Squirming motion in a Brinkman medium

2018 ◽  
Vol 855 ◽  
pp. 554-573 ◽  
Author(s):  
Herve Nganguia ◽  
On Shun Pak
Keyword(s):  
Viscous Fluid ◽  
Power Dissipation ◽  
Brinkman Equation ◽  
Reciprocal Theorem ◽  
Spatial Decay ◽  
Systematic Analysis ◽  
Fluid Medium ◽  
Swimming Efficiency ◽  
Micro Organisms ◽  
Brinkman Medium

Micro-organisms encounter heterogeneous viscous environments consisting of networks of obstacles embedded in a viscous fluid medium. In this paper we analyse the characteristics of swimming in a porous medium modelled by the Brinkman equation via a spherical squirmer model. The idealized geometry allows an analytical and exact solution of the flow surrounding a squirmer. The propulsion speed obtained agrees with previous results using the Lorentz reciprocal theorem. Our analysis extends these results to calculate the power dissipation and hence the swimming efficiency of the squirmer in a Brinkman medium. The analytical solution enables a systematic analysis of the structure of the flow surrounding the squirmer, which can be represented in terms of singularities in Brinkman flows. We also discuss the spatial decay of flows due to squirming motion in a Brinkman medium in comparison with the decay in a purely viscous fluid. The results lay the foundation for subsequent studies on hydrodynamic interactions, nutrient transport and uptake by micro-organisms in heterogeneous viscous environments.

Acoustic diffraction by a half-plane in a viscous fluid medium

2002 ◽  
Vol 112 (4) ◽  
pp. 1288-1296 ◽  
Author(s):  
Anthony M. J. Davis ◽  
Raymond J. Nagem
Keyword(s):  
Viscous Fluid ◽  
Half Plane ◽  
Fluid Medium ◽  
Acoustic Diffraction

Free vibration analysis of nano-plate in viscous fluid medium using nonlocal elasticity

2019 ◽  
Vol 74 ◽  
pp. 440-448 ◽  
Author(s):  
Shahrokh Hosseini-Hashemi ◽  
Reza Ahmadi Arpanahi ◽  
Sasan Rahmanian ◽  
Ali Ahmadi-Savadkoohi
Keyword(s):  
Viscous Fluid ◽  
Free Vibration ◽  
Nonlocal Elasticity ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Fluid Medium

scholarly journals A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190178 ◽  
Author(s):  
G. Corsi ◽  
A. De Simone ◽  
C. Maurini ◽  
S. Vidoli
Keyword(s):  
Viscous Fluid ◽  
Phase Speed ◽  
Travelling Wave ◽  
Viscous Fluids ◽  
Swimming Velocity ◽  
Active Materials ◽  
Seminal Paper ◽  
Transversal Displacement ◽  
Stable Equilibria ◽  
Micro Organisms

In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids.

scholarly journals Swimming mediated by ciliary beating: comparison with a squirmer model

2019 ◽  
Vol 874 ◽  
pp. 774-796 ◽  
Author(s):  
Hiroaki Ito ◽  
Toshihiro Omori ◽  
Takuji Ishikawa
Keyword(s):  
Cell Body ◽  
Hydrodynamic Interactions ◽  
Swimming Velocity ◽  
Energy Costs ◽  
Theoretical Studies ◽  
Free Swimming ◽  
Ciliary Beating ◽  
Aspect Ratios ◽  
Swimming Efficiency ◽  
Micro Organisms

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, like Paramecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

Axisymmetric Vibrations of a Piezoelectric Spherical Shell Submerged in a Compressible Viscous Fluid Medium

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Juxi Hu ◽  
Zhiping Qiu ◽  
Tsung-Chow Su
Keyword(s):  
Viscous Fluid ◽  
Natural Frequencies ◽  
Essential Feature ◽  
Elastic Shell ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Compressible Viscous Fluid ◽  
Previous Theory ◽  
Fluid Medium ◽  
Shell Motion

Axisymmetric vibrations of a hollow piezoelectric sphere submerged in a compressible viscous fluid medium are investigated. The piezoelectric sphere is radially polarized. The differential equations governing the shell motion are obtained by the use of Hamilton’s principle. Based on the classical bending theory of shells, it is shown that all the piezoelectric contributions can be included in the in vacuo natural frequencies and their corresponding mode shapes. As such, the previous theory on elastic shell vibration becomes readily extendable. The flow field, determined by the boundary layer theory, is coupled to the shell motion through no-slip and no-penetrating conditions. It is found that the contribution of the piezoelectric parameters in the thin shell’s free vibration is of small order and is negligible. Natural frequencies and their associated vibration characteristics are numerically obtained and presented for a Polyvinglindene fluoride (PVDF) shell submerged in water. Dynamic responses of a submerged piezoelectric sherical shell, and the associated radiation of sound are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. The vibrational, fluid loading, and energy flow characteristics are derived and evaluated for a PVDF shell submerged in water. The essential feature of the modal response is determined by various critical frequencies, such as resonant frequencies and vibration-absorbing frequencies. Viscous effect is found noticeable in several cases.

ULTRASONIC CONCENTRATION AND TRAPPING OF MICROSIZED PARTICLES IN A FLUID SUSPENSION

2012 ◽  
Vol 19 ◽  
pp. 196-205
Author(s):  
THEIN MIN HTIKE ◽  
KIAN-MENG LIM
Keyword(s):  
Acoustic Radiation ◽  
Radiation Force ◽  
Acoustic Energy ◽  
Ultrasonic Power ◽  
Fluidic Channel ◽  
Fluid Medium ◽  
Nodal Lines ◽  
Ultrasonic Standing Wave ◽  
Contrast Factor ◽  
Micro Organisms

We present a millimeter scale fluidic channel for concentrating and filtering microsized particles suspended in the fluid medium. The device takes on an h-shape with a narrow inlet and a wide outlet. By setting up an ultrasonic standing wave across the channel width, microparticles with positive acoustic contrast factor are constrained to move along pressure nodal lines within the fluid. The acoustic radiation force acts on the particles in the transverse direction, keeping the particles to the lower part of the outlet. As a result, a suspension with higher particle concentration is formed at the lower part of the outlet, while clean fluid can be extracted at the upper part of the outlet. A series of experimental results were obtained to study the performance of this concentration process for various volume flowrates and ultrasonic power used. For high ultrasonic power, the microparticles were found to be trapped in the fluid channel. A numerical model was also developed to study the strength of the acoustic energy density in the channel and its influence on the performance of the concentrator. This ultrasonic concentrator has potential in biomedical and environmental applications where cells and micro-organisms need to be filtered out from a fluid suspension.

Squirming in a viscous fluid enclosed by a Brinkman medium

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Herve Nganguia ◽  
Lailai Zhu ◽  
D. Palaniappan ◽  
On Shun Pak
Keyword(s):  
Viscous Fluid ◽  
Brinkman Medium
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