Swimming sheet in a density-stratified fluid

2019 ◽  
Vol 874 ◽  
pp. 210-234 ◽  
Author(s):  
Rajat Dandekar ◽  
Vaseem A. Shaik ◽  
Arezoo M. Ardekani
Keyword(s):  
Wave Amplitude ◽  
Perturbation Expansion ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Mixing Efficiency ◽  
Swimming Velocity ◽  
Aquatic Environments ◽  
Regular Perturbation ◽  
Swimming Efficiency

In this work, we theoretically investigate the swimming velocity of a Taylor swimming sheet immersed in a linearly density-stratified fluid. We use a regular perturbation expansion approach to estimate the swimming velocity up to second order in wave amplitude. We divide our analysis into two regimes of low ($\ll O(1)$) and finite Reynolds numbers. We use our solution to understand the effect of stratification on the swimming behaviour of organisms. We find that stratification significantly influences motility characteristics of the swimmer such as the swimming speed, hydrodynamic power expenditure, swimming efficiency and the induced mixing, quantified by mixing efficiency and diapycnal eddy diffusivity. We explore this dependence in detail for both low and finite Reynolds number and elucidate the fundamental insights obtained. We expect our work to shed some light on the importance of stratification in the locomotion of organisms living in density-stratified aquatic environments.

scholarly journals Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers

2009 ◽  
Vol 632 ◽  
pp. 49-68 ◽  
Author(s):  
KING YEUNG YICK ◽  
CARLOS R. TORRES ◽  
THOMAS PEACOCK ◽  
ROMAN STOCKER
Keyword(s):  
Time Lapse ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
Aquatic Environments ◽  
Fluid Viscosity ◽  
Vertical Fluxes ◽  
Small Reynolds Numbers ◽  
Density Interfaces ◽  
Time Lapse Photography

We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri0.51, where Ri = a3N2/(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N)1/2 surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.

Small Reynolds Number Convection in Rotating Spherical Annuli

1979 ◽  
Vol 101 (3) ◽  
pp. 427-433 ◽  
Author(s):  
R. W. Douglass ◽  
E. J. Shaughnessy ◽  
B. R. Munson
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Velocity Ratio ◽  
Perturbation Expansion ◽  
Reynolds Numbers ◽  
Regular Perturbation ◽  
Optimum Configuration ◽  
Wide Range ◽  
Boussinesq Fluid ◽  
Steady Convection

A fourth order regular perturbation expansion in powers of the Reynolds number is used to investigate the steady convection of a stratified Boussinesq fluid in rotating spherical annuli. The results include the primary and secondary flow patterns, temperature distributions, total heat flux, and torque characteristics emphasizing their dependence on a wide range of radius and angular velocity ratios. Maximum usable Reynolds numbers were found and usually were larger than 10. The optimum configuration for convective heat transfer is a radius ratio of 0.35 and an angular velocity ratio of +1/3. This same configuration gives the largest torque as well.

Costs of transport for the scyphomedusa Stomolophus meleagris L. Agassiz

1987 ◽  
Vol 65 (11) ◽  
pp. 2690-2695 ◽  
Author(s):  
R. J. Larson
Keyword(s):  
Output Power ◽  
Power Function ◽  
Power Output ◽  
Reynolds Numbers ◽  
Power Input ◽  
Cost Of Transport ◽  
Swimming Efficiency ◽  
Wet Weight ◽  
Planktonic Crustaceans ◽  
Stomolophus Meleagris

The rhizostome scyphomedusa Stomolophus meleagris swims continuously at speeds up to 15 cm∙s−1. Mean velocities increased as a power function of wet weight up to 70 g but were mostly constant thereafter. Bell pulsations ranged from 1.7 to 3.6 Hz. Reynolds numbers equalled 900 – 13 000. During activity, medusae consumed 0.05 mL O2∙h−1∙g WW−1 (1.2 mL O2∙h−1∙g DW−1), at 30 °C. Rates for inactive medusae were 50% less. The estimated cost of transport ranged from 2 J∙kg−1∙m−1 at 5 g to 1 J∙kg−1∙m−1 at 1 kg. These rates are comparable to those of fishes and about 1/50th that of planktonic crustaceans. These results were unexpected in light of the typical inefficiency (power output/power input) of jet swimming. However, S. meleagris has a very low respiration rate relative to crustaceans and fish, which probably compensated for low swimming efficiency.

Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

2011 ◽  
Vol 678 ◽  
pp. 221-247 ◽  
Author(s):  
P. M. VLAHOVSKA ◽  
Y.-N. YOUNG ◽  
G. DANKER ◽  
C. MISBAH
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscosity Ratio ◽  
Perturbation Expansion ◽  
Shear Plane ◽  
Creeping Flow ◽  
Regular Perturbation ◽  
Cell Dynamics ◽  
Initial Shape ◽  
Flow Equations

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

scholarly journals Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1055
Author(s):  
Alireza Farahinia ◽  
Jafar Jamaati ◽  
Hamid Niazmand ◽  
Wenjun Zhang
Keyword(s):  
Reynolds Number ◽  
Zeta Potential ◽  
Electroosmotic Flow ◽  
Molecular Diffusion ◽  
Slip Surface ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Slip Coefficient ◽  
Mixing Rate ◽  
Heterogeneous Distribution

