Equação de Köhler

A equação de Köhler aborda o processo no qual o vapor de água condensa e forma gotas de nuvem líquidas, e é baseado na termodinâmica do equilíbrio. Ele combina a equação de Kelvin, que descreve a mudança na pressão de vapor saturante devido à curvatura de uma superfície, e a lei de Raoult, que relaciona a pressão de vapor de saturação com a fração molar do solvente.^[1] É um processo importante no campo da nefologia. Foi inicialmente publicada em 1936 por Hilding Köhler, professor de meteorologia na Universidade de Uppsala. A equação se trata do seguinte:

$\ln \left({\frac {p_{w}}{p^{0}}}\right)={\frac {4M_{w}\sigma _{w}}{RT\rho _{w}D_{p}}}-{\frac {6n_{s}M_{w}}{\pi \rho _{w}D_{p}^{3}}},$

em que $p_{w}$ é a pressão de vapor da água na superfície da gota, $p^{0}$ é a pressão de vapor saturante correspondente sobre uma superfície plana, $\sigma _{w}$ é a tensão superficial da água, $\rho _{w}$ é a densidade da água pura, $n_{s}$ é o número de mols de soluto, $M_{w}$ é a massa molecular da água e $D_{p}$ é o diâmetro da gota.

Curva de Köhler

A curva de Köhler é a representação visual da equação de Köhler. Ele mostra a supersaturação na qual a gota de nuvem está em equilíbrio com o ambiente numa faixa de diâmetros dessas gotas. A forma exata da curva depende da quantidade e da composição dos solutos presentes na atmosfera. As curvas de Köhler onde o soluto é cloreto de sódio são diferentes de quando o soluto é nitrato de sódio ou sulfato de amônio, por exemplo.

A figura acima mostra três curvas Köhler referentes ao cloreto de sódio. Considere (para gotas contendo soluto com diâmetro igual a 0,05 micrômetros) um ponto no gráfico onde o diâmetro úmido é 0,1 micrômetros e a supersaturação é 0,35%. Como a umidade relativa está acima de 100%, a gota crescerá até que esteja em equilíbrio termodinâmico. Nesse caso, a gota cresce sem que chegue a alcançar o equilíbrio e, portanto, seu crescimento é ilimitado. Contudo, se a supersaturação for de apenas 0,3%, a gota crescerá apenas até cerca de 0,5 micrômetros. A supersaturação na qual a gota crescerá sem limite é chamada de supersaturação crítica e o diâmetro no qual a curva atinge o pico é chamado de diâmetro crítico.

Ver também

Referências

↑ «Köhler Theory 101». Consultado em 26 de junho de 2012

Köhler, H., 1936. O núcleo e o crescimento de gotículas higroscópicas. Trans. Faraday Soc., 32, 1152–1161.
Rogers, RR, MK Yau, 1989. Um Curso Breve em Física de Nuvens, 3ª Ed. Imprensa Pérgamo. 293 pp.
Young, KC, 1993. Processos Microfísicos em Nuvens. Oxford Press. 427 pp.
Wallace, JM, PV Hobbs, 1977. Ciência Atmosférica: Uma Pesquisa Introdutória. Imprensa Acadêmica. 467 pp.

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