53 research outputs found
The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
Elastic filaments are vital to biological, physical and engineering systems,
from cilia driving fluid in the lungs to artificial swimmers and
micro-robotics. Simulating slender structures requires intricate balance of
elastic, body, active, and hydrodynamic moments, all in three-dimensions. Here,
we present a generalised 3D coarse-graining formulation that is efficient,
simple-to-implement, readily extendable and usable for a wide array of
applications. Our method allows for simulation of collections of 3D elastic
filaments, capable of full flexural and torsional deformations, coupled
non-locally via hydrodynamic interactions, and including multi-body
microhydrodynamics of structures with arbitrary geometry. The method exploits
the exponential mapping of quaternions for tracking three-dimensional rotations
of each interacting element in the system, allowing for computation times up to
150 times faster than a direct quaternion implementation. Spheres are used as a
`building block' of both filaments and solid micro-structures for
straightforward and intuitive construction of arbitrary three-dimensional
geometries present in the environment. We highlight the strengths of the method
in a series of non-trivial applications including bi-flagellated swimming,
sperm-egg scattering, and particle transport by cilia arrays. Applications to
lab-on-a-chip devices, multi-filaments, mono-to-multi flagellated
microorganisms, Brownian polymers, and micro-robotics are straightforward. A
Matlab code is provided for further customization and generalizations.Comment: 16 pages, 6 figure
Swimming by spinning: spinning-top type rotations regularize sperm swimming into persistently symmetric paths in 3D
Sperm modulate their flagellar symmetry to navigate through complex
physico-chemical environments and achieve reproductive function. Yet it remains
elusive how sperm swim forwards despite the inherent asymmetry of several
components that constitutes the flagellar engine. Despite the critical
importance of symmetry, or the lack of it, on sperm navigation and its
physiological state, there is no methodology to date that can robustly detect
the symmetry state of the beat in free-swimming sperm in 3D.How does symmetric
progressive swimming emerge even for asymmetric beating, and how can beating
(a)symmetry be inferred experimentally? Here, we numerically resolve the fluid
mechanics of swimming around asymmetrically beating spermatozoa. This reveals
that sperm spinning critically regularizes swimming into persistently symmetric
paths in 3D, allowing sperm to swim forwards despite any imperfections on the
beat. The sperm orientation in three-dimensions, and not the swimming path, can
inform the symmetry state of the beat, eliminating the need of tracking the
flagellum in 3D. We report a surprising correspondence between the movement of
sperm and spinning-top experiments, indicating that the flagellum drives
''spinning-top'' type rotations during sperm swimming, and that this parallel
is not a mere analogy. These results may prove essential in future studies on
the role of (a)symmetry in spinning and swimming microorganisms and
micro-robots, as body orientation detection has been vastly overlooked in
favour of swimming path detection. Altogether, sperm rotation may provide a
foolproof mechanism for forward propulsion and navigation in nature that would
otherwise not be possible for flagella with broken symmetry
Filament mechanics in a half-space via regularised Stokeslet segments
We present a generalisation of efficient numerical frameworks for modelling
fluid-filament interactions via the discretisation of a recently-developed,
non-local integral equation formulation to incorporate regularised Stokeslets
with half-space boundary conditions, as motivated by the importance of
confining geometries in many applications. We proceed to utilise this framework
to examine the drag on slender inextensible filaments moving near a boundary,
firstly with a relatively-simple example, evaluating the accuracy of resistive
force theories near boundaries using regularised Stokeslet segments. This
highlights that resistive force theories do not accurately quantify filament
dynamics in a range of circumstances, even with analytical corrections for the
boundary. However, there is the notable and important exception of movement in
a plane parallel to the boundary, where accuracy is maintained. In particular,
this justifies the judicious use of resistive force theories in examining the
mechanics of filaments and monoflagellate microswimmers with planar flagellar
patterns moving parallel to boundaries. We proceed to apply the numerical
framework developed here to consider how filament elastohydrodynamics can
impact drag near a boundary, analysing in detail the complex responses of a
passive cantilevered filament to an oscillatory flow. In particular, we
document the emergence of an asymmetric periodic beating in passive filaments
in particular parameter regimes, which are remarkably similar to the power and
reverse strokes exhibited by motile 9+2 cilia. Furthermore, these changes in
the morphology of the filament beating, arising from the fluid-structure
interactions, also induce a significant increase in the hydrodynamic drag of
the filament.Comment: 21 pages, 9 figures. Supplementary Material available upon reques
Controlling non-controllable scallops
A swimmer embedded on an inertialess fluid must perform a non-reciprocal motion to swim forward. The archetypal demonstration of this unique motion-constraint was introduced by Purcell with the so-called "scallop theorem". Scallop here is a minimal mathematical model of a swimmer composed by two arms connected via a hinge whose periodic motion (of opening and closing its arms) is not sufficient to achieve net displacement. Any source of asymmetry in the motion or in the forces/torques experienced by such a scallop will break the time-reversibility imposed by the Stokes linearity and lead to subsequent propulsion of the scallop. However, little is known about the controllability of time-reversible scalloping systems. Here, we consider two individually non-controllable scallops swimming together. Under a suitable geometric assumption on the configuration of the system, it is proved that controllability can be achieved as a consequence of their hydrodynamic interaction. A detailed analysis of the control system of equations is carried out analytically by means of geometric control theory. We obtain an analytic expression for the controlled displacement after a prescribed sequence of controls as a function of the phase difference of the two scallops. Numerical validation of the theoretical results is presented with model predictions in further agreement with the literature
A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension
Nonlinear amplitude dynamics in flagellar beating
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating
Hydrodynamics of elastic micro-filaments : model comparison and applications
International audienc
Physical biomarkers of disease progression:on-chip monitoring of changes in mechanobiology of colorectal cancer cells
Disease can induce changes to subcellular components, altering cell phenotype and leading to measurable bulk-material mechanical properties. The mechanical phenotyping of single cells therefore offers many potential diagnostic applications. Cells are viscoelastic and their response to an applied stress is highly dependent on the magnitude and timescale of the actuation. Microfluidics can be used to measure cell deformability over a wide range of flow conditions, operating two distinct flow regimes (shear and inertial) which can expose subtle mechanical properties arising from subcellular components. Here, we investigate the deformability of three colorectal cancer (CRC) cell lines using a range of flow conditions. These cell lines offer a model for CRC metastatic progression; SW480 derived from primary adenocarcinoma, HT29 from a more advanced primary tumor and SW620 from lymph-node metastasis. HL60 (leukemia cells) were also studied as a model circulatory cell, offering a non-epithelial comparison. We demonstrate that microfluidic induced flow deformation can be used to robustly detect mechanical changes associated with CRC progression. We also show that single-cell multivariate analysis, utilising deformation and relaxation dynamics, offers potential to distinguish these different cell types. These results point to the benefit of multiparameter determination for improving detection and accuracy of disease stage diagnosis
How do freshwater fish sperm find the egg? The physicochemical factors guiding the gamete encounters of externally fertilizing freshwater fish
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