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Understanding spermatozoa transportation in the human female cervical canal, particularly in relation to the fertilization process, holds significant physiological importance. Present paper accords with the assessment of the self-propelling sheet of spermatozoa (SPSS) between porous cervical walls continuously secreting viscoelastic mucus in the human cervical canal (HCC). Mathematical modelling of the biological model yielded two inhomogeneous partial differential equations. These partial differential equations along with Saffman slip conditions are solved for exact solutions. It is delineated that an increase in the Reynolds number, Jeffrey parameter, and slip parameter results in an increase in the propulsive velocity and mucus velocity. Conversely, an increase in Darcy number results in a decrease in both propulsive and mucus velocity. When the secreting velocity is constant, the propulsive velocity is maximal, and when the secreting velocity is exponential, it is minimal. Spermatozoa move through the Jeffrey fluid more quickly than they do in the Newtonian fluid. The propulsive velocity through the channel is higher than in unbounded domain. The propulsive velocity of the spermatozoa in cervical canal is approximately 80μm/s in particular environment.

The exploration of higher-order and multicomponent extensions of the nonlinear Schrödinger equation holds significant importance across diverse applications, notably within the field of optics. Among these equations, the integrable Sasa–Satsuma equation stands out for its captivating soliton solutions. The Sasa–Satsuma equation serves as a mathematical representation for describing the propagation of femtosecond light pulses through optical fibers. The breather, multiwave, combined dark–bright, singular, dark, bright and periodic singular optical soliton solutions are derived in this paper by using the 1φ(ϑ),φ′(ϑ)φ(ϑ) and multivariate generalized exponential rational integral function approach. Furthermore, the paper emphasizes the essential fiber parameters essential for the emergence of these structures and offers visual representations of chosen solutions to elucidate their physical characteristics. The novelty of this work lies in the inaugural application of these methods to the Sasa–Satsuma equation and gives a significant advancement in the understanding of optical phenomena. This study not only opens avenues for further research but also introduces a fresh perspective on the Sasa–Satsuma model in the field of nonlinear physics with its applications in optical systems.

Introduction: The Glasgow Coma Scale (GCS) is a reproducible tool used to measure the depth and duration of the consciousness level of comatose patients, especially in emergency departments by healthcare professionals for neurological assessment. It is important for members of rehabilitation teams, specifically physical therapists (PTs) and nurses, to have knowledge of the GCS and the necessary skills to apply the scale and interpret the results. The present study is aimed to investigate and compare physiotherapist and nurses’ knowledge in using the GCS in hospital and clinical settings. Material & Methods: A cross-sectional study was conducted in which a convenience sample of 1,300 participants was chosen, considering nurses from government and private hospitals and PTs from hospitals and clinics in Faisalabad. SPSS Version 20 was used to enter and analyse the data. Pearson chi-square was used to find out association and Independent Samples t-test was used to compare the knowledge of PT and Nurses. Results: The findings of study revealed that majority of the PTs (84.1%) had good knowledge of the GCS, yet only 2.9% of nurses had good knowledge. Most participants with good basic knowledge of the GCS lacked knowledge in the application and interpretation of GCS. Age, gender, educational level, and type of health facility were strongly associated with level of knowledge with significant p value

In this paper, we analyze how Eyring fluid film behavior on a vertically upward moving slippery flat plate can help predictive models in engineering, notably in coating and lubrication operations. This paper deals with the stagnant points and uniform film analysis of Eyring fluid film flow on a vertically upward moving slippery flat plate. The formulated ordinary differential equation is solved for exact analytic solution. Exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant points are derived. A highly nonlinear algebraic equation is derived for film thickness. Equation is solved by Newton's method using Maple code. The thickness of film widens with increasing relaxation time, constant plate velocity, and fluid density, while it decreases with increasing fluid viscosity and constant slip parameter. The analysis delineates that the positions of stagnant points tend to relocate closer the slippery plate as the Stokes number, Deborah number, and constant slip parameter increase. A high Deborah number enhances drainage, causing stagnant points to relocate closer to the slippery plate and the development of a stable elastic layer adjacent to the plate. For stagnant points and fluid film thickness, a comparison between the Eyring fluid and existing studies (EPTT, LPTT, UCM, and Newtonian fluid) is also provided. The validity of this paper with the existing studies is also presented by reducing Eyring fluid model to Newtonian model. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design. [ABSTRACT FROM AUTHOR]

