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The Stability of a Hydrodynamic Bravais Lattice. Symmetry (Basel) 2022. [DOI: 10.3390/sym14081524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart.
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Del Giudice F, D'Avino G, Maffettone PL. Microfluidic formation of crystal-like structures. LAB ON A CHIP 2021; 21:2069-2094. [PMID: 34002182 DOI: 10.1039/d1lc00144b] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Crystal-like structures find application in several fields ranging from biomedical engineering to material science. For instance, droplet crystals are critical for high throughput assays and material synthesis, while particle crystals are important for particles and cell encapsulation, Drop-seq technologies, and single-cell analysis. Formation of crystal-like structures relies entirely on the possibility of manipulating with great accuracy the micrometer-size objects forming the crystal. In this context, microfluidic devices offer versatile tools for the precise manipulation of droplets and particles, thus enabling fabrication of crystal-like structures that form due to hydrodynamic interactions among droplets or particles. In this review, we aim at providing an holistic representation of crystal-like structure formation mediated by hydrodynamic interactions in microfluidic devices. We also discuss the physical origin of these hydrodynamic interactions and their relation to parameters such as device geometry, fluid properties, and flow conditions.
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Affiliation(s)
- Francesco Del Giudice
- System and Process Engineering Centre, College of Engineering, Fabian Way, Swansea, SA1 8EN, UK.
| | - Gaetano D'Avino
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Universitá degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Naples, Italy
| | - Pier Luca Maffettone
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Universitá degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Naples, Italy
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Georgiev RN, Toscano SO, Uspal WE, Bet B, Samin S, van Roij R, Eral HB. Universal motion of mirror-symmetric microparticles in confined Stokes flow. Proc Natl Acad Sci U S A 2020; 117:21865-21872. [PMID: 32839312 PMCID: PMC7486782 DOI: 10.1073/pnas.2005068117] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Comprehensive understanding of particle motion in microfluidic devices is essential to unlock additional technologies for shape-based separation and sorting of microparticles like microplastics, cells, and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.
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Affiliation(s)
- Rumen N Georgiev
- Process and Energy Department, Delft University of Technology, 2628CB Delft, The Netherlands
| | - Sara O Toscano
- Process and Energy Department, Delft University of Technology, 2628CB Delft, The Netherlands
| | - William E Uspal
- Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822
| | - Bram Bet
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, 3584 CC Utrecht, The Netherlands
| | - Sela Samin
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, 3584 CC Utrecht, The Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, 3584 CC Utrecht, The Netherlands
| | - Huseyin Burak Eral
- Process and Energy Department, Delft University of Technology, 2628CB Delft, The Netherlands;
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, 3584 CH Utrecht, The Netherlands
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Schaaf C, Stark H. Particle pairs and trains in inertial microfluidics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:50. [PMID: 32743755 DOI: 10.1140/epje/i2020-11975-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Accepted: 07/09/2020] [Indexed: 06/11/2023]
Abstract
Staggered and linear multi-particle trains constitute characteristic structures in inertial microfluidics. Using lattice-Boltzmann simulations, we investigate their properties and stability, when flowing through microfluidic channels. We confirm the stability of cross-streamline pairs by showing how they contract or expand to their equilibrium axial distance. In contrast, same-streamline pairs quickly expand to a characteristic separation but even at long times slowly drift apart. We reproduce the distribution of particle distances with its characteristic peak as measured in experiments. Staggered multi-particle trains initialized with an axial particle spacing larger than the equilibrium distance contract non-uniformly due to collective drag reduction. Linear particle trains, similar to pairs, rapidly expand toward a value about twice the equilibrium distance of staggered trains and then very slowly drift apart non-uniformly. Again, we reproduce the statistics of particle distances and the characteristic peak observed in experiments. Finally, we thoroughly analyze the damped displacement pulse traveling as a microfluidic phonon through a staggered train and show how a defect strongly damps its propagation.
