A. A. Avramenko

Effect of small particles on this stability of bioconvection in a suspension of gyrotactic microorganisms in a layer of finite depth

We investigate the effect of small particles that are heavier than water on the stability of a suspension of motile gyrotactic microorganisms in a horizontal fluid layer of finite depth. If bioconvection develops, it enhances mixing and slows down the settling of the particles, which may be important in pharmaceutical applications. A linear stability analysis is utilized to investigate this problem. It is established that the critical Rayleigh number increases with the increase of the average number density of small particles, which means that the particles make the suspension more stable

Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer

Processes of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a self-similar form. Self-similar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nano-particles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skin-friction coefficients, were elucidated.

Symmetry analysis and self-similar forms of fluid flow and heat-mass transfer in turbulent boundary layer flow of a nanofluid

Heat, momentum, and mass transport in turbulent boundary layer nanofluid flow over a flat plate were investigated. Boundary layer equations were reduced to self-similar forms and solved numerically. The Lie group technique, which is based on the symmetry properties of governing equations, was used to derive self-similar forms of these equations. Turbulent viscosity was predicted using the mixing-length model. Also, dependences of physical properties (viscosity, thermal conductivity, and diffusion coefficients) on the nanofluid concentration and temperature were accounted for. Influences of different dimensionless parameters and nanoparticle concentration on the velocity and temperature profiles, as well as on the relative Nusselt number and skin-friction coefficient, were investigated.

A macroscopic model of traffic jams in axons.

The purpose of this paper is to develop a minimal macroscopic model capable of explaining the formation of traffic jams in fast axonal transport. The model accounts for the decrease of the number density of positively (and negatively) oriented microtubules near the location of the traffic jam due to formation of microtubule swirls; the model also accounts for the reduction of the effective velocity of organelle transport in the traffic jam region due to organelles falling off microtubule tracks more often in the swirl region. The model is based on molecular-motor-assisted transport equations and the hydrodynamic model of traffic jams in highway traffic. Parametric analyses of the models predictions for various values of viscosity of the traffic flow, variance of the velocity distribution, diffusivity of microtubule-bound and free organelles, rate constants for binding to and detachment from microtubules, relaxation time, and average motor velocities of the retrograde and anterograde transport, are carried out.

Bio‐thermal convection caused by combined effects of swimming of oxytactic bacteria and inclined temperature gradient in a shallow fluid layer

– The aim of this paper is to investigate the onset of bio‐thermal convection in a shallow fluid layer; the convection is thus driven by the combined effect of swimming of oxytactic microorganisms and inclined temperature gradient., – Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method., – The most interesting outcome of this analysis is the correlation between three Rayleigh numbers, two traditional, “thermal” Rayleigh numbers, which are associated with the vertical and horizontal temperature gradients in the fluid layer, and the bioconvection Rayleigh number, which is associated with the density variation induced by the upswimming of microorganisms., – Further research should address the application of weakly nonlinear analysis to this problem., – The increase of the horizontal thermal Rayleigh number stabilizes the basic flow. The effect of increasing the horizontal thermal Rayleigh number is to distort the basic temperature profile away from the linear one. The increase of the Schmidt number stabilizes the basic flow. The increase of the Prandtl number first causes the bioconvection Rayleigh number to decrease and then to increase., – To the best of the authors’ knowledge, this is the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection.

Symmetry of turbulent boundary-layer flows: Investigation of different eddy viscosity models

SummaryThe symmetrical properties of the turbulent boundary-layer flows and other turbulent flows are studied utilizing the Lie group theory technique. The self-similar forms of the indepedent variables and the solution function for the turbulent boundary layer flows with three different models of the turbulent (eddy) viscosity are obtained. Proceeding from this analysis, a simple numerical method for computation of turbulent flows is developed.

A 2D analysis of stability of bioconvection in a fluid saturated porous medium — estimation of the critical permeability value

Abstract The main purpose of this paper is to perform a 2D stability analysis of bioconvection in a suspension of motile gyrotactic microorganisms in a fluid saturated porous medium and to obtain an analytical expression for the critical permeability of the porous medium. Recent numerical investigation by Kuznetsov and Jiang [1] suggests that permeability is a very important parameter for bioconvection in porous media. Their numerical results indicate that for small permeability bioconvection is stable (the microorganisms swim in the upward direction), while for large permeability it is unstable (variations of density are enhanced and macroscopic fluid circulation is induced). In the present investigation, a simple but elegant criterion of stability of the bioconvection is obtained. This criterion gives the critical permeability of the porous medium through the cell eccentricity, average swimming velocity, fluid viscosity, and other relevant parameters.

Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium

Despite a large number of publications on bioconvection in suspensions of motile microorganisms, bioconvection in a fluid saturated porous medium is a relatively new area of research. This paper is motivated by experimental research by Kessler (1986) who established that a porous medium prevents the development of convection instability in algal suspensions. This suggests that there may exist a critical value of the permeability of a porous medium. If the permeability is smaller than critical, the system is stable and bioconvection does not develop. If the permeability is larger than critical, bioconvection may develop. This paper presents a model of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium. The focus of this research is the determination of the critical value of permeability of a porous medium by a linear stability analysis. A simple but elegant analytical solution for the critical Darcy number is obtained.

Steady natural convection in a cylindrical cavity

We present a numerical and experimental study of steady natural convection in a small aspect ratio cylindrical cavity with circular cross section. The main objective of the present communication is to highlight some difficulties encountered when a comparison of theoretical and experimental velocity results is attempted. We keep the aspect ratio (radius/height), the Prandtl number and the Rayleigh number fixed to 0.28, 6 and 2.25 × 106 respectively and make observations in a vertical plane that contains the axis of symmetry of the cylinder with a particle image velocimetry (PIV) technique. The main structure present in the flow is a single non-axisymmetric cell with a horizontal rotation axis. Due to the symmetry of the geometry of the cavity and of the heating and cooling systems, the orientation of the convective structure is undefined by the boundaries. In order to make a theoretical-experimental comparison, it is necessary to make a full description of the three dimensional velocity field to find the plane that corresponds to the one observed in the experiment.

The onset of bio‐thermal convection in a suspension of gyrotactic microorganisms in a fluid layer with an inclined temperature gradient

Purpose – The purpose of this paper is to investigate a combined bioconvection and thermal instability problem in a horizontal layer of finite depth with a basic temperature gradient inclined to the vertical. The basic flow, driven by the horizontal component of temperature gradient, is the Hadley circulation, which becomes unstable when the vertical temperature difference and density stratification induced by upswimming of microorganisms that are heavier than water become sufficiently large.Design/methodology/approach – Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.Findings – The steady‐state solution of this problem is obtained. Linear stability analysis of this steady‐state solution for the case of three‐dimensional disturbances is performed; the numerical problem is solved using the collocation method. The stability problem is governed by three Rayleigh numbers: the bioconvection Rayleigh number and two thermal Rayleigh numbers ...