Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia

Computer model of non-Newtonian canalicular fluid flow in lacunar-canalicular system of bone tissue

Brittle bone diseases are a global healthcare problem for orthopaedic clinicians, that reduces bone strength and promotes bone fracture risk. In vivo studies reported that loading-induced fluid flow through the lacunar-canalicular channel (LCS) of bone tissue inhibit such bone loss and encourages osteogenesis i.e. new bone formation. Canalicular fluid flow converts mechanical signals into biological signals and regulates bone reconstruction by releasing signalling molecules responsible for mechanotransduction. In-silico model mostly considers canalicular fluid is Newtonian, however, physiological canalicular fluid may be non-Newtonian in nature as it contains nutrients and supplements. Accordingly, this study attempts to develop a two-dimensional in-silico model to compute loading-induced non-Newtonian canalicular fluid flow in a complex LCS of bone tissue. Moreover, canalicular fluid is considered as a Jeffery fluid, that can easily be reduced to Newtonian fluid as a special case. The results show that physiological loading modulates the canalicular fluid flow, wall shear stress (WSS) and streamline in bone LCS. Fluid velocity and WSS increases with increase in non-dimensional frequency and non-Newtonian parameter (Jeffery fluid parameters) and reduce with change in permeability. The outcomes of this study may provide new insights in the role of mechanical loading-induced non-Newtonian canalicular fluid flow dynamics in bone LCS. The key findings of this study can be used to improve the understanding of osteocyte mechanobiology involved inside the bone tissue.

Electroosmotically actuated peristaltic-ciliary flow of propylene glycol + water conveying titania nanoparticles

The main focus of this article is to mathematically formulate the microfluidics-based mechanical system for nanofluids. A 50:50 mixture of propylene glycol (PG) and water is used as a heat transfer fluid because of its tremendous anti-freezing properties, and nontoxicity and it is safe to be utilized at the domestic level. Titanium dioxide (titania) nanoparticles are suspended in the working fluid to enhance its heat transfer ability. The fluid flow is induced by electroosmosis in a microtube, which is further assisted by cilia beating. The impacts of Joule heating and non-linear thermal radiation are also considered. The simplification of the dimensionless system is done under lubrication theory and the Debye-Hückel linearization principle. The nonlinear system of equations is executed for a numerical solution by adopting the symbolic mathematical software Maple 17 using the command "dsolve" along with the additional command "numeric" to get the numerical solution. This command utilizes a low-ordered method along with accuracy-enhancing schemes such as the deferred correction technique and Richardson extrapolation to get a numerical answer of desired accuracy, where we can choose the accuracy level and mesh points according to our requirements. The detailed analysis of results obtained from the numerical treatment of the considered problem indicates that the efficiency of the PG + water enhances due to the suspension of the nanoparticles and heat is rapidly removed from the system. Further, the velocity of the fluid is augmented by decreasing the thickness of the electric double layer and raising the strength of the electric field in the forwarding direction.

Mass Transfer Effects on the Mucus Fluid with Pulsatile Flow Influence of the Electromagnetic Field

The influence of pulsatile flow on the oscillatory motion of an incompressible conducting boundary layer mucus fluid flowing through porous media in a channel with elastic walls is investigated. The oscillatory flow is treated as a cyclical time-dependent flux. The Laplace transform method using the Womersley number is used to solve non-linear equations controlling the motion through porous media under the influence of an electromagnetic field. The theoretical pulsatile flow of two liquid phase concurrent fluid streams, one kinematic and the other viscoelastic, is investigated in this study. To extend the model for various physiological fluids, we postulate that the viscoelastic fluid has several distinct periods. We also apply our analytical findings to mucus and airflow in the airways, identifying the wavelength that increases dynamic mucus permeability. The microorganism’s thickness, velocity, energy, molecular diffusion, skin friction, Nusselt number, Sherwood number, and Hartmann number are evaluated. Discussion is also supplied in various sections to investigate the mucosal flow process.

A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel

In the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.

Micropolar pulsatile blood flow conveying nanoparticles in a stenotic tapered artery: NON-Newtonian pharmacodynamic simulation

Two-dimensional rheological laminar hemodynamics through a diseased tapered artery with a mild stenosis present is simulated theoretically and computationally. The effect of different metallic nanoparticles homogeneously suspended in the blood is considered, motivated by drug delivery (pharmacology) applications. The Eringen micropolar model has been discussed for hemorheological characteristics in the whole arterial region. The conservation equations for mass, linear momentum, angular momentum (micro-rotation), and energy and nanoparticle species are normalized by employing suitable non-dimensional variables. The transformed equations are solved numerically subject to physically appropriate boundary conditions using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A good correlation is achieved between the FreeFEM++ computations and existing results. The effect of selected parameters (taper angle, Prandtl number, Womersley parameter, pulsatile constants, and volumetric concentration) on velocity, temperature, and micro-rotational (Eringen angular) velocity has been calculated for a stenosed arterial segment. Wall shear stress, volumetric flow rate, and hemodynamic impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing Prandtl number (Pr), the micro-rotational velocity decreases i.e., microelement (blood cell) spin is suppressed. Wall shear stress decreases with the increment in pulsatile parameters (B and e), whereas linear velocity increases with a decrement in these parameters. Furthermore, the velocity decreases in the tapered region with elevation in the Womersley parameter (α). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in hematology.

Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles

BACKGROUND AND OBJECTIVE

In this work, a numerical study is done on the blood flow inside an artery with a cone shape of stenosis. An artery has different stenosis angles. Also, blood flow is energized by constant heat flux which is applied on the wall. The finite volume method is employed to determine blood properties on the basis of a Sisko fluid model with different constant parameters.

METHODS

Firstly, the effects of applying constant heat flux of q'' = 4 W/m² are studied on the velocity profile of blood flow inside an artery with stenosis angles of φ = 0.5°. Afterward, effects of different stenosis angles of φ = 0.25, φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 is studied on blood flow temperature profile. Then, different values of the Sisko model are employed to investigate influences of Newtonian and non-Newtonian behaviors of blood fluid on the temperature profiles of blood flow inside an artery with stenosis angle of φ = 0.5°.

RESULTS

It is reported that with increasing stenosis angles, blood flow temperature is decreased due to velocity enhancement. This phenomenon is convinced by non-slip condition and sticking non-Newtonian blood fluid to the internal surface of artery wall which reduce velocity from wall surface region to central region of vessel. Also, it is concluded that changing behavior of blood fluid from non-Newtonian to Newtonian behaviors can empower the capability of blood in thermal energy transfer inside human body vessels.

CONCLUSIONS

Any treatment by balloon angioplasty, percutaneous transluminal angioplasty, and serum injection, which changes the behavior of blood flow inside body veins, can be effective on blood flow temperature.

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

In the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

Mathematical assessment of the spermatozoa transport through couple stress fluid in an asymmetric human cervical canal

Swimming of spermatozoa through couple stress fluid in an asymmetric human cervical canal is investigated in the present theoretical analysis. A couple of fourth-order partial differential equations arising from the mathematical modelling of the proposed model is solved analytically. Flow variables like pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Conspicuous features of the pumping characteristics are explored. It is found that pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas pressure drop by inverting the direction of spermatozoa controls the probability of pregnancy. Maximal propulsive velocity of the spermatozoa is reported in the absence of travelling waves along the cervical walls. Minute impact of phase difference on propulsive velocity is evident. An analogy of the current analysis with the existing literature is also made.

Signalling molecule transport analysis in lacunar-canalicular system

Mechanical loading-induced fluid flow in lacunar-canalicular space (LCS) of bone excites osteocyte cells to release signalling molecules which initiate osteo-activities. Theoretical models considered canaliculi as a uniform and symmetrical space/channel in bone. However, experimental studies reported that canalicular walls are irregular and curvy resulting in inhomogeneous fluid motion which may influence the molecular transport. Therefore, a new mathematical model of LCS with curvy canalicular walls is developed to characterize cantilever bending-induced canalicular flow behaviour in terms of pore-pressure, fluid velocity, and streamlines. The model also analyses the mobility of signalling molecules involved in bone mechanotransduction as a function of loading frequency and permeability of LCS. Inhomogeneous flow is observed at higher loading frequency which amplifies mechanotransduction; nevertheless, it also promotes trapping of signalling molecules. The effects of shape and size of signalling molecules on transport behaviour are also studied. Trivially, signalling molecules larger in size and weight move slower as compared to molecules small in size and weight which validates the findings of the present study. The outcomes will ultimately be useful in designing better biomechanical exercise in combination with pharmaceutical agents to improve the bone health.

Computational Study of MHD Nanofluid Flow Possessing Micro-Rotational Inertia over a Curved Surface with Variable Thermophysical Properties

This work presents a numerical investigation of viscous nanofluid flow over a curved stretching surface. Single-walled carbon nanotubes were taken as a solid constituent of the nanofluids. Dynamic viscosity was assumed to be an inverse function of fluid temperature. The problem is modeled with the help of a generalized theory of Eringen Micropolar fluid in a curvilinear coordinates system. The governing systems of non-linear partial differential equations consist of mass flux equation, linear momentum equations, angular momentum equation, and energy equation. The transformed ordinary differential equations for linear and angular momentum along with energy were solved numerically with the help of the Keller box method. Numerical and graphical results were obtained to analyze the flow characteristic. It is perceived that by keeping the dynamic viscosity temperature dependent, the velocity of the fluid away from the surface rose in magnitude with the values of the magnetic parameter, while the couple stress coefficient decreased with rising values of the magnetic parameter.

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.