8 results
Migration of confined micro-swimmers subject to anisotropic diffusion
- Mingyang Guan, Weiquan Jiang, Luoyi Tao, Guoqian Chen, Joseph H.W. Lee
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- Journal:
- Journal of Fluid Mechanics / Volume 985 / 25 April 2024
- Published online by Cambridge University Press:
- 29 April 2024, A44
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Shear-induced migration of elongated micro-swimmers exhibiting anisotropic Brownian diffusion at a population scale is investigated analytically in this work. We analyse the steady motion of confined ellipsoidal micro-swimmers subject to coupled diffusion in a general setting within a continuum homogenisation framework, as an extension of existing studies on macro-transport processes, by allowing for the direct coupling of convection and diffusion in local and global spaces. The analytical solutions are validated successfully by comparison with numerical results from Monte Carlo simulations. Subsequently, we demonstrate from the probability perspective that symmetric actuation does not yield net vertical polarisation in a horizontal flow, unless non-spherical shapes, external fields or direct coupling effects are harnessed to generate steady locomotion. Coupled diffusivities modify remarkably the drift velocity and vertical migration of motile micro-swimmers exposed to fluid shear. The interplay between stochastic swimming and preferential alignment could explain the diverse concentration and orientation distributions, including rheological formations of depletion layers, centreline focusing and surface accumulation. Results of the analytical study shed light on unravelling peculiar self-propulsion strategies and dispersion dynamics in active-matter systems, with implications for various transport problems arising from the fluctuating shape, size and other external or inter-particle interactions of swimmers in confined environments.
Streamwise dispersion of soluble matter in solvent flowing through a tube
- Mingyang Guan, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 980 / 10 February 2024
- Published online by Cambridge University Press:
- 02 February 2024, A33
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For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.
Dispersion of a gyrotactic micro-organism suspension in a vertical pipe: the buoyancy–flow coupling effect
- Bohan Wang, Weiquan Jiang, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 962 / 10 May 2023
- Published online by Cambridge University Press:
- 05 May 2023, A39
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Understanding the transport of micro-organisms in pipes is crucial to many fundamental problems, such as bioconvection and biodiesel production. In this work, we investigate the velocity profile and dispersion of a suspension of negatively buoyant, gyrotactic micro-organisms in a vertical pipe. With an imposed flow rate, the non-uniform radial cell concentration typical of gyrotaxis distorts the simple Poiseuille flow through inhomogeneous buoyancy, which in turn affects the cell concentration distribution. By solving the fundamental Smoluchowski equation and the Navier–Stokes equation simultaneously, we account for this bidirectional buoyancy–flow coupling effect. Asymptotic dispersion coefficients, namely, drift velocity and dispersivity, are further calculated with the obtained radial velocity and cell concentration profiles, which are assumed to be steady, symmetric and axially invariant. Using the gyrotactic micro-organism Chlamydomonas augustae as an example, detailed results are given to illustrate the effect of buoyancy–flow coupling. In downwelling flows, the buoyancy–flow coupling effect intensifies with the Richardson number $Ri$ quantifying the mean cell concentration, but is strongest at a moderate flow strength. The buoyancy–flow coupling effect significantly enhances the velocity and cell concentration in the central region, as well as the drift velocity and dispersivity. In contrast, the buoyancy–flow coupling effect is comparatively limited in upwelling flows, due to the dominant influence of the no-slip boundary condition imposed at the wall. Comparisons with predictions of existing approximate models are also presented.
Pre-asymptotic dispersion of active particles through a vertical pipe: the origin of hydrodynamic focusing
- Mingyang Guan, Weiquan Jiang, Bohan Wang, Li Zeng, Zhi Li, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 962 / 10 May 2023
- Published online by Cambridge University Press:
- 27 April 2023, A14
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When motile algal cells are exposed to gyrotactic torques, their swimming directions are guided to form radial accumulation, well known as hydrodynamic focusing. The origin of hydrodynamic focusing from the effects of active swimming, ambient flow and particle anisotropy is elucidated in the present study on the pre-asymptotic dispersion of active particles through a vertical pipe. With an extension of the Galerkin method to pipe flows, time-dependent solutions directly from the Smoluchowski equation in the position and orientation space are derived by series expansions of spherical harmonics and Bessel functions. Ballistic and diffusive scaling laws are examined with the predominance of self-propelled swimming, and computation is validated against an explicit benchmark solution and Lagrangian particle simulation. In the limit of extreme shear, the competitive roles of shear dispersion and Brownian rotation are reflected concretely in the pre-asymptotic phase of hydrodynamic focusing. For flows with various shear strengths, a concentration peak in near-wall regions with a smooth transition to hydrodynamic focusing is illustrated with richer phenomena in upwelling and downwelling flows. A newly observed regime through a vertical pipe, named transient effective trapping, is revealed as a transitional mode towards hydrodynamic focusing. The pre-asymptotic approach to hydrodynamic focusing is elaborated intensively through extensive solutions of concentration moments and macroscopic transport coefficients characterised by swimming and flow Péclet numbers. The unique findings for the origin of hydrodynamic focusing could provide insight into related micro-algae reactor technology and contribute to flow control and biomass transfer in confined environments.
Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation
- Bohan Wang, Weiquan Jiang, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 939 / 25 May 2022
- Published online by Cambridge University Press:
- 31 March 2022, A37
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Thin phytoplankton layers with vertically compressed structures found in stratified lakes and coastal water bodies have been a hot-spot in marine science and fluid mechanics. Although extensive efforts have been made to explore gyrotactic trapping as a possible mechanism, obvious inconsistencies remain there between the generalised Taylor dispersion method and individual-based model. In this work, a study directly from the fundamental Smoluchowski equation is carried out on the gyrotactic trapping mechanism in representative simple shear flows. With no approximation made to the fundamental equation and applying a biorthogonal expansion to the local moments of the probability density function, the evolution and steady state of the transport process are in good agreement with results of individual-based model, thus removing the gap between the continuum approach and individual-based model. The influences of strongly varying shear rate and boundary effect are reasonably scrutinised. The average swimming orientation with fixed local shear is highlighted as time-dependent rather than steady as previously assumed. The variations of characteristic time of the transient thin layer as functions of the flow intensity, gyrotaxis intensity and swimming ability are characterised. Sedimentation of the micro-swimmers is considered in some cases to reflect that micro-organisms are possibly negatively buoyant, with corresponding boundary conditions devised. A steady thin layer can be realised in the solution by adding a small settling speed to counteract the gravitactic focusing at the upper surface.
Transient dispersion process of active particles
- Weiquan Jiang, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 927 / 25 November 2021
- Published online by Cambridge University Press:
- 21 September 2021, A11
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Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For the active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1–34; vol. 899, 2020, A18), this work makes a semi-analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section–orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, initial condition, wall accumulation and particle shape on the transient dispersion process. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Although the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but impacts slightly on the drift and the skewness.
Dispersion of gyrotactic micro-organisms in pipe flows
- Weiquan Jiang, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 889 / 25 April 2020
- Published online by Cambridge University Press:
- 24 February 2020, A18
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The transport of motile micro-organisms exhibits rich and complex phenomena, of significance to various biological and environmental applications. For dilute suspensions of gyrotactic algae dispersing in vertical pipe flows, previous studies obtained only approximate values for the overall drift and dispersivity in the longitudinal direction, using two-step averaging methods with the Pedley–Kessler (PK) model and the generalized Taylor dispersion (GTD) model. These two-step methods impose restrictive assumptions: both the swimming Péclet number and the variation of shear rates relative to swimming must be sufficiently small. Thus, it is difficult to analyse the gyrotactic dispersion process in the ‘breakdown’ parameter region. Following a recent study of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1–34), this paper applies the integrated and precise one-step GTD method to study the overall dispersion process and performs a quantitative test for the applicability of two-step methods. An appropriate function basis for series expansions in the GTD method is proposed to deal with reflective boundary conditions imposed at the tube wall. Detailed results for Chlamydomonas nivalis are presented to illustrate the influence of the gyrotactic focusing on the overall dispersion process, for both downwelling and upwelling flows. The overall drift above the mean flow increases monotonically with the flow rate. However, the overall dispersivity will first decrease, then increase, and finally saturate as the flow rate increases, due to a combined effect of gyrotaxis, swimming and convection. Shear alignments of prolate cells will weaken the focusing, and thus reduce the drift and enhance the dispersivity. The predictions by two-step methods with the PK and GTD models are found to be successful inside their required parameter region. Within the ‘breakdown’ region, the two-step GTD method still gives reasonable results for the local distribution and the drift, but fails in the predictions of dispersivity.
Dispersion of active particles in confined unidirectional flows
- Weiquan Jiang, Guoqian Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 877 / 25 October 2019
- Published online by Cambridge University Press:
- 16 August 2019, pp. 1-34
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Transport of micro-organisms in confined flows can be characterized by a one-dimensional overall dispersion mechanism, of importance to various biotechnological applications. Based on Brenner’s generalized Taylor dispersion theory, an overall dispersion model is analytically studied in the present work for a dilute suspension of active particles in confined unidirectional flows. With the confined section of the channel and the swimming orientation space taken together as the local space and the longitudinal coordinate standing for the one-dimensional global space, this model is analytically accurate and possessed of wide adaptability in terms of the swimming Péclet number. The Robin boundary condition is introduced to account for wall accumulation of active particles, and compared with a typical reflection boundary condition. Complications associated with the boundary conditions for analytical derivation are removed respectively by a decomposition of the distribution function and an extension of the flow field. Interesting solutions are concretely found and intensively illustrated. Detailed case studies on the transport of spherical and rod-like particles to illustrate the dispersion mechanism are presented with respect to a Couette flow and a plane Poiseuille flow. Associated with the local distribution of particles, extensive descriptions are given for the dynamical system behaviours such as accumulation near both stable points/lines and boundaries, symmetric polarization structure, closed orbits, trapping effect, nematic alignments and bimodalization of swimming direction. For spherical particles, the accumulation is shown leading to a reduction of the overall dispersivity in both of the flows, while for rod-like active particles in the Couette flow, the accumulation can result in an enhancement of dispersion, due to the nematic alignments of particles towards streamlines.