Fractal concepts in relation to soil water diffusivity

Fractal geometry would appear to offer promise for new insight on water transport in unsaturated soils, This study was conducted to evaluate possible fractal influence on soil water diffusivity, and/or the relationships from which it arises, for several different soils, Fractal manifestations, consisting of a time-dependent diffusion coefficient and anomalous diffusion arising out of fractional Brownian motion, along with the notion of space-filling curves were gleaned from the literature, It was found necessary to replace the classical Boltzmann variable and its time t(1/2) factor with the basic fractal power function and its t(n) factor, For distinctly unsaturated soil water content theta, exponent n was found to be less than 1/2, but it approached 1/2 as theta approached its sated value, This function n = n(theta), in giving rise to a time-dependent, anomalous soil water diffusivity D, was identified with the Hurst exponent H of fractal geometry, Also, n approaching 1/2 at high water content is a behavior that makes it possible to associate factal space filling with soil that approaches water saturation, Finally, based on the fractally interpreted n = n(theta), the coalescence of both D and 8 data is greatly improved when compared with the coalescence provided by the classical Boltzmann variable.

FRACTAL CHARACTERISTICS OF THE HORIZONTAL MOVEMENT OF WATER IN SOILS

Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to t(n), where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.

Improvement of water transport and carotenoid retention during drying of papaya by applying ultrasonic osmotic pretreatment

The effect of ultrasound and osmotic dehydration pretreatments on papaya drying kinetics was investigated. The ultrasound pretreatment was carried out in an ultrasonic bath at 30 A degrees C. The osmotic pretreatment in sucrose solution was carried out in an incubator at 34 A degrees C and agitation of 80 rpm for 210 min. The drying process was conducted in a fixed bed dryer at 70 A degrees C. Experimental data were fitted successfully using the Page model for dried fresh and pretreated fruits, with coefficient of determination greater than 0.9992 and average relative error lower that 14.4 %. The diffusional model was used to describe the moisture transfer, and the effective water diffusivity was identified in the order of 10(-9) m(2) s(-1). It was found that drying rates of osmosed fruits were the lowest due to the presence of infused solutes, while the ultrasound pretreatment contributed to faster drying rates. Evaluation of the dried fruit was performed by means of total carotenoids retention. Ultrasound treatments in distilled water prior to air-drying gave rise to dried papayas with retention of carotenoids in the range 30.4-39.8 % and the ultrasonic-assisted osmotic dehydration of papayas showed carotenoids retention values up to 64.9 %, whereas the dried fruit without pretreatment showed carotenoids retention lower than 24 %.

Cinética de secagem de abóboras (Curcubita moschata) pré-tratadas osmoticamente em soluções contendo sacarose

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Efeitos dos agentes de impregnação e coberturas comestíveis sobre a secagem e sobre a qualidade física e nutricional do abacaxi

Pós-graduação em Engenharia e Ciência de Alimentos - IBILCE

Thermophysical Properties of Lemon Juice as Affected by Temperature and Water Content

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Drying of persimmon: Mathematical model for diffusivity as a simultaneous function of moisture content and shrinkage

Fresh persimmon has a high moisture content (about 85% wet basis) making it highly perishable and requiring adequate drying conditions to obtain an acceptable dehydrated product. Drying kinetics of persimmon cv. Rama Forte was studied in a fixed bed dryer at temperatures ranging from 50 to 80 degreesC and air velocity of 0.8 m/s. Shrinkage during drying was described by a linear correlation with respect to water content. Evaluation of effective diffusivity as a function of moisture content, with undergoing shrinkage during drying was based on Fourier series solution of Fick's diffusion equation. Effective diffusivity values at moisture contents between 0.09 - 4.23 kg water/kg dry matter were found to be in the range of 2.6 x 10(-10) m(2)/s to 5.4 x 10(-10) m(2)/s, and its dependence on air drying temperature was represented by an Arrhenius type equation. Activation energy increased with decreasing water content in persimmons.

Temperature and water content influence on thermophysical properties of coffee extract

Specific heat, thermal conductivity, thermal diffusivity, and density of coffee extract were experimentally determined in the range of 0.49 to 0.90 (wet basis) water content and at temperatures varying from 30 to 82 degreesC. Thermal conductivity and specific heat were measured by means of the same apparatus- a cell constituted of two concentric cylinders - operating at steady and unsteady state, respectively. The thermal diffusivity was measured by the well-known Dickerson's method and density was determined by picnometry. The results obtained were used to derive mathematical models for predicting these properties as a function of concentration and temperature.

Thermophysical Properties of Brazilian Orange Juice as Affected by Temperature and Water Content

The specific heat, thermal conductivity, thermal diffusivity and density of Brazilian orange juice were determined between 0.34 and 0.73 (w/w) water content and with temperatures from 0.5 to 62°C. The experimental data were fitted as functions of temperature and water content and all properties showed a linear dependency with these variables. In the tested range, the water content exhibited a greater influence on the analyzed properties than temperature. © 1998 Elsevier Science Limited. All rights reserved.

Physical, Thermal and Water-Sorption Properties of Passion Fruit Seeds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)