One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.

Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Feasibility in Using Technological Resources for Implementing the Environmental Culture Cross-Cutting Factor for Sustainable Development in the Costa Rican Basic General Education

The purpose of this research was to analyze whether the use of technological resources may be feasible in the implementation of the environmental culture cross-cutting factor for sustainable development, which focuses on environmental issues related to the contents of the Science study program for the seventh year of the basic general education. The research design is qualitative with a dominant approach and uses some quantitative elements specifically in the design of instruments and some data analysis techniques. The type of study was developed with a multi-method approach; a trend that has been shaping a research style which integrates various methods in a single design. For this, we identified the didactic strategies and their relationship to both, technology and the environmental axis for sustainable development, used by six Science teachers of the 7th grade, in public institutions of the province of Heredia, Central Valley, Costa Rica, as well as the opinion of 20 students from that same grade. The main results include the opinions of the students, who showed a considerable interest in classes where technological resources are used. However, teachers do not show great interest or positive opinions on this matter; in addition, they are not well trained on the use of technological resources. It was also identified that the teaching personal who participated in the study do not develop this curricular axis.

Towards a single crystal Raman spectrum of kaolinite at 77 K

The Raman spectra at 77 K of the hydroxyl stretching of kaolinite were obtained along the three axes perpendicular to the crystal faces. Raman bands were observed at 3616, 3658 and 3677 cm−1 together with a distinct band observed at 3691 cm−1 and a broad profile between 3695 and 3715 cm−1. The band at 3616 cm−1 is assigned to the inner hydroxyl. The bands at 3658 and 3677 cm−1 are attributed to the out-of-phase vibrations of the inner surface hydroxyls. The Raman spectra of the in-phase vibrations of the inner-surface hydroxyl-stretching region are described in terms of transverse and longitudinal optic splitting. The band at 3691 cm−1 is assigned to the transverse optic and the broad profile to the longitudinal optic mode. This splitting remained even at liquid nitrogen temperature. The transverse optic vibration may be curve resolved into two or three bands, which are attributed to different types of hydroxyl groups in the kaolinite.