Diffusion of swimming model micro-organisms in a semi-dilute suspension

2007 ◽  
Vol 588 ◽  
pp. 437-462 ◽  
Author(s):  
TAKUJI ISHIKAWA ◽  
T. J. PEDLEY
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Reynolds Numbers ◽  
Surface Velocity ◽  
Biased Random Walk ◽  
Long Time ◽  
Upward Velocity ◽  
Micro Organisms ◽  
Diffusive Behaviour

The diffusive behaviour of swimming micro-organisms should be clarified in order to obtain a better continuum model for cell suspensions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 or 27 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. In the case of (non-bottom-heavy) squirmers, both the translational and the orientational spreading of squirmers is correctly described as a diffusive process over a sufficiently long time scale, even though all the movements of the squirmers were deterministically calculated. Scaling of the results on the assumption that the squirmer trajectories are unbiased random walks is shown to capture some but not all of the main features of the results. In the case of (bottom-heavy) squirmers, the diffusive behaviour in squirmers' orientations can be described by a biased random walk model, but only when the effect of hydrodynamic interaction dominates that of the bottom-heaviness. The spreading of bottom-heavy squirmers in the horizontal directions show diffusive behaviour, and that in the vertical direction also does when the average upward velocity is subtracted. The rotational diffusivity in this case, at a volume fractionc=0.1, is shown to be at least as large as that previously measured in very dilute populations of swimming algal cells (Chlamydomonas nivalis).

scholarly journals Mathematical analysis of bio-convective micropolar nanofluid

2019 ◽  
Vol 6 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Sohail Nadeem ◽  
Muhammad Naveed Khan ◽  
Noor Muhammad ◽  
Shafiq Ahmad
Keyword(s):  
Differential Equations ◽  
Microbial Fuel Cells ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Convection Flow ◽  
Micropolar Nanofluid ◽  
Exponentially Stretching ◽  
Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

Numerical study of nanofluid flow and heat transfer over a rotating disk using Buongiorno’s model

2017 ◽  
Vol 27 (1) ◽  
pp. 221-234 ◽  
Author(s):  
Junaid Ahmad Khan ◽  
M. Mustafa ◽  
T. Hayat ◽  
Mustafa Turkyilmazoglu ◽  
A. Alsaedi
Keyword(s):  
Brownian Motion ◽  
Volume Fraction ◽  
Numerical Study ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Rotating Disk ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Buongiorno Model

Purpose The purpose of the present study is to explore a three-dimensional rotating flow of water-based nanofluids caused by an infinite rotating disk. Design/methodology/approach Mathematical formulation is performed using the well-known Buongiorno model which accounts for the combined influence of Brownian motion and thermophoresis. The recently suggested condition of passively controlled wall nanoparticle volume fraction has been adopted. Findings The results reveal that temperature decreases with an increase in thermophoresis parameter, whereas it is negligibly affected with a variation in the Brownian motion parameter. Axial velocity is negative because of the downward flow in the vertical direction. Originality/value Two- and three-dimensional streamlines are also sketched and discussed. The computations are found to be in very good agreement with the those of existing studies in the literature for pure fluid.

A computational model of the collective fluid dynamics of motile micro-organisms

2002 ◽  
Vol 455 ◽  
pp. 149-174 ◽  
Author(s):  
MATTHEW M. HOPKINS ◽  
LISA J. FAUCI
Keyword(s):  
Fluid Dynamics ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Point Sources ◽  
Physical Factors ◽  
Modelling Framework ◽  
Long Time ◽  
Micro Organisms