Analyzing Phan-Thien Tanner fluid film behavior on a vertically upward moving tube can help predictive models in engineering, notably in coating and lubrication operations. This paper provides a theoretical analysis of the dynamics of stagnant rings and uniform Phan-Thien Tanner fluid film adhered to a vertically upward moving tube. Formulated ordinary differential equations are solved to get exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant rings. Highly nonlinear algebraic equations are solved using Newton's method in MAPLE to find the linear and exponential Phan-Thien Tanner film thicknesses. The uniform film thickness widens with increasing constant tube velocity, while it decreases with increasing Deborah number, Stokes number, and elongation parameter. The analysis delineates that stagnant rings shrink around the tube as the Stokes number, Deborah number, and elongation parameter increase. The minimal Stokes condition for the existence of a realistic stagnant ring is also determined. It has been established that whenever the Stokes number is less than the minimal Stokes condition, stagnant rings do not form. A comparison between the exponential Phan-Thien Tanner, linear Phan-Thien Tanner, upper convected Maxwell, and Newtonian fluids is also provided for stagnant rings and fluid film thickness. Following the application of an efficient approximation on tube geometry, plate geometry is approximated, and the outcomes are consistent with existing literature. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design. [ABSTRACT FROM AUTHOR]

Theoretical analysis of time-dependent drainage of Sisko fluid film slowly down a stationary vertical belt is presented in this paper. Employing [C. Gutfinger and J. A. Tallmadge, AIChE J. 10, 774 (1964)] approach the subsequent nonlinear partial differential equation is simplified. The Adomian decomposition method is then used to solve the simplified nonlinear partial differential equation to obtain the analytic expression for velocity. The analytic expressions for volume flow rate, shear stress, average film velocity, surface profile and film mean thickness are also derived. It is delineated that the velocity decreases by an increment in the Sisko fluid parameter and time while it increases by an increment in the fluid behavior index. The elevation of the Sisko surface profile decreases when the values of Sisko fluid parameter are increased, whereas it increases when the values of fluid behavior index and time are increased. The variable film thickness of four different lubricating greases is estimated by using experimental values of material constants and fluid behavior index [A. W. Sisko, Ind. Eng. Chem. Res. 50, 1789 (1958) and M. A. Delgado et al., Chem. Eng. Process. 44, 805 (2005)]. Furthermore, the flow variables studied for the Sisko fluid are also studied for the Newtonian fluid, and comparisons between both are provided. [ABSTRACT FROM AUTHOR]

This paper investigates the thin film flow of Phan-Thien Tanner (PTT) fluid on a vertically moving belt. Three different models, namely, the upper convected Maxwell model (UCM), linear version of Phan-Thien Tanner model (LPTT), and exponential version of Phan-Thien Tanner model (EPTT), are taken into consideration. Exact expressions for velocity profiles, flow rates, average velocities, film thicknesses, shear stresses, and normal stresses are obtained. Special consideration is given to the predictions of stationary points in withdrawal of these fluids from the belt. It is observed that the stationary point of the UCM model lies closer to the free surface and the stationary point of the LPTT model lies in the middle of the stationary points of UCM and EPTT models. It is also observed that the stationary points tend to move towards the belt with the increase in Stokes number, Deborah number, and elongational parameter. Graphical results are also presented for various dimensionless flow parameters. Key words: thin film flow, stationary points, exact solution, PTT fluid model, uniform film thickness. Nous etudions ici l'ecoulement en film mince d'un fluide de Phan-Thien Tanner (PTT) sur une courroie en mouvement vertical. Nous considerons trois differents modeles, le modele de Maxwell convecte superieur (UCM), la version lineaire du modele PTT ou LPTT, et la version exponentielle du modele PTT ou EPTT. Nous obtenons des expressions exactes pour les profils de vitesse, les taux d'ecoulement, les vitesses moyennes, les epaisseurs du film, les efforts de cisaillement et les efforts normaux. Nous portons une attention particuliere a la prediction des points stationnaires de retrait du fluide de la courroie. Nous notons que le point stationnaire du modele UCM est plus pres de la surface libre et que celui du modele LPTT se retrouve entre les points stationnaires des modeles UCM et EPTT. Nous notons aussi que les points stationnaires tendent fi se deplacer vers la courroie avec l'augmentation du nombre de Stokes, du nombre de Deborah et du parametre d'elongation. Nous presentons sous forme graphique les differents parametres d'ecoulement, exprimes sans dimension. [Traduit par la Redaction] Mots-cles: ecoulement en film mince, points stationnaires, solution exacte, modele de fluide de Phan-Thien Tanner, epaisseur uniforme de film., 1. Introduction The study of thin film flow of fluids adhering to a vertically upward moving belt has gained considerable interest of many researchers and scientists [1-5]. Along with the [...]

