D. G. Blinov

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.

Numerical modeling of molecular-motor-assisted transport of adenoviral vectors in a spherical cell.

Viral gene delivery in a spherical cell is investigated numerically. The model of intracellular trafficking of adenoviruses is based on molecular-motor-assisted transport equations suggested by Smith and Simmons. These equations are presented in spherical coordinates and extended by accounting for the random component of motion of viral particles bound to filaments. This random component is associated with the stochastic nature of molecular motors responsible for locomotion of viral particles bound to filaments. The equations are solved numerically to simulate viral transport between the cell membrane and cell nucleus during initial stages of viral infection.

Effect of cytoskeletal element degradation on merging of concentration waves in slow axonal transport

The aim of this paper is to investigate, by means of a numerical simulation, the effect of the half-life of cytoskeletal elements (CEs) on superposition of several waves representing concentrations of running, pausing, and off-track anterograde and retrograde CE populations. The waves can be induced by simultaneous microinjections of radiolabeled CEs in different locations in the vicinity of a neuron body; alternatively, the waves can be induced by microinjecting CEs at the same location several times, with a time interval between the injections. Since the waves spread out as they propagate downstream, unless their amplitude decreases too fast, they eventually superimpose. As a result of superposition and merging of several waves, for the case with a large half-life of CEs, a single wave is formed. For the case with a small half-life the waves vanish before they have enough time to merge.

Investigation of stability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium

Instability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium is investigated on the basis of a modified Orr-Sommerfeld equation. This equation takes into account three drag terms: the Darcy term that describes friction between the fluid and the porous matrix, the Forchheimer quadratic drag term that describes a form drag due to the solid obstacles, and the Brinkman term, which is a viscous term similar to the Laplacian term in the Navier-Stokes equations. Numerical analysis is carried out using the collocation method. The dependence of the critical Reynolds number on porosity and permeability of the porous medium is analyzed numerically.

Self-similar analysis of fluid flow, heat, and mass transfer at orthogonal nanofluid impingement onto a flat surface

Momentum, heat, and mass transfer in the vicinity of a stagnation point at uniform impingement of a nanofluid onto a flat plate were investigated. The novelty of the work consists in obtaining self-similar forms for the Hiemenz flow of a nanofluid and the self-similar representation of the velocity, thermal, and diffusion boundary layer equations derived on the basis of symmetry analysis using discrete symmetries. Momentum, energy, and concentration equations in the self-similar form were solved numerically. In frames of this analysis, functional dependence of the physical properties of nanofluids (viscosity, thermal conductivity, and diffusion coefficient) on concentration and temperature profiles was included as a part of the mathematical model, whose form enables including different models for the thermophysical properties of the nanofluid. Also novel are numerical results that revealed the influence of the nanoparticle concentration on the velocity, temperature, and concentration profiles, as well as ...

MODELING LEFTWARD FLOW IN THE EMBRYONIC NODE

The establishment of the left-right asymmetry during the development of vertebrates is a fascinating phenomenon that is still not fully understood. Extensive research suggests that in mice a small triangular cavity, called the ventral node, is responsible for breaking the left-right symmetry. A mouse node is ∼ 50 microns across and ∼10 microns deep. The surface of the nodal pit is covered by 200–300 monocilia whose rotation is responsible for the leftward flow in the node. We developed a simplified method of modeling the extraembryonic fluid flow and morphogen transport in a nodal cavity. We simplified the problem as flow in a 2D cavity; the effect of rotating cilia was modeled by specifying a constant vorticity at the edge of the ciliated layer. We also developed approximate solutions for morphogen transport in the nodal pit. The solutions were obtained utilizing the proper generalized decomposition method. We compared our approximate solutions with the results of numerical simulation of flow caused by the rotation of 81 cilia, and obtained reasonable agreement in most of the flow domain. We discuss locations where agreement is less accurate. The obtained semi-analytical solutions enable a quick analysis of flow and morphogen distribution in a nodal pit.Copyright

Error correction in intracellular transport: Numerical investigation of rerouting of a pulse of misdirected axonal cargos in a dendrite

This paper develops a transient three-kinetic state model that simulates rerouting of a pulse of axonal cargos that were initially misdirected to a dendrite. The following three cargo populations are included in the model: (i) anterogradely running cargos, (ii) retrogradely running cargos, and (iii) free (diffusion-driven) cargos that are detached from microtubules. The dynamics of cargo concentrations in various kinetic states are studied. It is demonstrated that the profile of the total cargo concentration is comprised of two major components. The first component is a pulse composed of anterogradely running cargos and the second component is a tail behind this pulse that is composed of free (diffusion-driven) and retrogradely running cargos. The total number of misdirected axonal cargos in the dendrite is also computed. The dependence of this quantity on the amount of time that passed from the moment when the pulse entered the dendrite and on kinetic constants describing transition rates between various kinetic states of misdirected cargos is investigated.

Simulation of Traffic Jam Formation in Fast Axonal Transport

Many neurodegenerative diseases, such as Alzheimer’s disease, are linked to swellings occurring in long arms of neurons. Many scientists believe that these swellings result from traffic jams caused by the failure of intracellular machinery responsible for fast axonal transport; such traffic jam can plug an axon and prevent the sufficient amount of organelles to be delivered toward the synapse of the axon. Mechanistic explanation of the formation of traffic jams in axons induced by overexpression of tau protein is based on the hypothesis that the traffic jam is caused not by the failure of molecular motors to transport organelles along individual microtubules but rather by the disruption of the microtubule system in an axon, by the formation of a swirl of disoriented microtubules at a certain location in the axon. This paper investigates whether a microtubule swirl itself, without introducing into the model microtubule discontinuities in the traffic jam region, is capable of capturing the traffic jam formation. The answer to this question can provide important insight into the mechanics of the formation of traffic jams in axons.© 2009 ASME