Acclimatize experimental approach to adjudicate hydraulic coefficients under different bed material configurations and slopes with and without weir.

The primary purpose of this study was to evaluate the hydraulic coefficient of coarse aggregate grain size beds and hydraulic parameters under random and perpendicular bed configurations, as well as to explore the discharge coefficient for rectangular weirs. The research objectives were to compare flow resistance coefficients, evaluate the discharge coefficient for rectangular weirs, investigate the relationship between roughness coefficient and hydraulic parameters, and validate the theoretical hydraulic equation for the rectangular weir. This was achieved by analysing different bed configurations, bed slopes, and 20 and 30-mm bed materials. Sieve analysis was conducted on bed materials using American-standard sieves to determine their particle size distribution. The experiment was performed in a rectangular flume measuring 12 m in length, 0.31 m in width, and 0.45 m in depth. In a laboratory experiment, water was pumped into a flume using centrifugal pumps, and a rectangular weir was attached downstream for discharge measurement. The experiment investigated factors such as Manning roughness coefficient, bed material geometry, bed slope, and weir shapes. Approximately 1680 tests were conducted to analysed the impact of these factors on discharge and the coefficient of discharge. The average Manning's roughness coefficients for a grain size of 20 mm were 0.019 (with weir) and 0.019 (without weir) in a random bed configuration, and 0.028 (with weir) and 0.027 (without weir) in a perpendicular flow bed configuration. For a grain size of 30 mm, the coefficients were 0.023 (with weir) and 0.022 (without weir) in a random bed configuration, and 0.033 (with weir) and 0.026 (without weir) in a perpendicular flow bed configuration. The presence of a weir has affected Manning's roughness coefficients and discharge coefficients. With a weir, the roughness coefficients have generally been higher compared to without a weir, indicating increased roughness in the channel. The discharge coefficient for a rectangular weir with a grain size of 20 mm ranged from 0.39 to 0.84 (random bed) and 0.27 to 0.68 (perpendicular flow bed), while for a grain size of 30 mm it ranged from 0.31 to 0.81 (random bed) and 0.23 to 0.48 (perpendicular flow bed). The discharge coefficients have varied depending on the grain size and bed configuration, reflecting different flow efficiencies over the weir. Rough particles influenced flow and Manning's roughness coefficient value, then reduced discharge and velocity values. Under two bed configurations and slopes, beds with a grain size of 30 mm have higher roughness coefficients compared to those with a grain size of 20 mm. The models have shown that the roughness coefficient is inversely proportional to the discharge and directly proportional to the tailgate water levels. The coefficient of roughness and discharge coefficient are mainly influenced by the channel slopes, bed roughness, bed grain size, and bed configuration. A randomly configured bed with a 20 mm grain size gravel bed is preferred over a perpendicular bed configuration to handle high discharges. Using a 20 mm grain-size gravel bed in open-channel flow is more suitable than a 30 mm grain-size bed. Relying on the constant friction factor, Manning's n, is not recommended as it may result in design errors. These findings have the potential to improve hydraulic engineering design practices, enhancing the accuracy and efficiency of open-channel flow systems.

Turbulence model study for aerodynamic analysis of the leading edge tubercle wing for low Reynolds number flows.

A turbulence model study was performed to analyze the flow around the Tubercle Leading Edge (TLE) wing. Five turbulence models were selected to evaluate aerodynamic force coefficients and flow mechanism by comparing with existing literature results. The selected models are realizable k-ε, k-ω Shear Stress Transport (SST), ( γ - R e θ ) SST model, Transition k-k l -ω model and Stress- ω Reynolds Stress Model (RSM). For that purpose, the TLE wing model was developed by using the NACA0021 airfoil profile. The wing model is designed with tubercle wavelength of 0.11c and amplitude of 0.03c. Numerical simulation was performed at chord-based Reynolds number of Rec = 120,000. The Computational Fluid Dynamic (CFD) simulation reveals that among the selected turbulence models, Stress- ω RSM estimated aerodynamic forces (i.e. lift and drag) coefficients closest to that of the experimental values followed by realizable k-ε, ( γ - R e θ ) SST model, k-ω SST model and k-k l -ω model. However, at a higher angle of attacks i.e. at 16° & 20° k-ω SST model predicted closest drag and lift coefficient to that of the experimental values. Additionally, the critical observation of pressure contour confirmed that at the lower angle of attack Stress- ω RSM predicted strong Leading Edge (LE) suction followed by realizable k-ε, ( γ - R e θ )SST model, k-ω SST model and k-k l -ω model. Thus, the superiority of Stress- ω RSM in predicting the aerodynamic force coefficients is shown by the flow behavior. In addition to this pressure contours also confirmed that k-k l -ω model failed to predict tubercled wing aerodynamic performance. At higher angles of attacks k-ω SST model estimated aerodynamic force coefficients closest to that of the experimental values, thus k-ω SST model is used at 16° & 20° AoAs. The observed streamline behavior for different turbulence models showed that the Stress- ω RSM model and k-k l -ω model failed to model flow behavior at higher AoAs, whereas k-ω SST model is a better approach to model separated flows that experience strong flow recirculation zone.