A mathematical model and numerical method for studying the collective dynamics of geotactic, gyrotactic and chemotactic micro-organisms immersed in a viscous fluid is presented. The Navier–Stokes equations of fluid dynamics are solved in the presence of a discrete collection of micro-organisms. These microbes act as point sources of gravitational force in the fluid equations, and thus affect the fluid flow. Physical factors, e.g. vorticity and gravity, as well as sensory factors affect swimming speed and direction. In the case of chemotactic microbes, the swimming orientation is a function of a molecular field. In the model considered here, the molecules are a nutrient whose consumption results in an upward gradient of concentration that drives its downward diffusion. The resultant upward chemotactically induced accumulation of cells results in (Rayleigh–Taylor) instability and eventually in steady or chaotic convection that transports molecules and affects the translocation of organisms. Computational results that examine the long-time behaviour of the full nonlinear system are presented.The actual dynamical system consisting of fluid and suspended swimming organisms is obviously three-dimensional, as are the basic modelling equations. While the computations presented in this paper are two-dimensional, they provide results that match remarkably well the spatial patterns and long-time temporal dynamics of actual experiments; various physically applicable assumptions yield steady states, chaotic states, and bottom-standing plumes. The simplified representation of microbes as point particles allows the variation of input parameters and modelling details, while performing calculations with very large numbers of particles (≈104–105), enough so that realistic cell concentrations and macroscopic fluid effects can be modelled with one particle representing one microbe, rather than some collection of microbes. It is demonstrated that this modelling framework can be used to test hypotheses concerning the coupled effects of microbial behaviour, fluid dynamics and molecular mixing. Thus, not only are insights provided into the differing dynamics concerning purely geotactic and gyrotactic microbes, the dynamics of competing strategies for chemotaxis, but it is demonstrated that relatively economical explorations in two dimensions can deliver striking insights and distinguish among hypotheses.

scholarly journals Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Raffaele Colombi ◽  
Niclas Rohde ◽  
Michael Schlüter ◽  
Alexandra Von Kameke
Keyword(s):  
Three Dimensional ◽  
Vertical Direction ◽  
Velocity Fields ◽  
Surface Flow ◽  
Energy Cascade ◽  
Surface Velocity ◽  
Faraday Waves ◽  
Piv Measurements ◽  
Fluid Surface ◽  
Inverse Energy Cascade

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at  the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

scholarly journals Three-Dimensional Time Series Movement of the Cuolangma Glaciers, Southern Tibet with Sentinel-1 Imagery

2020 ◽  
Vol 12 (20) ◽  
pp. 3466
Author(s):  
Liye Yang ◽  
Chaoying Zhao ◽  
Zhong Lu ◽  
Chengsheng Yang ◽  
Qin Zhang
Keyword(s):  
Time Series ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Surface Velocity ◽  
Tibet Plateau ◽  
High Mountain ◽  
Southern Tibet ◽  
Central Himalayas ◽  
Glacier Velocity ◽  
Small Baseline

Many debris-covered glaciers are broadly distributed across High Mountain Asia and have made a number of contributions to water circulation for Qinghai-Tibet Plateau (QTP). The formation of large supraglacial lakes poses risks for glacier lake outburst floods (GLOFs). Therefore, it is important to monitor the movement of glaciers and to analyze their spatiotemporal characteristics. In this study we take Cuolangma glaciers in the central Himalayas as study targets, where glacier No.1 is a lake-terminating debris-covered glacier and glacier No.2 is a land-terminating debris-covered glacier. The 3D deformation time series is firstly estimated by using the Pixel Offset-Small Baseline Subsets (PO-SBAS) based on the ascending and descending Sentinel-1 datasets spanning from January to December 2018. Then the horizontal and vertical time series displacements are obtained to show their spatiotemporal features. The velocities of glacier No.1 in horizontal and vertical direction were up to 16.0 ± 0.04 m/year and 3.4 ± 0.42 m/year, respectively, and the ones of the glacier No.2 were 12.0 ± 0.07 m/year and 2.0 ± 0.27 m/year, respectively. Next, the correlation between the precipitation and the surface velocity suggests that the glacier velocity does not show a clear association with daily precipitation alone. Finally, the debris-covered glaciers evolution is evaluated which shows that the tongue of the glacier No.1 is wasting away and the transition of glacier No.2 from land-terminating to lake-terminating is a probable scenario in the later period of glacier wastage. This research can significantly serve for glacier multidimensional monitoring and the mitigation of hazardous disaster caused by debris-covered glaciers in the central Himalayas.

