Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible affects transient dispersion, Zhang, Hesse & Wang ( J. Fluid Mech. , vol. 828, 2017, pp. 733–752) have investigated temporal evolution moments using Laplace transform method. Owing to difficulties introduced by adsorption–desorption boundary condition, great challenges arise from inverse transform:...

Understanding the statistics of bedload particle motions is great importance. To model hop events which are defined as trajectories particles moving successively from start to end their motions, recently, Wu et al. ( Water Resour. Res. , vol. 56, 2020, p. e2019WR025116) have successfully performed individual-based simulations according Fokker–Planck equation for velocities. However, analytical solutions still not available due (i) difficulties in treating velocity-dependent diffusivity, and...

Abstract The rich and complex phenomena of the transport active particles like microorganisms in shear flows are great significance to various biological environmental applications. Recent studies have shown that motility gyrotaxis algae could greatly influence their waters. However, little attention has been paid initial transient regime when classical Taylor dispersion model is not applicable. To tackle this problem, we resort Gill's generalized for passive solute, which potential...

Transport of micro-organisms in confined flows can be characterized by a one-dimensional overall dispersion mechanism, importance to various biotechnological applications. Based on Brenner’s generalized Taylor theory, an model is analytically studied the present work for dilute suspension active particles unidirectional flows. With section channel and swimming orientation space taken together as local longitudinal coordinate standing global space, this accurate possessed wide adaptability...

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 confined ellipsoidal subject to coupled general setting within continuum homogenisation framework, as an extension existing studies on macro-transport processes, by allowing for direct coupling convection and local global spaces. The analytical solutions are validated successfully comparison with numerical...

Motivated by emerging applications in bio-microfluidic devices, the present study rigorously examines generalized Taylor–Gill hydrodynamic dispersion of a point source solute injected into microchannel, influenced constant axial static electric field along channel and charged surface with different wall potentials. The engages first-order irreversible chemical reaction at both microchannel walls. By incorporating potentials absorptive coefficients lower upper walls, current transport model...

The analysis of Taylor dispersion in a fluid flowing through narrow pipe is considerable interest among the scientific community. Most studies on primarily considered transversely uniform release contaminant at initial moment, while only few have addressed influence condition process tube flow. present work investigates transient with ring-source solute by means an unsteady two-dimensional transport model. An irreversible absorptive type first-order reaction also considered. model solved...

Oriented locomotion in micro-swimmer populations is commonly observed response to various stimuli through self-propulsion (taxis). In simple linear orienting fields, swimmers align by rotating with the field. However, their mean does not always follow gradient, and theory for overall orientational spatial dynamics of micro-swimmers still needs be developed. Following Shaik et al. [Soft Matter 19, 1384 (2023)] Théry [Phys. Rev. Lett. 132, 108301 (2024)], we investigate how manipulate...

Many particles, whether passive or active, possess elongated shapes. When these particles settle swim in shear flows, they often form regions of accumulation and depletion. Additionally, the density contrast between fluid can further alter flow by increasing local suspension density, resulting a two-way buoyancy–flow coupling mechanism. This study investigates coupled dispersion active spheroids, examining effects elongation, orientation-dependent settling gyrotaxis vertical pipe subjected...

We consider a setting with two infinite parallel plates, where the diffusive substance is adsorbed at lower plate, simultaneously advected longitudinally by main flow and vertically crossflow. utilize classical method of moments along eigenfunction expansion to calculate up fourth-order, thus effects non-Gaussian properties can be reflected. Compared result Brownian dynamics simulations, present work shown sufficient cover pre-asymptotic dispersion regime out reach generalized Taylor (GTD)...

Abstract Predicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications water resources. While a semianalytical study has been made steady dispersion with continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907 ), an in‐depth analytical investigation yet to be performed more complicated case transient due instantaneous release. In regard pioneering benchmark observation (Murphy 2007,...

Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by Taylor dispersion model, are of great practical interest to various applications. For active process flows, previous analytical studies focused on long-time asymptotic values characteristics. Only several numerical preliminarily investigated temporal evolution. Extending recent Jiang & Chen ( J. Fluid Mech. , vol. 877, 2019, pp. 1–34; 899, 2020, A18), this work makes...

Thin phytoplankton layers with vertically compressed structures found in stratified lakes and coastal water bodies have been a hot-spot marine science fluid mechanics. Although extensive efforts made to explore gyrotactic trapping as possible mechanism, obvious inconsistencies remain there between the generalised Taylor dispersion method individual-based model. In this work, study directly from fundamental Smoluchowski equation is carried out on mechanism representative simple shear flows....

When motile algal cells are exposed to gyrotactic torques, their swimming directions guided form radial accumulation, well known as hydrodynamic focusing. The origin of focusing from the effects active swimming, ambient flow and particle anisotropy is elucidated in present study on pre-asymptotic dispersion particles through a vertical pipe. With an extension Galerkin method pipe flows, time-dependent solutions directly Smoluchowski equation position orientation space derived by series...

Abstract Research on active particles has primarily focused transport in relatively weak flows, during which their swimming plays a significant role. However, natural or manmade waterways, the ambient flow velocity and water depth can be order of approximately 1 m/s m, respectively, generating turbulent diffusion that may strong enough to potentially dominate process, so might negligible. In this paper, we propose theoretical framework aiming at identifying threshold effects become...

The accumulation of swimming microorganisms at surfaces is an essential feature various physical, chemical, and biological processes in confined spaces. To date, this mainly assumed to depend on the change speed angular velocity caused by cell-wall contact hydrodynamic interaction. Here, we measured trajectories Heterosigma akashiwo (a biflagellate marine alga) near vertical horizontal rigid boundaries. We observed that probability sharp turns greatly increased a wall, resulting significant...

Previous studies of solute transport in two-zone packed tube flows focused only on the cross-sectional mean concentration, a Gaussian distribution with advection velocity and Taylor dispersivity. This work analytically investigates complete spatial concentration distribution. The two-dimensional (longitudinal transverse) is obtained, by Chatwin’s long-time asymptotic technique: Edgeworth expansion. Non-Gaussian effects like skewness kurtosis are included solution. Three cases different...