Hygroscopic particle-vapor equilibrium

Panicle huental Pressure Laplace s Formula 257 Limit of Applicability of Kelvin Relation 258 Hygroscopic Particle-Vapor Equilibrium 259 Charged Particle-Vapor Equilibria 263 Solid-Particle-Vapor Equilibrium 265... 

Hygroscopic behavior has been well characterized in laboratory studies for a variety of materials, for example, ammonium sulfate (Figure 14), an important atmospheric material. When an initially dry particle is exposed to increasing RH it rapidly accretes water at the deliquescence point. If the RH increases further the particle continues to accrete water, consistent with the vapor pressure of water in equilibrium with the solution. The behavior of the solution at RH above the deliquescence point is consistent with the bulk thermodynamic properties of the solution. However, when the RH is lowered below the deliquescence point, rather than crystallize as would a bulk solution, the material in the particle remains as a supersaturated solution to RH well below the deliquescence point. The particle may or may not undergo a phase transition (efflorescence) to give up some or all of the water that has been taken up. For instance, crystalline ammonium sulfate deliquesces at 79.5% RH at 298 K, but it effloresces at a much lower RH, 35% (Tang and Munkelwitz, 1977). This behavior is termed a hysteresis effect, and it can be repeated over many cycles. 

This analysis can be applied to a small dry salt particle exposed to increasing relative humidity. The particle remains solid until, if it is hygroscopic, a characteristic relative humidity less than 100% at which it absorbs water and dissolves, forming a saturated solution. The relative humidities at which this occurs for saturated solutions of various salts are shown in Table 9.3. These values will vary with crystal size because of the Kelvin effect. For sodium chloride,. solution takes place at a relative humidity of 75% at which the diameter about doubles. With increasing relative humidity, the equilibrium relationship between drop size and vapor pressure is determined by the interaction of the Kelvin effect and vapor pressure lowering. 

In the immediate vicinity of the interface between free water and vapor, the vapor pressure at equilibrium is the saturated vapor pressure. Very moist products have a vapor pressure at the interface almost equal to the saturation vapor pressure. If the concentration of solids is increased by the removal of water, then the dissolved hygroscopic solids produce a fall in the vapor pressure due to osmotic forces. Further removal of water finally results in the surface of the product dried. Water now exists only in the interior in very small capillaries, between small particles, between large molecules, and bound to the molecules themselves. This binding produces a considerable lowering of vapor pressure. Such a product can therefore be in equilibrium only with an external atmosphere in which the vapor pressure is considerably decreased. 

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