Influence of vegetation on heavy metal Cr release process from bottom sediment under unidirectional flows and regular waves.

As human activities become more intensive, a substantial number of heavy metals are discharged into estuarine or wetland environments. Due to the poor degradability, heavy metals are prone to adsorption and deposition on suspended particles in bottom sediments. Subsequently, under the influence of disturbances, there is a potential for their re-release, causing secondary pollution. To investigate the release process of the heavy metal Cr from sediment, laboratory experiments were conducted under both unidirectional flow and regular wave conditions. At the initial stage, the temporal trends of particulate (CrP) and dissolved (CrD) Chromium concentrations were both characterized by initial increments followed by stabilization and continuous escalation. Vertically, the stable concentrations of CrP and CrD increased with the presence of vegetation and the enhancement of hydrodynamics. The Elovich equation, pseudo-second-order kinetic equation, Double constant equation (Freundlich model), and parabolic diffusion equation were employed to predict the release process of CrD from bottom sediment. The Elovich equation proved most suitable for describing the release process of CrD, with an R2 exceeding 0.9. In order to assess the influence of vegetation on the Cr release process, the Stem-Reynolds were introduced to modify the Elovich equation. The final maximum error was 12 % (excluding the initial stage), which was much lower than that using the original Elovich equation (maximum error of 32 %). The study findings provide practical support for estuarine and wetland managers to formulate effective heavy metal management measures, which contribute to the conservation and sustainable management of aquatic ecosystems.

A Novel Experimental Apparatus for Characterizing Flow Regime in Mechanically Stirred Tanks through Force Sensors.

Pressure fluctuations in a mixing tank can provide valuable information about the existing flow regime within the tank, which in turn influences the degree of mixing that can be achieved. In the present work, we propose a prototype for identifying the flow regime in mechanically stirred tanks equipped with four vertical baffles through the characterization of pressure fluctuations. Our innovative proposal is based on force sensors strategically placed in the baffles of the mixing tank. The signals coming from the sensors are transmitted to an electronic module based on an Arduino UNO development board. In the electronic module, the pressure signals are conditioned, amplified and sent via Bluetooth to a computer. In the computer, the signals can be plotted or stored in an Excel file. In addition, the proposed system includes a moving average filtering and a hierarchical bottom-up clustering analysis that can determine the real-time flow regime (i.e., the Reynolds number, Re) in which the tank was operated during the mixing process. Finally, to demonstrate the versatility of the proposed prototype, experiments were conducted to identify the Reynolds number for different flow regimes (static, laminar, transition and turbulent), i.e., 0≤Re≤ 42,955. Obtained results were in agreement with the prevailing consensus on the onset and developed from different flow regimes in mechanically stirred tanks.

Performance evaluation of nanofluid-based photovoltaic thermal (PVT) system with regression analysis.

The recent global energy crisis has shocked Bangladesh's power sectors, and experts recommend using alternative energy sources to conserve natural gas, fossil fuels, and electricity. Numerous investigations on the photovoltaic thermal (PVT) system have been carried out to get the source efficiently. As a result, a parametric evaluation of the PVT system's efficiency in Dhaka, Bangladesh, is investigated numerically using CNT nanofluid as a coolant. The numerical simulation is performed using the Galerkin weighted residual based finite element method. For accurate computations, the meteorological data for Dhaka, Bangladesh, is taken from open sources of Renewables.ninja. The effect of regulating parameters Reynolds number (200 ≤ Re ≤ 1000), solar irradiation (200 W/m2 ≤ G ≤ 1000 W/m2), and the monthly influence on performance such as cell temperature, fluid domain exit temperature, efficiencies, and energy are discussed. In addition, regression analyses of electrical efficiency and thermal efficiency are discussed for the input variables Reynolds number and solar irradiation. After postprocessing, empirical results are compiled and presented as 3D surface graphs, tables, and line diagrams. As the Reynolds number increased, the cell temperature and discharge temperature decreased, resulting in increased efficiency. However, the opposite situation is found for solar irradiation. Month-to-month variation also has a considerable impact on photovoltaic thermal performance. This research will help to improve the efficacy of PVTs in Dhaka, Bangladesh, by identifying useful alternative renewable energy sources.