The first effects of fluid inertia on flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 213-241 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Drag Force ◽  
Stokes Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Random Arrays ◽  
Long Time

Theory and lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at small Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is determined at small but finite Reynolds numbers, at solid volume fractions up to the close-packed limits of the arrays. For small solid volume fraction, the simulations are compared to theory, showing that the first inertial contribution to the drag force, when scaled with the Stokes drag force on a single sphere in an unbounded fluid, is proportional to the square of the Reynolds number. The simulations show that this scaling persists at solid volume fractions up to the close-packed limits of the arrays, and that the first inertial contribution to the drag force relative to the Stokes-flow drag force decreases with increasing solid volume fraction. The temporal evolution of the spatially averaged velocity and the drag force is examined when the fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. Theory for the short- and long-time behaviour is in good agreement with simulations, showing that the unsteady force is dominated by quasi-steady drag and added-mass forces. The short- and long-time added-mass coefficients are obtained from potential-flow and quasi-steady viscous-flow approximations, respectively.

scholarly journals Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

2015 ◽  
Vol 773 ◽  
pp. 154-177 ◽  
Author(s):  
Basile Gallet ◽  
Charles R. Doering
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Threshold Value ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Static Approximation ◽  
Long Time

We investigate the behaviour of flows, including turbulent flows, driven by a horizontal body force and subject to a vertical magnetic field, with the following question in mind: for a very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2-D, with no dependence along the vertical direction? We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number, $\mathit{Rm}\ll 1$: we prove that the flow becomes exactly 2-D asymptotically in time, regardless of the initial condition and provided that the interaction parameter $N$ is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2-D flow. We then consider the full magnetohydrodynamic (MHD) equations and prove that, for low enough $\mathit{Rm}$ and large enough $N$, the flow becomes exactly 2-D in the long-time limit provided the initial vertically dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2-D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3-D attractors may also exist and be attained for strong enough initial 3-D perturbations. These results shed some light on the existence of a dissipation anomaly for MHD flows subject to a strong external magnetic field.

Development of coherent structures in concentrated suspensions of swimming model micro-organisms

2008 ◽  
Vol 615 ◽  
pp. 401-431 ◽  
Author(s):  
TAKUJI ISHIKAWA ◽  
J. T. LOCSEI ◽  
T. J. PEDLEY
Keyword(s):  
Coherent Structures ◽  
Hydrodynamic Interaction ◽  
Volume Fraction ◽  
Surface Velocity ◽  
Concentrated Suspensions ◽  
Stokesian Dynamics ◽  
Concentrated Suspension ◽  
Collective Motions ◽  
Tangential Surface ◽  
Micro Organisms

A swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity and referred to as a squirmer. The centre of mass of the sphere may be displaced from the geometric centre, and the effects of inertia and Brownian motion are neglected. The well-known Stokesian dynamics method is modified in order to simulate squirmer motions in a concentrated suspension. The movement of 216 identical squirmers in a concentrated suspension without any imposed flow is simulated in a cubic domain with periodic boundary conditions, and the coherent structures within the suspension are investigated. The results show that (a) a weak aggregation of cells appears as a result of the hydrodynamic interaction between cells; (b) the cells generate collective motions by the hydrodynamic interaction between themselves; and (c) the range and duration of the collective motions depend on the volume fraction and the squirmers' stresslet strengths. These tendencies show good qualitative agreement with previous experiments.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

About the Development of Brick-Design in Russia

2020 ◽  
Vol 787 (12) ◽  
pp. 21-24
Author(s):  
Y.A. Bozhko ◽  
◽  
K.A. Lapunova ◽  
Keyword(s):  
Functional Role ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Basic Unit ◽  
Design Development ◽  
European Cities ◽  
Unique Material ◽  
Decisive Action ◽  
Color Combinations ◽  
Insufficient Number

The article reflects the authors view on the technical and aesthetic side of the use of face bricks in the architecture of our country. The term brick design combines such indicators of brickwork as the color, size and surface of the brick itself, as well as the type of masonry and seam parameters. Unfortunately, the analysis of the current situation shows that the culture of consumption of face bricks in Russia remains at a low level, which is due to the lack of proper knowledge and insufficient number of qualified master masons. The main goal of brick design development is to popularize various types of three-dimensional masonry and reveal the potential of using bricks as a basic unit. The comparison shows the architecture of European cities, which does not differ in the complexity of architectural forms, but has advantages in the form of unusual masonry, color combinations, vertical direction of masonry and other elements of technical aesthetics. The use of bricks in various levels of brick design will allow you to avoid using architectural decoration on the facades of buildings, while preserving its authenticity and individuality. The brick, as a basic unit, is self-sufficient and is able to fulfill not only its functional role, but also its aesthetic one. In this situation, a necessary and decisive action will be competent communication with industry specialists, architects and designers, leading manufacturers and technologists who realize that we have a unique material that does not need additional wrapping when used efficiently.

Sign in / Sign up

Export Citation Format

Share Document