Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Slip flows of Newtonian and viscoelastic fluids in a 4:1 contraction

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.

Fathers’ emotional involvement with the neonate: impact of the umbilical cord cutting experience

Aims. This paper is a report on a study analysing the effect of the umbilical cord cutting experience on fathers’ emotional involvement with their infants. Background. Participation in childbirth offers an opportunity for father and mother to share the childbirth experience, so it is vital that midwives improve the fathers’ participation in this event. Design. A quasi-experimental study with a quantitative methodology was implemented. Methods. One hundred and five fathers were recruited as part of a convenience sample in a Maternity Public Hospital in a Metropolitan City in Portugal, between January and May of 2008. The Bonding Scale, the Portuguese version of the ‘Mother-to-Infant Bonding Scale’ was used to evaluate the fathers’ emotional involvement with the neonate at different moments: before childbirth, first day after childbirth and first month after childbirth. After childbirth, the fathers were divided into three separate groups depending on their umbilical cord cutting experience. Results. The results demonstrate that the emotional involvement between father and child tends to increase during the first days after childbirth and to decrease when evaluated 1 month after birth, for fathers who did not cut the umbilical cord. However, fathers who cut the umbilical cord demonstrate an improvement in emotional involvement 1 month later. Conclusion. Results suggest that the umbilical cord cutting experience benefits the father’s emotional involvement with the neonate, supporting the benefits of his participation and empowerment in childbirth.