied Physics, Tokyo University of Science, 6-3-1 Niijuku, Katsushika, Tokyo, 125-8585, Japan.
| | - Ryo Yamashita
- Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto, 610-0321, Japan
| | - Kazuki Miyaji
- Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto, 610-0321, Japan
| | - Hiroaki Ishikawa
- Department of Physics, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan
| | - Maho Otani
- Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto, 610-0321, Japan
| | - Daigo Yamamoto
- Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto, 610-0321, Japan
| | - Erika Okita
- Department of Chemical Engineering, Osaka Metropolitan University, Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531, Japan
| | - Yasunao Okamoto
- Research Center for Membrane and Film Technology, Kobe University, Kobe, 657-8501, Japan
| | - Marie Pierre Krafft
- Institut Charles Sadron (CNRS), University of Strasbourg, 23 rue du Loess, 67034, Strasbourg, France.
| | - Kenichi Yoshikawa
- Faculty of Life and Medical Sciences, Doshisha University, Kyoto, 610-0394, Japan
- Center for Integrative Medicine and Physics, Institute for Advanced Study, Kyoto University, Kyoto, 606-8501, Japan
| | - Akihisa Shioi
- Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto, 610-0321, Japan.
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10
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Ureña Marcos JC, Liebchen B. Inverted Sedimentation of Active Particles in Unbiased ac Fields. PHYSICAL REVIEW LETTERS 2023; 131:038201. [PMID: 37540873 DOI: 10.1103/physrevlett.131.038201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 06/26/2023] [Indexed: 08/06/2023]
Abstract
Gaining control over the motion of active particles is crucial for applications ranging from targeted cargo delivery to nanomedicine. While much progress has been made recently to control active motion based on external forces, flows, or gradients in concentration or light intensity, which all have a well-defined direction or bias, little is known about how to steer active particles in situations where no permanent bias can be realized. Here, we show that ac fields with a vanishing time average provide an alternative route to steering active particles. We exemplify this route for inertial active particles in a gravitational field, observing that a substantial fraction of them persistently travels in the upward direction upon switching on the ac field, resulting in an inverted sedimentation profile at the top wall of a confining container. Our results offer a generic control principle that could be used in the future to steer active motion, direct collective behaviors, and purify mixtures.
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Affiliation(s)
- José Carlos Ureña Marcos
- Institut für Physik Kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, 64289 Darmstadt, Germany
| | - Benno Liebchen
- Institut für Physik Kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, 64289 Darmstadt, Germany
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11
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Kailasham R, Khair AS. Non-Brownian diffusion and chaotic rheology of autophoretic disks. Phys Rev E 2023; 107:044609. [PMID: 37198791 DOI: 10.1103/physreve.107.044609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 03/29/2023] [Indexed: 05/19/2023]
Abstract
The dynamics of a two-dimensional autophoretic disk is quantified as a minimal model for the chaotic trajectories undertaken by active droplets. Via direct numerical simulations, we show that the mean-square displacement of the disk in a quiescent fluid is linear at long times. Surprisingly, however, this apparently diffusive behavior is non-Brownian, owing to strong cross correlations in the displacement tensor. The effect of a shear flow field on the chaotic motion of an autophoretic disk is examined. Here, the stresslet on the disk is chaotic for weak shear flows; a dilute suspension of such disks would exhibit a chaotic shear rheology. This chaotic rheology is quenched first into a periodic state and ultimately a steady state as the flow strength is increased.
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Affiliation(s)
- R Kailasham
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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12
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Castonguay AC, Kailasham R, Wentworth CM, Meredith CH, Khair AS, Zarzar LD. Gravitational settling of active droplets. Phys Rev E 2023; 107:024608. [PMID: 36932547 DOI: 10.1103/physreve.107.024608] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled-micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (α) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of α) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of α occurs for an active settling droplet is proposed.