Influence of the internal structure of straight microchannels on inertial transport behavior of particles.

The rapid advancement of Micro-Electro-Mechanical Systems (MEMS) technology has established microfluidics as a pivotal field. This technology marks the onset of a new era in various applications, including drug testing, cell culture, and disease monitoring, underscoring its extensive practicality and potential for future exploration. This research delves into the intricate behavior of particle inertial migration within microchannels, particularly focusing on the impact of different channel structures and Reynolds numbers (Re). Our studies reveal that particles in microchannels with one-sided sharp-cornered microstructures migrate towards the sharp corner at a relative position of 0.4 under low flow rates, and towards the straight wall side at a relative position of 0.8 under high flow rates. The migration pattern of equilibrium positions varies with different arrangements of sharp-corner structures, achieving stability at the channel's center only when the sharp corners are symmetrically arranged on both sides. Our investigation into the shape of microstructures indicates that sharp-cornered structures generate a more stable secondary flow compared to rectangular and semi-circular structures, preventing particle aggregation at the outlet. To address the challenges associated with handling variable cross-section geometries and solid-wall boundaries in dissipative particle dynamics methods effectively, we have developed a dissipative particle dynamics model specifically for analyzing such microchannels. Building upon our previous research, this model introduces a conservative force coefficient for particles within the microstructured region and an interaction zone that only involves repulsive forces, aligning well with experimental outcomes. Through the study of microstructures' geometric shapes, this paper offers guidance for designing microchannels for particle enrichment. Furthermore, the dissipative particle dynamics model established for the particle flow and solid structure interaction within microstructured channels provides insights into the mesoscale dynamics of liquid-solid two-phase flow and particle motion. In conclusion, this paper aims to enhance particle motion sample preparation techniques, thereby broadening the scope of microfluidic applications in the biomedical field.

Numerical Simulation of the Advantages of the Figure-Eight Flapping Motion of an Insect on Aerodynamics under Low Reynolds Number Conditions.

In proceeding with the advanced development of small unmanned aerial vehicles (UAVs), which are small flying machines, understanding the flight of insects is important because UAVs that use flight are attracting attention. The figure-eight trajectory of the wing tips is often observed in the flight of insects. In this study, we investigated the more efficient figure-eight motion patterns in generating lift during the hovering motion and the relationship between figure-eight motion and Reynolds number. For this purpose, we compared the ratios of the cycle-averaged lift coefficient to the power coefficient generated from each motion by varying the elevation motion angle, which is the rotational motion that represents the figure-eight motion, and the Reynolds number. The result showed that the motion with a smaller initial phase of the elevation motion angle (φe0≤90°) could generate lift more efficiently at all Reynolds numbers. In addition, the figure-eight motion was more effective when the Reynolds number was low.

The influence of needleless connectors and inserted catheters on flow rates through vascular introducer sheaths.

SummaryA vascular introducer sheath is often used for rapid volume replacement. However, common manipulations such as the addition of needleless connectors to infusion ports and the insertion of catheters or other devices through the introducer sheath may impede flow. In this study we utilised a rapid infuser to deliver room-temperature normal saline through two introducer sheath configurations with and without the addition of needleless connectors and the placement of catheters through the introducer sheaths. The maximal flow rate delivered by the rapid infuser was 1000 mL/min, which was observed with both introducer sheath sizes tested without additional resistive elements. However, with the addition of a needleless connector, flow rates through the introducer sheaths were substantially lower (64 (standard deviation (SD) 6) mL/min and 61 (SD 7) mL/min for the 8.5 Fr and 9 Fr introducers, respectively). Flow rates were also reduced when catheters were placed within the sheaths (298 (SD 9) mL/min with the 7 Fr catheter and 74 (SD 9) mL/min with the 8 Fr catheter placed in an 8.5 Fr sheath; 649 (SD 6) mL/min with the 7 Fr catheter and 356 (SD 14) mL/min with the 8 Fr catheter placed in the 9 Fr sheath). These findings indicated that both needleless connectors and the placement of catheters through vascular introducer sheaths substantially reduced potential flow rates. Even 'large' vascular introducer sheaths capable of delivering high flow rates could be rendered minimally effective for rapid fluid administration when used in this way. Clinicians should consider these impediments to flow when rapid fluid administration is required, and obtain alternative vascular access if necessary.

