This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The previously developing equation for Power-Law model is a simple ordinary differential type. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Casson model) that continuously flows into a circular tube by surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that the theoretical predictions of the governing equation were in good agreement with the results for considering the Newtonian model.

This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The present study introduces detailed mathematical procedures for Casson viscosity model. The equations of velocity distribution and flow rate are developed to describe the displacement of a non-Newtonian fluid that continuously flew into a circular tube by surface tension. The equation of modified volumetric flow shows the complicated form of (10) due to yield stress term, and the equation of velocity distribution which includes the yield stress and inclination angle of circular tube is composed of terms of r and rc as form of (14).

This paper presents the theoretical analysis for the flow driven by surface tension and gravity force in an inclined circular tube. The governing equation is developed to describe the displacement of a Newtonian fluid that continuously flew into a circular tube by surface tension, which represents a second-order, nonlinear, nonhomogeneous and ordinary differencial form. It was found that the theoretical predictions of the governing equation were excellent agreement with the unsteady state solutions for horizontal tube and the results of force balance equation for steady state.

This study investigated whether orthodontic force influences the production of osteoprotegerin (OPG) and receptor activator of nuclear factor-kappa B ligand (RANKL) in vivo, both of which are affected by cortical activation. Mechanical force was applied to the maxillary premolars of orthodontic patients by fitting the transpalatal arch prior to cortical activation of the gingival tissue. Gingival crevicular fluid (GCF) samples were then collected from each patient using paper strips before and after 1, 3, 7 or 14 days of treatment. The OPG and RANKL levels in the GCF were determined by enzyme-linked immunosorbent assays. The levels of OPG were significantly increased after 1 day of fitting the appliance and decreased to basal levels at 3 days after fitting. In contrast, the RANKL levels were dramatically decreased at 1 day after fitting, but recovered to those of the untreated control at 3 days after the force application. The force-mediated changes in the OPG and RANKL levels of the GCF were unaffected by cortical activation during these experimental periods. Collectively, these results suggest that an acute and severe change between the OPG and RANKL levels plays an important role in stimulating the cellular responses required for alveolar bone remodeling by orthodontic treatment.