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Affiliation(s)
- Alexander C Castonguay
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - R Kailasham
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Ciera M Wentworth
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Caleb H Meredith
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Lauren D Zarzar
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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13
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Synchronized motion of two camphor disks on a water droplet levitated under microgravity. Colloids Surf A Physicochem Eng Asp 2022. [DOI: 10.1016/j.colsurfa.2022.130321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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14
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Suda S, Suda T, Ohmura T, Ichikawa M. Motion of a swimming droplet under external perturbations: A model-based approach. Phys Rev E 2022; 106:034610. [PMID: 36266827 DOI: 10.1103/physreve.106.034610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 09/01/2022] [Indexed: 06/16/2023]
Abstract
Microdroplets driven by the Marangoni effect are known to continue to swim for hours despite their simple composition. This swimming microdroplet changes its motion from straight to curvilinear and further to chaotic as the Péclet number increases. In this study, we investigate the effect of external perturbations on the three-dimensional axis-asymmetric model of a droplet driven by the Marangoni effect. The aim here is to elucidate the contribution of external perturbation to the complex motion of the droplet and the change in its effect according to the droplet size. In this paper, first we provide a detailed explanation on the derivation of the model introduced in our previous work, which is next used to describe the motion of the droplet in the numerical study of the angular response to random perturbations. The numerical simulation of droplet motion with different types of noise indicates that the model does not converge them into a certain type of motion but rather helps to reflect the external perturbations. The obtained results suggest that the types and properties of external perturbation have a considerable effect on the droplet motion.
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Affiliation(s)
- Saori Suda
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Tomoharu Suda
- Department of Mathematics, Keio University, Yokohama 223-8522, Japan
| | - Takuya Ohmura
- Biozentrum, University of Basel, Basel 4056, Switzerland
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We the Droplets: A Constitutional Approach to Active and Self-Propelled Emulsions. Curr Opin Colloid Interface Sci 2022. [DOI: 10.1016/j.cocis.2022.101623] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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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.
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Hokmabad BV, Nishide A, Ramesh P, Krüger C, Maass CC. Spontaneously rotating clusters of active droplets. SOFT MATTER 2022; 18:2731-2741. [PMID: 35319552 DOI: 10.1039/d1sm01795k] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient instability into a steady rotational state. We analyse the collective rotational dynamics as a function of droplet activity and cluster size and further propose that the stable collective rotation in the cluster is caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.
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Affiliation(s)
- Babak Vajdi Hokmabad
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
- Institute for the Dynamics of Complex Systems, Georg August Universität, Göttingen, Germany
| | - Akinori Nishide
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
- Center for Exploratory Research, R&D group, Hitachi Ltd., Higashi-Koigakubo 1-280, Kokubunji-shi, Tokyo 185-8601, Japan
| | - Prashanth Ramesh
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, MESA+ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands
| | - Carsten Krüger
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
| | - Corinna C Maass
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
- Institute for the Dynamics of Complex Systems, Georg August Universität, Göttingen, Germany
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, MESA+ Institute and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands
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Verhille G, Inoue C, Villermaux E. Architecture of a self-fragmenting droplets cascade. Phys Rev E 2021; 104:L053101. [PMID: 34942737 DOI: 10.1103/physreve.104.l053101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 10/18/2021] [Indexed: 11/07/2022]
Abstract
We report quantitative imaging experiments describing the three-dimensional (3D) bursting cascade of droplets from a liquid melt reacting with the oxygen of air which explode sequentially to produce ever smaller fragments. The 3D space-time resolved trajectories of the fragmenting drops reveal an arborescent structure of branchings defining the cascade steps, each random in direction and shortening along the cascade, in a way we determine. The phenomenon is a unique and prototypical illustration of the so-called Richardson regime, namely, an accelerated cascade towards smaller scales. The phenomenon, which coincides with the early time dispersion period of a Brownian motion, featuring here ever shrinking steps, is well captured by a Langevin dynamics.
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Affiliation(s)
- Gautier Verhille
- Aix Marseille Université, CNRS, and Centrale Marseille, IRPHE Marseille, Marseille, France
| | - Chihiro Inoue
- Kyushu University, Department of Aeronautics and Astronautics, Fukuoka, Japan
| | - Emmanuel Villermaux
- Aix Marseille Université, CNRS, and Centrale Marseille, IRPHE Marseille, Marseille, France.,Institut Universitaire de France, Paris, France
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