Leveraging elasticity of blood stenosis to detect the role of a non-Newtonian flow midst an arterial tube: Mazumdar and Keller models.

Blood stenosis is considered one of the most serious risks which face humanity nowadays. In addition, it is also one of the most apparent symptoms of COVID (19) (Corona Virus). Consequently, this research is shedding light on studying the blood flow in case of having blood clots and artery elasticity in the presence of stenosis during studying the flow. Hematopoiesis requires a model of the yield stress fluid, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). Navier stokes equation is used to simulate this subject in a mathematical way. The elasticity on the stenosis arterial walls is simulated by Rubinow & Keller model [24] and Mazumdar model [25]. The results reveal exciting behaviors that, in turn, require adequate study of non-Newtonian fluid flow phenomena, especially the results showed that the increase in the parameters related to the elasticity of the walls facilitating the flow of blood through the stenosis area. In addition, a comparison between two elasticity models (Rubinow & Keller model and Mazumdar model) is considered. Further, for normal artery without stenosis, our results are the same as those obtained by Vajravelu et.al [22].

Electro-magnetically modulated self-propulsion of swimming sperms via cervical canal.

The purpose of this study is to theoretically investigate the electro-magneto-biomechanics of the swimming of sperms through cervical canal in the female reproductive system. During sexual intercourse, millions of sperms migrate into the cervix in large groups, hence we can approximately model their movement activity by a swimming sheet through the electrically-conducting biofluid. The Eyring-Powell fluid model is considered as the base fluid to simulate male's semen with self-propulsive sperms. An external magnetic field is applied on the flow in transverse direction. The governing partial differential system of equations is analytically solved. Creeping flow regimen is employed throughout the channel due to self-propulsion of swimmers along with long wavelength approximation. Solutions for the stream function, velocity profile, and pressure gradient (above and below the swimming sheet) are obtained and plotted with the pertinent parameters. The prominent features of pumping characteristics are also investigated. Results indicate that the propulsive velocity is reduced with an increase in the electric field which is an important feature that can be used in controlling the transport of spermatozoa inside the cervical canal. Not only is the present analysis valid for living micro-organisms, but also valid for artificially designed electro-magnetic micro-swimmers which is further utilized in electro-magnetic therapy taking place in female's lubricous cervical canal filled with mucus.

Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: fertilization and implantation.

The monitoring of the ciliated walls in the uterine tube has supreme importance in enhancing the sperm to reach the egg (capacitation processes), and at peristaltic ciliary flow has a more favorable residual time along the canal when compared to the peristaltic flow. Based on the importance of this study, a mathematical simulation of this process has been carried out by studying the behavior of a non-Newtonian magnetized fluid with a Darcy flow model with an oscillating wall having an internal ciliated surface. The governing equation is formed with Eyring-Powell fluid (tubal fallopian fluid) without using any approximations and solved using the Adomian analysis method. Using the vorticity formula, the components of the velocity function, pressure gradient, and stream function are obtained. The influence of relevant parameters is explained through diagramming and discussion. We also analyzed the residue time effects on the flow parameters. The results indicate that peristaltic ciliary flow has a more favorable residual time along the canal when compared to peristaltic flow.