Biorheological aspects of arterial flow near bifurcations

AbstractThe manner in which the steady flow of a low viscous fluid (representing blood) divides at a junction (where a straight single branch leaves the straight parent trunk) is numerically investigated by adopting conformal mapping techniques in terms of the significant dimensionless parameters: the entrance flow rate index p, the branch diameter ratio β, and the angle of branching α. The ratio of the flow rate in the side branch to the flow rate in the main branch, γ, is found to increase with a reduction in the flow index p and with an increase in β. The problem is analyzed by a numerical approach and a visualization technique is employed to establish the existence of two interdependent separation regions, one in each branch. The location of the occurrence of separation and the size of the separated regions are found to be dependent on the value of γ. The study depicts the formation, growth, and shedding of vortices in the separated region of the main branch and the double-helicoidal flow in the side branch

A mathematical model for the study of interstitial fluid movement vis-a-vis the non-newtonian behaviour of blood in a constricted artery

AbstractA mathematical model is developed with an aim to study the transport of interstitial fluid in the wall of a constricted artery by taking into account the microrotation of the erythrocytes of blood. The movement of the interstitial fluid has been described by the Debye-Brinkman equation. Exact solutions are obtained for the displacement of the solid matrix of the porous interstitial space, the velocity of the interstitial fluid movement, and the pressure distribution in the constricted arterial segment, for large and small consolidation times. Expression for the wall shear stress is also obtained for the constricted segment of the artery. Theoretical estimates of the distributions of the axial velocity of blood in the stenosed zone, rotational velocity of the erythrocytes, wall shear stress, and wall displacement, as well as the pressure and velocity profiles for the interstitial fluid movement, have been presented in the form of graphs

Peristaltic transport of a particle-fluid suspension in a cylindrical tube

AbstractPeristaltic pumping induced by a sinusoidal travelling wave of moderate amplitude is analysed in the axisymmetrical case for a viscous incompressible and Newtonian fluid mixed with rigid spherical particles which are of identical size. A perturbation method has been employed to find the solution of the problem, choosing the amplitude ratio (i.e., wave amplitude/tube radius) as a parameter. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms, and the nonslip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth order terms yield the Poiseuille flow and the first order terms give the Orr-Sommerfeld equation. In the absence of the pressure gradient and the wall motion, the mean flows (for the fluid and the solid particles) and the mean pressure gradient (averaged over time) are all found to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating complicated groups of the products of Bessel functions by polynomials. It is observed that a reversal of flow occurs when the pressure gradient exceeds the critical value; this is favoured by the presence of the solid particles. The reversal of flow may take place near the boundaries also

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of the blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.Comment: Accepted for publication in Communications in Nonlinear Science and Numerical Simulation, Elsevier. arXiv admin note: text overlap with arXiv:1006.017

Mass-losing accretion discs around supermassive black holes

We study the effects of outflow/wind on the gravitational stability of accretion discs around supermassive black holes using a set of analytical steady-state solutions. Mass-loss rate by the outflow from the disc is assumed to be a power-law of the radial distance and the amount of the energy and the angular momentum which are carried away by the wind are parameterized phenomenologically. We show that the mass of the first clumps at the self-gravitating radius linearly decreases with the total mass-loss rate of the outflow. Except for the case of small viscosity and high accretion rate, generally, the self-gravitating radius increases as the amount of mass-loss by the outflow increases. Our solutions show that as more angular momentum is lost by the outflow, then reduction to the mass of the first clumps is more significant.Comment: Accepted for publication in Astrophysics & Space Scienc

Unravelling marker trait associations linking nutritional value with pigmentation in rice seed

Open Access JournalWhile considerable breeding effort has focused on increasing the yields of staple crops such as rice and the levels of micronutrients such as iron and zinc, breeding to address the problems of the double-burden of malnutrition has received less attention. Pigmented rice has higher nutritional value and greater health benefits compared to white rice. However, the genetic associations underlying pericarp coloration and accumulation of nutritionally valuable compounds is still poorly understood. Here we report the targeted genetic analysis of 364 rice accessions, assessing the genetic relationship between pericarp coloration (measured using multi-spectral imaging) and a range of phenolic compounds with potential nutritional and health-promoting characteristics. A genome-wide association study resulted in the identification of over 280 single nucleotide polymorphisms (SNPs) associated with the traits of interest. Many of the SNPs were associated with more than one trait, colocalization occurring between nutritional traits, and nutritional and color-related traits. Targeted association analysis identified 67 SNPs, located within 52 candidate genes and associated with 24 traits. Six haplotypes identified within the genes Rc/bHLH17 and OsIPT5 indicated that these genes have an important role in the regulation of a wide range of phenolic compounds, and not only those directly conferring pericarp color. These identified genetic linkages between nutritionally valuable phenolic compounds and pericarp color present not only a valuable resource for the enhancement of the nutritional value of rice but an easy method of selection of suitable genotypes

Dispersion of Ordered Stripe Phases in the Cuprates

A phase separation model is presented for the stripe phase of the cuprates, which allows the doping dependence of the photoemission spectra to be calculated. The idealized limit of a well-ordered array of magnetic and charged stripes is analyzed, including effects of long-range Coulomb repulsion. Remarkably, down to the limit of two-cell wide stripes, the dispersion can be interpreted as essentially a superposition of the two end-phase dispersions, with superposed minigaps associated with the lattice periodicity. The largest minigap falls near the Fermi level; it can be enhanced by proximity to a (bulk) Van Hove singularity. The calculated spectra are dominated by two features -- this charge stripe minigap plus the magnetic stripe Hubbard gap. There is a strong correlation between these two features and the experimental photoemission results of a two-peak dispersion in La$_{2-x}$Sr$_x$CuO$_4$, and the peak-dip-hump spectra in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The differences are suggestive of the role of increasing stripe fluctuations. The 1/8 anomaly is associated with a quantum critical point, here expressed as a percolation-like crossover. A model is proposed for the limiting minority magnetic phase as an isolated two-leg ladder.Comment: 24 pages, 26 PS figure

Electroosmotic flow of biorheological micropolar fluids through microfluidic channels

An analysis is presented in this work to assess the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel. The walls of the channel are assumed as sinusoidal wavy to analyze the peristaltic flow nature. We consider that the wavelength of the wall motion is much larger as compared to the channel width to validate the lubrication theory. To simplify the Poisson Boltzmann equation, we also use the Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV). We consider governing equation for micropolar fluid in absence of body force and couple effects however external electric field is employed. The solutions for axial velocity, spin velocity, flow rate, pressure rise and stream functions subjected to given physical boundary conditions are computed. The effects of pertinent parameters like Debye length and Helmholtz-Smoluchowski velocity which characterize the EDL phenomenon and external electric field, coupling number and micropolar parameter which characterize the micropolar fluid behavior, on peristaltic pumping are discussed through the illustrations. The results show that peristaltic pumping may alter by applying external electric fields. This model can be used to design and engineer the peristalsis-lab-on-chip and micro peristaltic syringe pumps for biomedical applications