Intrinsic dissolution rate modeling for the pharmacopoeia apparatus rotating disk compared to flow channel method.

For a solid understanding of drug characteristics, in vitro measurement of the intrinsic dissolution rate is important. Hydrodynamics are often emphasized as the decisive parameter influencing the dissolution. In this study, experiments and computational fluid dynamic (CFD) simulations showed that the mixing behavior in the rotating disc apparatus causes an inhomogeneous flow field and a systematic error in the calculation of the intrinsic dissolution rate. This error is affected by both the experimental time and the velocity. Due to the rotational movement around the tablet center, commonly utilized in pharmacopeia methods, a broad variance is present with regard to the impact of fluid velocity on individual particles of the specimen surface. As this is significantly reduced in the case of uniform overflow, the flow channel is recommended for investigating the dissolution behavior. It is shown that rotating disc measurements can be compared with flow channel measurements after adjusting the measured data for the rotating disc based on a proposed, representative Reynolds number and a suggested apparatus-dependent correction factor. Additionally, modeling the apparatus-independent intrinsic dissolution rate for different temperatures in the rotating disc apparatus is possible using the adapted Levich's equation.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics.

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

Frequency dependence of ultrasonic effects on the kinetics of hen egg white lysozyme fibrillation.

Our study aimed to investigate the effects of ultrasound on the fibrillation kinetics of HEWL (hen egg white lysozyme) and its physicochemical properties. Ultrasound, a mechanical wave, can induce conformational changes in proteins. To achieve this, we developed an ultrasound exposure system and used various biophysical techniques, including ThT fluorescence spectroscopy, ATR-FTIR, Far-UV CD spectrophotometry, Fluorescence microscopy, UV-spectroscopy, and seeding experiments. Our results revealed that higher frequencies significantly accelerated the fibrillation of lysozyme by unfolding the native protein and promoting the fibrillation process, thereby reducing the lag time. We observed a change in the secondary structure of the sonicated protein change to the ß-structure, but there was no difference in the Tm of native and sonicated proteins. Furthermore, we found that higher ultrasound frequencies had a greater seeding effect. We propose that the effect of frequency can be explained by the impact of the Reynolds number, and for the Megahertz frequency range, we are almost at the transition regime of turbulence. Our results suggest that laminar flows may not induce any significant change in the fibrillation kinetics, while turbulent flows may affect the process.

Effect of porous density of twisted tape inserts on heat transfer performance inside a closed conduit.

This study examines the impact of varying the porosity density of twisted tape inserts (TTI) on the temperature distribution, fluid velocities, heat transfer coefficients (HTC), Nusselt numbers (Nu), turbulent kinetic energy (TKE), and performance from 5000 to 12500 Reynolds numbers (Re). The entire process involved the design of TTIs and double pipe heat exchangers using SolidWorks. Subsequently, a three-dimensional fluid flow model was employed to solve equations related to energy mass, energy, and momentum within the ANSYS Fluent interfaces. The findings highlight the noteworthy impact of high porosity TTIs, which consistently reduce temperature spans, increase fluid velocities, and greatly HTC and Nu when compared to low porosity TTI, typical TTI, and plain tubes. Furthermore, high porosity TTI significantly increases TKE, indicating increased fluid turbulence and higher heat transfer efficiency, especially at Re = 12500. The assessment of PEC emphasizes the superiority of high porosity TTI, demonstrating their significant performance increase potential of over 6.44 % over low porosity TTI and a staggering 62.5 % above typical TTI. In conclusion, high porosity TTI emerges as a potential solution for improving heat transfer efficiency and overall system performance in a variety of industrial applications, promising enhanced energy efficiency and superior performance.

Asymmetric bistability of chiral particle orientation in viscous shear flows.

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a nonchiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here, we use a high-resolution microprinting technique to fabricate microparticles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these microparticles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments, we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations, and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport and bacterial rheotaxis and might allow the development of targeted delivery applications.

Nonreciprocal interactions give rise to fast cilium synchronization in finite systems.

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.

Simulations of Flows via CFD in Microchannels for Characterizing Entrance Region and Developing New Correlations for Hydrodynamic Entrance Length.

