Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Panorametry: suggestion of a method for mandibular measurements on panoramic radiographs

<p>Abstract</p> <p>Background</p> <p>Orthopantomography (panoramic radiography) has been used for the study of measurements involving particularly the prediction of the eruption of impacted lower third molars and analyses of measurements of the ramus and head of mandible. The discrepancies involved with the projection of this radiographic image has stimulated the search for further ways to use it, particularly in orthodontic treatments and oral and maxillofacial surgeries. The author proposes a graphimetric method for the mandible, based on panoramic radiography. The results are expressed in linear and angular measurements, aiming at bilateral comparisons as well as the determination of the proportion of skeletal and dental structures, individually and among themselves as a whole. The method has been named Panorametry, and allows measurement of the mandible (Mandibular Panorametry) or the posterior mandibular teeth (Dental Panorametry). When combining mandible and maxilla, it should be referred to as Total Panorametry. It may also be used, in the future, with Cone Beam computed tomography (CT) images, and in this case it may be mentioned as CT Panorametry.</p