Capillary condensation, illustrated in Figure 6, results from capillary force and changes in partial vapor pressures as a result of increased curvature, as defined by the Kelvin equation. Capillary forces increase in relationship to the RH of the ambient air and the presence of porous structures, where the high curvature of the pore in the solid results in the lowering of the vapor pressure of water. This vapor pressure-lowering effect results in small amounts of water vapor to condense to liquid water at lower relative humidities of 10% to 50% RH. When nonporous solid particles are exposed to a RH greater than 65% RH, fluid condenses in the space between the adjacent nonporous solid particles. This leads to liquid bridges as a consequence of the interfacial attractive forces due to the intrinsically high surface tension of water.
For a smooth spherical particle with radius R, the force, FH, experienced is where y is the surface tension.
A thin film of liquid confined at the interface of two solid bodies gives rise to boundary forces. A pressure difference, Pc, arises and is known as the capillary pressure. This can be calculated from the Laplace equation.
where y is the surface tension at the liquid-gas interface and and R2 are the principal radii of curvature of the interface. The pulmonary mechanics of alveolar function and the work of breathing is often described by the Laplace equation, in the context of the process of exhalation/inhalation and the modulation of lung surface tension to decrease the work of breathing by normally maintaining a constantly low Pc. The Laplace equation describes the interrelationship and the elegant balance between the surface tension of the nanofilm of lung surfactant lining the alveolus and alveolar diameter. In respiratory distress syndrome (i.e., the absence or dysfunction of alveolar lung surfactant) present in premature babies and adults with pulmonary disease, the work of breathing increases significantly because of an increase in Pc as a result of an abnormal increase in the surface tension of the aqueous nanofilm lining the interior of the alveoli. Consequently, the rise in alveolar capillary forces leads to alveolar collapse and a severe decrease in alveolar gas exchange. It should also be remembered that surface asperities might increase the potential for mechanical interlocking (structural cohesion) of particles, which will influence the aggregation state and ease of dispersion of particles.
The formulation of DPIs is dependent on the nature of particles employed in the formulation. The delivery of dry powder products is dependent on effective dispersion of particles in respirable size ranges. This has been brought about by blending with carrier
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