Devices with microchannels are relatively new, and many correlations are not yet developed to design them efficiently. In microchannels, the flow regime is primarily laminar, where entrance length may occupy a significant section of the flow channel. Therefore, several computational fluid dynamic simulations were performed in this research to characterize the developing flow regime. The new correlations of entrance length were developed from a vast number of numerical results obtained from these simulations. A three-dimensional laminar flow for 37 Reynolds numbers (0.1, 0.2, …, 1, 2, …, 10, 20, …, 100, 200, …, 1000), primarily in low regime with water flow through six rectangular microchannels (aspect ratio: 1, 0.75, 0.5, 0.25, 0.2, 0.125), has been modeled, conducting 222 simulations to characterize flow developments and ascertain progressive velocity profile shapes. Examination of the fully developed flow condition was considered using traditional criteria such as velocity and incremental pressure drop number. Additionally, a new criterion was presented based on fRe. Numerical results from the present simulations were validated by comparing the fully developed velocity profile, friction factor, and hydrodynamic entrance length for Re > 100 in rectangular channels, for which accurate data are available in the literature. There is a need for hydrodynamic entrance length correlations in a low Reynolds number regime (Re < 100). So, the model was run numerous times to generate a vast amount of numerical data that yielded two new correlations based on the velocity and fRe criteria.

Hydrodynamic interactions between squirmers near walls: far-field dynamics and near-field cluster stability.

Confinement increases contacts between microswimmers in dilute suspensions and affects their interactions. In particular, boundaries have been shown experimentally to lead to the formation of clusters that would not occur in bulk fluids. To what extent does hydrodynamics govern these boundary-driven encounters between microswimmers? We consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through far-field interaction of a pair of weak squirmers, as well as the lubrication interactions occurring after contact between two or more squirmers. In the far field, the orientation of microswimmers is controlled by the wall and the squirming parameter. The presence of a second swimmer influences the orientation of the original squirmer, but for weak squirmers, most of the interaction occurs after contact. We thus analyse next the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilize clusters of pullers, while the opposite is true for pushers; to be stable, clusters of pushers thus need to be governed by other interactions (e.g. phoretic). This simplified approach to the phenomenon of active clustering enables us to highlight the hydrodynamic contribution, which can be hard to isolate in experimental realizations.

Mobile mechanical signal generator for macrophage polarization.

The importance of mechanical signals in regulating the fate of macrophages is gaining increased attention recently. However, the recently used mechanical signals normally rely on the physical characteristics of matrix with non-specificity and instability or mechanical loading devices with uncontrollability and complexity. Herein, we demonstrate the successful fabrication of self-assembled microrobots (SMRs) based on magnetic nanoparticles as local mechanical signal generators for precise macrophage polarization. Under a rotating magnetic field (RMF), the propulsion of SMRs occurs due to the elastic deformation via magnetic force and hydrodynamics. SMRs perform wireless navigation toward the targeted macrophage in a controllable manner and subsequently rotate around the cell for mechanical signal generation. Macrophages are eventually polarized from M0 to anti-inflammatory related M2 phenotypes by blocking the Piezo1-activating protein-1 (AP-1）-CCL2 signaling pathway. The as-developed microrobot system provides a new platform of mechanical signal loading for macrophage polarization, which holds great potential for precise regulation of cell fate.

Reduction of fluid forces for flow past side-by-side cylinders using downstream attached splitter plates.

A two-dimensional numerical simulation is performed to investigate the drag reduction and vortex shedding suppression behind three square cylinders with attached splitter plates in the downstream region at a low Reynolds number (Re = 150). Numerical calculations are carried out using the lattice Boltzmann method. The study is carried out for various values of gap spacing between the cylinders and different splitter plate lengths. The vortices are completely chaotic at very small spacing, as observed. The splitter plates are critical in suppressing shedding and reducing drag on the objects. The splitter plates with lengths greater than two fully control the jet interaction at low spacing values. There is maximum percentage reduction in CDmean for small spacing and the selected largest splitter plate length. Furthermore, systematic investigation reveals that splitter plates significantly suppress the fluctuating lift in addition to drastically reducing the drag.

Squirmer hydrodynamics near a periodic surface topography.

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Transport of a passive scalar in wide channels with surface topography: An asymptotic theory.

We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our asymptotic theory relies on a domain perturbation approach for small roughness amplitudes of the channel and holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e. the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion diffusion tensor.