The use of the Boltzmann transform function, λ(θ), to solve the Richards equation when the diffusivity, D, is a function of only soil water content, θ, is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform λ(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(θ). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform λ(θ). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air‐filled pore‐size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well‐known analysis pioneered by Green and Ampt in 1911.
Fig. 2. Normalized moisture content θ/θ s as a function of the normalized Boltzmann variable ϕ/ϕ a (solid line). Th e dashes show θ/θ s = 0.
Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore‐size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten's parameters α and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.
RESUMOCom o objetivo de avaliar o efeito de polímeros hidroretentores na capacidade de infiltração e na profundidade alcançada pela frente de molhamento em dois diferentes meios porosos, um de natureza argilosa e outro de origem marinha, foram realizados alguns experimentos em colunas. As concentrações de polímeros utilizadas foram: 0; 4 e 8 kg m -3 . Conforme os resultados, os polímeros não alteraram a capacidade de infiltração da água e nem a profundidade alcançada pela frente de molhamento, quando os tempos de infiltração foram curtos (1290 s para o material argiloso e 1500 s para a areia marinha) e os polímeros se encontravam secos no tempo zero da infiltração. Para períodos longos de infiltração, porém, com os polímeros completamente hidratados, a taxa de infiltração foi reduzida em cerca de até 13 vezes, somente no meio poroso argiloso. A ausência de efeitos na areia marinha foi atribuída à presença de cloretos, mas estudos específicos necessitam ser conduzidos para esclarecer essa questão.Palavras-chave: Profundidade de molhamento; hidrogéis; condutividade hidráulica. ABSTRACTWith the objective of evalulating the effect of water-retaining polymers on the infiltration capacity and the depth reached by the wet front in two different porous media, one of a clay nature and the other of a beach sand, experiments in laboratory were performed. The polymer concentrations used were 0; 4 and 8 kg m -3 . The results showed that the polymers did not affect either the infiltration capacity or the depth reached by the wet front when the infiltration times were relatively short and the polymers were dry at time zero. For long periods of infiltration, when the polymers were completely hydrated, the rate of infiltration was reduced 13-fold, but only in the clay-based porous medium. The absence of effects in the sandy medium could not be explained.
RESUMOA avaliação do processo da redistribuição da água no solo, em condições de campo, demanda considerável tempo e apreciável custo, porque as propriedades hidráulicas do solo sofrem extensa variabilidade espacial e estão sujeitas a freqüentes alterações no tempo. O presente trabalho propõe dois modelos analíticos para estimar a dinâmica desse processo, a partir da adoção do gradiente de potencial hidráulico unitário na equação de Richards. O primeiro modelo estima a umidade do solo e o segundo estima a densidade de fluxo, ambos de acordo com o tempo de drenagem interna para a profundidade de interesse. Os resultados gerados pelos modelos confrontam-se satisfatoriamente física e estatisticamente com os valores medidos da umidade e densidade de fluxo durante o período de drenagem em diferentes profundidades numa Areia Marinha submetida a esse processo em condições de campo. Os modelos propostos exigem somente o conhecimento prévio dos dados da curva de retenção e da condutividade hidráulica do solo na profundidade de interesse.Termos de indexação: redistribuição da água no solo, equação de Richards, modelos analíticos.
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