This paper considered the transient drainage of a linearly viscous magnetohydrodynamic (MHD) fluid down a vertical flat slippery belt. An inhomogeneous partial differential equation with an inhomogeneous boundary condition was developed. Exact solutions for the velocity distribution, flow rate, surface profile, and variable thickness were then computed. The effect of MHD and the slip parameter on the velocity, flow rate, and surface profile were then considered. The effect of the magnetic field on the derived flow properties was discussed and represented graphically. It was determined that the absence of the magnetic field and the assumption of no-slip boundary conditions reduced the problem to the well-known Jeffreys problem. Key words: thin film flow, linearly viscous fluid model, MHD, exact solutions, transient drainage, slippery belt. Nous etudions ici le drainage transitoire d'un fluide MHD a viscosite lineaire, descendant sur une courroie verticale, plate et glissante. Afin de le decrire, nous developpons une equation differentielle aux derivees partielles inhomogene avec une condition limite inhomogene. Nous calculons des solutions exactes pour la distribution de vitesse, le taux d'ecoulement, le profil de surface et l'epaisseur variable. Nous considerons alors l'effet du caractere MHD et du parametre de glissement sur la vitesse, le taux d'ecoulement et le profil de surface. Nous discutons l'effet d'un champ magnetique sur les proprietes d'ecoulement et representons cet effet graphiquement. Nous determinons ensuite, qu'en l'absence de champ magnetique et sans condition limite de glissement, le probleme se reduit au probleme bien connu de Jeffreys. [Traduit par la Redaction] Mots-cles: ecoulement d'un film mince, modele de fluide a viscosite lineaire, MHD, solutions exactes, drainage transitoire, courroie glissante. PACS Nos.: 01, 47, 02.30., 1. Introduction The flow of fluid in the form of thin layers is called thin-film flow. A thin film consists of an expanse of liquid bounded by a solid body [...]

In this paper, we investigate the time-dependent drainage of a thin film of Eyring fluid of variable thickness, flowing down a vertical plate. The exact solutions for the velocity distribution, flow rate, mean thickness, average velocity, vorticity vector, and stress are obtained. Graphical results are presented and discussed for various flow variables like the velocity profile and the variable thickness. PACS Nos.: 01, 47. Nous etudions ici le drainage dependant du temps d'un film mince de fluide de Eyring d'epaisseur variable qui s'ecoule le long d'une plaque verticale. Nous obtenons les solutions exactes pour la distribution de vitesse, le taux d'ecoulement, l'epaisseur moyenne, la vitesse moyenne, le vecteur tourbillon et l'effort de contrainte. Nous presentons les resultats de facon graphique et discutons differentes variables, comme le profil de vitesse et l'epaisseur variable., 1. Introduction The problem of unsteady drainage of a linearly viscous fluid down a vertical wall was originally studied by Jeffreys [1]. He assumed that the inertial forces were negligibly [...]

This paper presents an analytic study for the steady drainage of magnetohydrodynamic (MHD) Sisko fluid film down a vertical belt. The fluid film is assumed to be electrically conducting in the presence of a uniform transverse magnetic field. An analytic solution for the resulting non linear ordinary differential equation is obtained using the Adomian decomposition method. The effects of various available parameters especially the Hartmann number are observed on the velocity profile, shear stress and vorticity vector to get a physical insight of the problem. Furthermore, the shear thinning and shear thickening characteristics of the Sisko fluid are discussed. The physical quantities discussed for the Sisko fluid film have also been discussed for the Newtonian fluid film and comparison between them made. [ABSTRACT FROM AUTHOR]

This paper deals with the drainage of Sisko fluid film down a vertical belt. It provides an approximate solution of the resulting non-linear and inhomogeneous ordinary differential equation using perturbation method (PM) and Adomian decomposition method (ADM). Comparison of the results obtained by both methods demonstrate that these series solutions are strictly identical but ADM is easy to compute and can be extended to any higher order. The important physical quantities like velocity profile, volume flow rate, average film velocity, shear stress, force exerted by the fluid film and vorticity vector are derived. The effects of fluid behaviour index, Stokes number and Sisko fluid parameter on some of these physical quantities are observed. Furthermore, we also made a comparison between the Sisko fluid film and Newtonian fluid film. [ABSTRACT FROM AUTHOR]

Understanding the film lifting and draining of fluid on a vertical belt with surface tension is crucial for improving predictive models in coating and lubrication processes. This paper presents a theoretical study on the film lifting and drainage of a third-grade fluid with surface tension. The driving mechanisms on a vertical belt are the belt’s upward movement, the gradient of surface tension, and gravity. The formulated nonlinear ordinary differential equation (ODE) is solved for a series-form solution using the Adomian decomposition method. Numerical computations are used to determine the stationary point placements and the thickness of the uniform film. The study elucidated that lift velocity shows a decreasing trend, while drainage velocity exhibits an increasing trend with increasing values of inverse capillary number C and Stokes number St. The lift velocity shows an increase, whereas the drainage velocity demonstrates a decrease with an increase in the Deborah number De. With increasing values of St and C, the stationary points shift away from the fluid–air interface, while an increase in De causes them to move towards the interface. Surface tension plays a role in supporting drainage and leads to a shift in the stationary points towards the belt. Newtonian and third-grade fluids are also compared in terms of velocity, stationary points, uniform film, and surface tension, providing insight into their behavior. [ABSTRACT FROM AUTHOR]