1
|
Liao CT, Lemus A, Gürbüz A, Tsang ACH, Pak OS, Daddi-Moussa-Ider A. Propulsion of a three-sphere microrobot in a porous medium. Phys Rev E 2024; 109:065106. [PMID: 39020945 DOI: 10.1103/physreve.109.065106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Accepted: 04/18/2024] [Indexed: 07/20/2024]
Abstract
Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impacts their propulsion performance compared with the case of that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this paper, we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.
Collapse
|
2
|
Abstract
Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.
Collapse
|
3
|
Daddi-Moussa-Ider A, Lisicki M, Mathijssen AJTM, Hoell C, Goh S, Bławzdziewicz J, Menzel AM, Löwen H. State diagram of a three-sphere microswimmer in a channel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:254004. [PMID: 29757157 DOI: 10.1088/1361-648x/aac470] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.
Collapse
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | | | | | | | | | | | | | | |
Collapse
|
4
|
Daddi-Moussa-Ider A, Lisicki M, Hoell C, Löwen H. Swimming trajectories of a three-sphere microswimmer near a wall. J Chem Phys 2018; 148:134904. [DOI: 10.1063/1.5021027] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Maciej Lisicki
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| |
Collapse
|
5
|
Wang Q, Othmer HG. Analysis of a model microswimmer with applications to blebbing cells and mini-robots. J Math Biol 2018; 76:1699-1763. [PMID: 29497820 DOI: 10.1007/s00285-018-1225-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Revised: 01/05/2018] [Indexed: 11/25/2022]
Abstract
Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of models for movement of cells by blebbing and of nano-robots in a viscous fluid at low Reynolds number. At the level of individuals, the shape changes comprise volume exchanges between connected spheres that can control their separation, which are simple enough that significant analytical results can be obtained. Our goal is to understand how the efficiency of movement depends on the amplitude and period of the volume exchanges when the spheres approach closely during a cycle. Previous analyses were predicated on wide separation, and we show that the speed increases significantly as the separation decreases due to the strong hydrodynamic interactions between spheres in close proximity. The scallop theorem asserts that at least two degrees of freedom are needed to produce net motion in a cyclic sequence of shape changes, and we show that these degrees can reside in different swimmers whose collective motion is studied. We also show that different combinations of mode sharing can lead to significant differences in the translation and performance of pairs of swimmers.
Collapse
Affiliation(s)
- Qixuan Wang
- 540R Rowland Hall, University of California, Irvine, Irvine, USA.
| | - Hans G Othmer
- School of Mathematics, 270A Vincent Hall, University of Minnesota, Minneapolis, USA
| |
Collapse
|
6
|
Koens L, Lauga E. Rotation of slender swimmers in isotropic-drag media. Phys Rev E 2016; 93:043125. [PMID: 27176408 DOI: 10.1103/physreve.93.043125] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Indexed: 12/20/2022]
Abstract
The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force- and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generating translational versus rotational propulsion.
Collapse
Affiliation(s)
- Lyndon Koens
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| |
Collapse
|
7
|
Riley EE, Lauga E. Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J Theor Biol 2015; 382:345-55. [DOI: 10.1016/j.jtbi.2015.06.045] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Revised: 06/24/2015] [Accepted: 06/28/2015] [Indexed: 01/19/2023]
|
8
|
Pande J, Smith AS. Forces and shapes as determinants of micro-swimming: effect on synchronisation and the utilisation of drag. SOFT MATTER 2015; 11:2364-2371. [PMID: 25675985 DOI: 10.1039/c4sm02611j] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this analytical study we demonstrate the richness of behaviour exhibited by bead-spring micro-swimmers, both in terms of known yet not fully explained effects such as synchronisation, and hitherto undiscovered phenomena such as the existence of two transport regimes where the swimmer shape has fundamentally different effects on the velocity. For this purpose we employ a micro-swimmer model composed of three arbitrarily-shaped rigid beads connected linearly by two springs. By analysing this swimmer in terms of the forces on the different beads, we determine the optimal kinematic parameters for sinusoidal driving, and also explain the pusher/puller nature of the swimmer. Moreover, we show that the phase difference between the swimmer's arms automatically attains values which maximise the swimming speed for a large region of the parameter space. Apart from this, we determine precisely the optimal bead shapes that maximise the velocity when the beads are constrained to be ellipsoids of a constant volume or surface area. On doing so, we discover the surprising existence of the aforementioned transport regimes in micro-swimming, where the motion is dominated by either a reduction of the drag force opposing the beads, or by the hydrodynamic interaction amongst them. Under some conditions, these regimes lead to counter-intuitive effects such as the most streamlined shapes forming locally the slowest swimmers.
Collapse
Affiliation(s)
- Jayant Pande
- Institute for Theoretical Physics, Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany.
| | | |
Collapse
|
9
|
|
10
|
Jabbarzadeh M, Hyon Y, Fu HC. Swimming fluctuations of micro-organisms due to heterogeneous microstructure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:043021. [PMID: 25375607 DOI: 10.1103/physreve.90.043021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2014] [Indexed: 06/04/2023]
Abstract
Swimming microorganisms in biological complex fluids may be greatly influenced by heterogeneous media and microstructure with length scales comparable to the organisms. A fundamental effect of swimming in a heterogeneous rather than homogeneous medium is that variations in local environments lead to swimming velocity fluctuations. Here we examine long-range hydrodynamic contributions to these fluctuations using a Najafi-Golestanian swimmer near spherical and filamentous obstacles. We find that forces on microstructures determine changes in swimming speed. For macroscopically isotropic networks, we also show how the variance of the fluctuations in swimming speeds are related to density and orientational correlations in the medium.
Collapse
Affiliation(s)
- Mehdi Jabbarzadeh
- Department of Mechanical Engineering, University of Nevada at Reno, Reno, Nevada 89557 USA
| | - YunKyong Hyon
- Division of Computational Sciences in Mathematics, National Institute for Mathematical Sciences, Daejeon, Republic of Korea 305-811
| | - Henry C Fu
- Department of Mechanical Engineering, University of Nevada at Reno, Reno, Nevada 89557 USA
| |
Collapse
|
11
|
Spagnolie SE, Liu B, Powers TR. Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes. PHYSICAL REVIEW LETTERS 2013; 111:068101. [PMID: 23971615 DOI: 10.1103/physrevlett.111.068101] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2013] [Indexed: 06/02/2023]
Abstract
The motion of a rotating helical body in a viscoelastic fluid is considered. In the case of force-free swimming, the introduction of viscoelasticity can either enhance or retard the swimming speed and locomotive efficiency, depending on the body geometry, fluid properties, and the body rotation rate. Numerical solutions of the Oldroyd-B equations show how previous theoretical predictions break down with increasing helical radius or with decreasing filament thickness. Helices of large pitch angle show an increase in swimming speed to a local maximum at a Deborah number of order unity. The numerical results show how the small-amplitude theoretical calculations connect smoothly to the large-amplitude experimental measurements.
Collapse
Affiliation(s)
- Saverio E Spagnolie
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706, USA.
| | | | | |
Collapse
|