Equivalence of Two Different Integral Representations of Droplet Distribution Moments in Condensing Flow

It is proved that two different and independently derived integral representations of droplet size distribution moments encountered in the literature are equivalent and, moreover, consistent with the general dynamic equation that governs the droplet size distribution function. One of these representations consists of an integral over the droplet radius while the other representation consists of an integral over time. The proof is based on analytical solution of the general dynamic equation in the absence of coagulation but in the presence of both growth and nucleation. The solution derived is explicit in the droplet radius, which is in contrast with the literature where solutions are presented along characteristics. This difference is essential for the equivalence proof. Both the case of nonconvected vapor as well as the case of convected vapor are presented

Solution of the general dynamic equation along approximate fluid trajectories generated by the method of moments

We consider condensing flow with droplets that nucleate and grow, but do not slip with respect to the surrounding gas phase. To compute the local droplet size distribution, one could solve the general dynamic equation and the fluid dynamics equations simultaneously. To reduce the overall computational effort of this procedure by roughly an order of magnitude, we propose an alternative procedure, in which the general dynamic equation is initially replaced by moment equations complemented with a closure assumption. The key notion is that the flow field obtained from this so-called method of moments, i.e., solving the moment equations and the fluid dynamics equations simultaneously, approximately accommodates the thermodynamic effects of condensation. Instead of estimating the droplet size distribution from the obtained moments by making assumptions about its shape, we subsequently solve the exact general dynamic equation along a number of selected fluid trajectories, keeping the flow field fixed. This alternative procedure leads to fairly accurate size distribution estimates at low cost, and it eliminates the need for assumptions on the distribution shape. Furthermore, it leads to the exact size distribution whenever the closure of the moment equations is exact

Upper airway pressure distribution during nasal high-flow therapy

Two working mechanisms of Nasal High-Flow Therapy (NHFT) are washout of anatomical dead space and provision of positive end-expiratory pressure (PEEP). The extent of both mechanisms depends on the respiration aerodynamics and the corresponding pressure distribution: at end-expiration the onset of uniform pressure indicates the jet penetration length, and the level of the uniform pressure is the PEEP. The clinical problem is that adequate measurements in patients are presently impossible. In this study, the respiratory pressure distribution is therefore measured in 3D-printed anatomically correct upper-airway models of an adult and an infant. Assuming that elastic fluctuations in airway anatomy are sufficiently small, the aerodynamics in these rigid models will be very similar to the aerodynamics in patients. It appears that, at end-expiration, the jet penetrates into or slightly beyond the nasal cavity, hardly depending on cannula size or NHFT flow rate. PEEP is approximately proportional to the square of the flow rate: it can be doubled by increasing the flow rate by 40%. In the adult model, PEEP is accurately predicted by the dynamic pressure at the prong-exits, but in the infant model this method fails. During respiration, large pressure fluctuations occur when the cannula is relatively large compared to the nostrils

On the relation between tidal and forced spirometry

Spirometry is a lung function test involving deep inhalation and forceful deep exhalation. It is widely used to obtain objective information about airflow limitation and to diagnose lung diseases. In contrast, tidal spirometry is based on normal breathing and therefore much more convenient, but it is hardly used in medical care and its relation with conventional (forced) spirometry is largely unknown. Therefore, the objective of this work is to reveal the relation between tidal and forced spirometry. Employing the strong correspondence between the forced flow-volume curves and the Tiffeneau-Pinelli (TP) index, we present a method to obtain (a) the expected tidal flow-volume curve for a given TP-index, and (b) the expected TP-index for a given tidal curve. For patients with similar values of the TP-index, the tidal curves show a larger spread than the forced curves, but their average shape varies in a characteristic way with varying index. Therefore, just as with forced curves, the TP-index provides a useful objective ranking of the average of tidal curves: upon decreasing TP-index the expiratory flow rate changes in that its peak shifts towards smaller expiratory volumes, and its post-peak part becomes dented.</p