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Affiliation(s)
- Christian Schaaf
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623, Berlin, Germany.
| | - Holger Stark
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623, Berlin, Germany
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Walter C, Seemann R, Fleury JB. Flowing droplet interface bilayers: A microfluidic tool to control droplet trajectories and to study mechanical properties of unsupported lipid bilayers. BIOMICROFLUIDICS 2020; 14:044109. [PMID: 32742537 PMCID: PMC7390600 DOI: 10.1063/5.0011489] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We introduce the concept of Flowing Droplet Interface Bilayers (FDIBs) that are made of two droplets maintained in contact due to the presence of an adhesive lipidic surfactant. This system is similar to a flowing dumbbell made of two droplets interconnected by a lipid bilayer and driven by an external flow. Interestingly, such a dumbbell does not show a straight flow trajectory, but it oscillates between the sidewalls while moving along the microchannel. The origin of this unusual motion is hydrodynamic interactions, as demonstrated by analytical calculations and micro particle image velocimentry (µPiV) measurements. The hydrodynamic motion appears to be highly sensitive to the mechanical properties of the lipid bilayer connecting the two droplets (FDIB). Thus, droplet trajectories can be controlled by tuning the lipid bilayer composition, which enables in turn investigating mechanical properties of free-standing lipid bilayers.
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Thomson SJ, Durey M, Rosales RR. Collective vibrations of a hydrodynamic active lattice. Proc Math Phys Eng Sci 2020; 476:20200155. [PMID: 32831612 PMCID: PMC7426053 DOI: 10.1098/rspa.2020.0155] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 06/05/2020] [Indexed: 11/12/2022] Open
Abstract
Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.
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Affiliation(s)
- S. J. Thomson
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA02139, USA
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Khangholi N, Seemann R, Fleury JB. Simultaneous measurement of surface and bilayer tension in a microfluidic chip. BIOMICROFLUIDICS 2020; 14:024117. [PMID: 32549923 PMCID: PMC7188485 DOI: 10.1063/1.5137810] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 04/10/2020] [Indexed: 06/11/2023]
Abstract
Freestanding lipid bilayers are one of the most used model systems to mimic biological cell membranes. To form an unsupported bilayer, we employ two aqueous fingers in a microfluidic chip surrounded by an oily phase that contains lipids. Upon pushing two aqueous fingers forward, their interface becomes decorated with a lipid monolayer and eventually zip to form a bilayer when the monolayers have nanoscopic contact with each other. Using this straightforward approach, the quick and easy bilayer formation is facilitated by oil draining into the microfluidic device material consisting of polydimethylsiloxane. However, the oil drainage limits the lifetime of a bilayer to about 1 h. We demonstrate that this drainage can be managed, resulting in superior bilayer stability and an increased lifetime of several hours when using a pressure-controlled system. Applying different pressures to the aqueous fingers in the microfluidic chip, the formed bilayer can even be bent to a desired curvature. Extracting the contact angle and the resulting curvature of the bilayer region, for a given applied pressure difference, both the bilayer tension and the surface tension of each lipid monolayer can be derived from a single experiment using the Young Laplace pressure equation.
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Affiliation(s)
- Navid Khangholi
- Experimental Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Ralf Seemann
- Experimental Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Jean-Baptiste Fleury
- Experimental Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
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Schaaf C, Rühle F, Stark H. A flowing pair of particles in inertial microfluidics. SOFT MATTER 2019; 15:1988-1998. [PMID: 30714602 DOI: 10.1039/c8sm02476f] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
A flowing pair of particles in inertial microfluidics gives important insights into understanding and controlling the collective dynamics of particles like cells or droplets in microfluidic devices. They are applied in medical cell analysis and engineering. We study the dynamics of a pair of solid particles flowing through a rectangular microchannel using lattice Boltzmann simulations. We determine the inertial lift force profiles as a function of the two particle positions, their axial distance, and the Reynolds number. Generally, the profiles strongly differ between particles leading and lagging in flow and the lift forces are enhanced due to the presence of a second particle. At small axial distances, they are determined by viscous forces, while inertial forces dominate at large separations. We identify cross-streamline pairs as stable fixed points in the lift force profiles and argue that same-streamline configurations are only one-sided stable. Depending on the initial conditions, the two-particle lift forces in combination with the Poiseuille flow give rise to three types of unbound particle trajectories, called moving-apart, passing, and swapping, and one type of bound trajectory, where the particles perform damped oscillations towards the cross-stream line configuration. The damping rate scales with Reynolds number squared, since inertial forces are responsible for driving the particles to their steady-state positions.
