A heavy sphere is free to move inside a rotating horizontal cylinder filled with viscous liquid. The steady motion is essentially Stokesian, and the sphere rotates at a fixed location with a lubrication layer between the ball and the wall. The symmetry of the flow field suggests there will be no force to balance the normal component of the ball's weight. However, we show that a normal force can arise when a cavitation bubble is present. The bubble size was measured as a function of the cylinder rotation rate and agrees well with a model which uses the force and torque balances on the sphere.

We present the results of an investigation of a novel dynamical system in which one, two or three solid spheres are free to move in a horizontal rotating cylinder which is completely filled with a highly viscous fluid. At low rotation rates, steady motion is found where the balls adopt stable equilibrium positions rotating adjacent to the rising wall at a speed which is in agreement with available theory. At higher cylinder speeds time-dependent motion sets in via Hopf bifurcations, and when one or two balls are present the motion is strictly periodic. Perhaps surprisingly, it is found that three balls are required to produce low-dimensional chaos.

A spatial, viscous stability analysis of Poiseuille pipe flow with superimposed solid body rotation is considered. For each value of the swirl parameter ͑inverse Rossby number͒ LϾ0, there exists a critical Reynolds number Re c (L) above which the flow first becomes convectively unstable to nonaxisymmetric disturbances with azimuthal wave number nϭϪ1. This neutral stability curve confirms previous temporal stability analyses. From this spatial stability analysis, we propose here a relatively simple procedure to look for the onset of absolute instability that satisfies the so-called Briggs-Bers criterion. We find that, for perturbations with nϭϪ1, the flow first becomes absolutely unstable above another critical Reynolds number Re t (L)ϾRe c (L), provided that LϾ0.38, with Re t →Re c as L→ϱ. Other values of the azimuthal wave number n are also considered. For Re ϾRe t (L), the disturbances grow both upstream and downstream of the source, and the spatial stability analysis becomes inappropriate. However, for ReϽRe t , the spatial analysis provides a useful description on how convectively unstable perturbations become absolutely unstable in this kind of flow.

Computational fluid dynamics (CFD) is a mathematical tool to analyse airflow. As currently CFD is not a usual tool for rhinologists, a group of engineers in collaboration with experts in Rhinology have developed a very intuitive CFD software. The program MECOMLAND only required snapshots from the patient's cross-sectional (tomographic) images, being the output those results originated by CFD, such as airflow distributions, velocity profiles, pressure, temperature, or wall shear stress. This is useful complementary information to cover diagnosis, prognosis, or follow-up of nasal pathologies based on quantitative magnitudes linked to airflow. In addition, the user-friendly environment NOSELAND helps the medical assessment significantly in the post-processing phase with dynamic reports using a 3D endoscopic view. Specialists in Rhinology have been asked for a more intuitive, simple, powerful CFD software to offer more quality and precision in their work to evaluate the nasal airflow. We present MECOMLAND and NOSELAND which have all the expected characteristics to fulfil this demand and offer a proper assessment with the maximum of quality plus safety for the patient. These programs represent a non-invasive, low-cost (as the CT scan is already performed in every patient) alternative for the functional study of the difficult rhinologic case. To validate the software, we studied two groups of patients from the Ear Nose Throat clinic, a first group with normal noses and a second group presenting septal deviations. Wall shear stresses are lower in the cases of normal noses in comparison with those for septal deviation. Besides, velocity field distributions, pressure drop between nasopharynx and the ambient, and flow rates in each nostril were different among the nasal cavities in the two groups. These software modules open up a promising future to simulate the nasal airflow behaviour in virtual surgery intervention scenarios under different pressure or temperature conditions to understand the effects on nasal airflow.

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