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

Development of digital computer program for thermal network correction. Phase 2 - Program development. Phase 3 - Demonstration/application Final report

Developing digital computer program for correcting soft parameters of thermal network by Kalman filtering metho

Development of digital computer program for thermal network correction. Phase 1 - Investigation/feasibility study Final report

Feasibility of analytical error analysis applied to thermal network solution

Automated identification of flagella from videomicroscopy via the medial axis transform

Ubiquitous in eukaryotic organisms, the flagellum is a well-studied organelle that is well-known to be responsible for motility in a variety of organisms. Commonly necessitated in their study is the capability to image and subsequently track the movement of one or more flagella using videomicroscopy, requiring digital isolation and location of the flagellum within a sequence of frames. Such a process in general currently requires some researcher input, providing some manual estimate or reliance on an experiment-specific heuristic to correctly identify and track the motion of a flagellum. Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella are of approximately constant width when viewed by microscopy. We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae. ImageJ Macros for flagellar identification are provided, and high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic, enabling in general the automated generation of digitised kinematic descriptions of flagellar beating from videomicroscopy.Comment: 10 pages, 5 figures. Author accepted manuscript. Supplementary Material available at https://doi.org/10.1038/s41598-019-41459-

Systematic parameterizations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming

Systematic parameterizations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming.</p

A hydrodynamic slender-body theory for local rotation at zero Reynolds number

Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. While much research has focused on the local translational motion of these slender bodies, relatively little attention has been given to local rotation, even though it can be the dominant component of motion. In this study, we explore a classically motivated ansatz for the Stokes flow around a rotating slender body via superposed rotlet singularities, which leads us to pose an alternative ansatz that accounts for both translation and rotation. Through an asymptotic analysis that is supported by numerical examples, we determine the suitability of these flow ansatzes for capturing the fluid velocity at the surface of a slender body, assuming local axisymmetry of the object but allowing the cross-sectional radius to vary with arclength. In addition to formally justifying the presented slender-body ansatzes, this analysis reveals a markedly simple relation between the local angular velocity and the torque exerted on the body, which we term resistive torque theory. Though reminiscent of classical resistive force theories, this local relation is found to be algebraically accurate in the slender-body aspect ratio, even when translation is present, and is valid and required whenever local rotation contributes to the surface velocity at leading asymptotic order

Systematic parameterisations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multi-timescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we highlight and exemplify how a straightforward asymptotic analysis of these non-autonomous models can result in effective, systematic parameterisations of minimal models of microswimming

Boundary behaviours of Leishmania mexicana: a hydrodynamic simulation study

It is well established that the parasites of the genus Leishmania exhibit complex surface interactions with the sandfly vector midgut epithelium, but no prior study has considered the details of their hydrodynamics. Here, the boundary behaviours of motile Leishmania mexicana promastigotes are explored in a computational study using the boundary element method, with a model flagellar beating pattern that has been identified from digital videomicroscopy. In particular a simple flagellar kinematics is observed and quantified using image processing and mode identification techniques, suggesting a simple mechanical driver for the Leishmania beat. Phase plane analysis and long-time simulation of a range of Leishmania swimming scenarios demonstrate an absence of stable boundary motility for an idealised model promastigote near passive or repulsive surfaces, with behaviours ranging from boundary capture to deflection into the bulk. Indeed, the inclusion of a repulsive surface force results in the deflection of all surface-bound promastigotes, suggesting that the documented surface detachment of infective metacyclic promastigotes may be the result of morphological adaptation and simple hydrodynamics. Further, simulation elucidates a remarkable morphology-dependent hydrodynamic mechanism of boundary approach, hypothesised to be the cause of the well-established phenomenon of tip-first epithelial attachment of Leishmania promastigotes to the sandfly vector midgut.Comment: 12 pages, 9 figures. Supplementary Material available upon reques