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Affiliation(s)
- Christian Schaaf
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
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Fiorucci G, Padding JT, Dijkstra M. Small asymmetric Brownian objects self-align in nanofluidic channels. SOFT MATTER 2019; 15:321-330. [PMID: 30556572 DOI: 10.1039/c8sm02384k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Although the self-alignment of asymmetric macro-sized objects of a few tens of microns in size have been studied extensively in experiments and theory, access to much smaller length scales is still hindered by technical challenges. We combine molecular dynamics and stochastic rotation dynamics techniques to investigate the self-orientation phenomenon at different length scales, ranging from the micron to the nano scale by progressively increasing the relative strength of diffusion over convection. To this end, we model an asymmetric dumbbell particle in Hele-Shaw flow and explore a wide range of Péclet numbers (Pe) and different particle shapes, as characterized by the size ratio of the two dumbbell spheres (R[combining tilde]). By independently varying these two parameters we analyse the process of self-orientation and characterize the alignment of the dumbbell with the direction of the fluid flow. We identify three different regimes of strong, weak and no alignment and we map out a state diagram in Pe versus R[combining tilde] plane. Based on these results, we estimate dimensional length scales and flow rates for which these findings would be applicable in experiments. Finally, we find that the characteristic reorientation time of the dumbbell is a monotonically decreasing function of the dumbbell anisotropy.
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Affiliation(s)
- Giulia Fiorucci
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
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Tsang ACH, Shelley MJ, Kanso E. Activity-induced instability of phonons in 1D microfluidic crystals. SOFT MATTER 2018; 14:945-950. [PMID: 29319100 DOI: 10.1039/c7sm01335c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
One-dimensional crystals of passively-driven particles in microfluidic channels exhibit collective vibrational modes reminiscent of acoustic 'phonons'. These phonons are induced by the long-range hydrodynamic interactions among the particles and are neutrally stable at the linear level. Here, we analyze the effect of particle activity - self-propulsion - on the emergence and stability of these phonons. We show that the direction of wave propagation in active crystals is sensitive to the intensity of the background flow. We also show that activity couples, at the linear level, transverse waves to the particles' rotational motion, inducing a new mode of instability that persists in the limit of large background flow, or, equivalently, vanishingly small activity. We then report a new phenomenon of phonons switching back and forth between two adjacent crystals in both passively-driven and active systems, similar in nature to the wave switching observed in quantum mechanics, optical communication, and density stratified fluids. These findings could have implications for the design of commercial microfluidic systems and the self-assembly of passive and active micro-particles into one-dimensional structures.
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Affiliation(s)
- Alan Cheng Hou Tsang
- Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA. and Bioengineering, Stanford University, Stanford, California 94305, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Eva Kanso
- Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA. and Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Schiller UD, Krüger T, Henrich O. Mesoscopic modelling and simulation of soft matter. SOFT MATTER 2017; 14:9-26. [PMID: 29211098 DOI: 10.1039/c7sm01711a] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.
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Affiliation(s)
- Ulf D Schiller
- Department of Materials Science and Engineering, Clemson University, 161 Sirrine Hall, Clemson, SC 29634, USA
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Beatus T, Shani I, Bar-Ziv RH, Tlusty T. Two-dimensional flow of driven particles: a microfluidic pathway to the non-equilibrium frontier. Chem Soc Rev 2017; 46:5620-5646. [DOI: 10.1039/c7cs00374a] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We discuss the basic physics of the flow of micron-scale droplets in 2D geometry.
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Affiliation(s)
- Tsevi Beatus
- The Rachel and Selim Benin School of Computer Science and Engineering
- The Alexander Grass Center for Bioengineering, and The Silberman Institute of Life Science
- The Hebrew University of Jerusalem
- Israel
| | - Itamar Shani
- Institute for Research in Electronics and Applied Physics
- University of Maryland
- College Park
- MD
- USA
| | - Roy H. Bar-Ziv
- Dept. of Materials and Interfaces
- Weizmann Institute of Science
- Rehovot
- Israel
| | - Tsvi Tlusty
- Center for Soft and Living Matter
- Institute for Basic Science (IBS)
- Ulsan
- Korea
- Dept. of Physics
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