One approach to achieve a homogeneous mixture in microfluidic systems in the quickest time and shortest possible length is to employ electroosmotic flow characteristics with heterogeneous surface properties. Mixing using electroosmotic flow inside microchannels with homogeneous walls is done primarily under the influence of molecular diffusion, which is not strong enough to mix the fluids thoroughly. However, surface chemistry technology can help create desired patterns on microchannel walls to generate significant rotational currents and improve mixing efficiency remarkably. This study analyzes the function of a heterogeneous zeta-potential patch located on a microchannel wall in creating mixing inside a microchannel affected by electroosmotic flow and determines the optimal length to achieve the desired mixing rate. The approximate Helmholtz–Smoluchowski model is suggested to reduce computational costs and simplify the solving process. The results show that the heterogeneity length and location of the zeta-potential patch affect the final mixing proficiency. It was also observed that the slip coefficient on the wall has a more significant effect than the Reynolds number change on improving the mixing efficiency of electroosmotic micromixers, benefiting the heterogeneous distribution of zeta-potential. In addition, using a channel with a heterogeneous zeta-potential patch covered by a slip surface did not lead to an adequate mixing in low Reynolds numbers. Therefore, a homogeneous channel without any heterogeneity would be a priority in such a range of Reynolds numbers. However, increasing the Reynolds number and the presence of a slip coefficient on the heterogeneous channel wall enhances the mixing efficiency relative to the homogeneous one. It should be noted, though, that increasing the slip coefficient will make the mixing efficiency decrease sharply in any situation, especially in high Reynolds numbers.

A Planar Labyrinth Micromixer

2010 ◽  
Author(s):  
Jeremy T. Cogswell ◽  
Peng Li ◽  
Mohammad Faghri
Keyword(s):  
Soft Lithography ◽  
Lab On A Chip ◽  
Fluorescein Isothiocyanate ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Mixing Length ◽  
Two Fluids ◽  
Curved Channels ◽  
Passive Mixing ◽  
Important Challenge

Rapid mixing of two fluids in microchannels has posed an important challenge to the development of many integrated lab-on-a-chip systems. In this paper, we present a planar labyrinth micromixer (PLM) to achieve rapid and passive mixing by taking advantage of a synergistic combination of the Dean vortices in curved channels, a series of perturbation to the fluids from the sharp turns, and an expansion and contraction of the flow field via a circular chamber. The PLM is constructed in a single soft lithography step and the labyrinth has a footprint of 7.32 mm × 7.32 mm. Experiments using fluorescein isothiocyanate solutions and deionized water demonstrate that the design achieves fast and uniform mixing within 9.8 s to 32 ms for Reynolds numbers between 2.5 and 30. Compared to the mixing in the prevalent serpentine design, our design results in 38% and 79% improvements on the mixing efficiency at Re = 5 and Re = 30 respectively. An inverse relationship between mixing length and mass transfer Pe´clet number (Pe) is observed, which is superior to the logarithmic dependence of mixing length on Pe in chaotic mixers. Having a simple planar structure, the PLM can be easily integrated into lab-on-a-chip devices where passive mixing is needed.

Effects of Packing and Aspect Ratio on Mixing and Heterogeneous Catalysis in Microchannels

2007 ◽  
Author(s):  
Robert T. Bailey ◽  
Stephen Ryan ◽  
Frank Jones ◽  
Stephanie Wilson ◽  
James Hiestand
Keyword(s):  
Heterogeneous Catalysis ◽  
Aspect Ratio ◽  
Computational Models ◽  
Chemical Conversion ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Substantial Impact ◽  
Channel One ◽  
Aqueous Streams ◽  
Channel Aspect Ratio

Many industrial chemical processes involve the mixing of two or more liquids. By reducing chemical reactors to microscale dimensions, engineers seek to take advantage of decreased diffusion lengths, leading to increased effectiveness (e.g., higher purity of product) over larger process components. In this study, computational models developed using the commercial multiphysics code CFD-ACE+ are used to predict flow within microreactor channels. Two aqueous streams enter a channel—one containing a contaminant and the other devoid of the contaminant. Changes in two geometric attributes are investigated with respect to their effect on mixing of the streams: 1) packing feature layout within the channel and 2) channel aspect ratio. Reynolds numbers (Re) for the simulations range between 0.1 and 100. Results indicate that both packing feature position within the channel and channel aspect ratio can have a substantial impact on mixing. Between Re = 0.1 and Re = 1, mixing efficiency generally decreases with increasing Re; however, as the Re is increased from 1 to 100, fluid flow patterns in the channel are altered, and wake regions and streamline changes created by the packing features lead to improved mixing. Examples showing enhanced chemical conversion during heterogeneous catalysis as a result of better mixing are also presented.

A NOVEL 3D MICROMIXER WITH QUARTIC KOCH CURVE FRACTAL

2021 ◽  
pp. 2150049
Author(s):  
SIYUE XIONG ◽  
XUEYE CHEN
Keyword(s):  
Numerical Simulation ◽  
Deflection Angle ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Flow State ◽  
Koch Curve ◽  
Mixing Performance ◽  
Chaotic Convection ◽  
The Deflection Angle ◽  
High Application

In this paper, we mainly study the mixing performance of the micromixer with quartic Koch curve fractal (MQKCF) by numerical simulation. Changing the structure of the microchannel based on the fractal principle can significantly improve the fluid flow state in the microchannel and improve the mixing efficiency of the micromixer. This paper discussed the effects of different fractal deflection angles, microchannel heights and different fractal times on the mixing efficiency under four different Reynolds numbers (Re). It is found that changing the deflection angle of the fractal can bring extremely high benefits, which makes the fluid deflect and fold in the microchannel, enhancing the chaotic convection in the microchannel, and improve the mixing efficiency of the fluid. Under the reasonable arrangement of the quartic Koch curve fractal principle, it can give the micro-mixture more than 99% mixing efficiency. Based on the excellent mixing performance of MQKCF, it also has extremely high application value in the biochemical neighborhood.

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