Solutions of Diffusion Equation With Constant Diffusion and Surface Emission Coefficients

Liu, Jen Y.; Simpson, William T.

doi:10.1080/07373939708917370

Cited by 42 publications

(12 citation statements)

References 10 publications

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“…These experiments were conducted by immersing the films into water and by measuring the decrease of UV absorbance A ( t ) with time. As demonstrated by others , and detailed in the Supporting Information, the initial absorbance due to the dye in the film ( A (0)) and the diffusion coefficient D can be estimated according to which is valid for times at which A ( t ) > 0.48 A (0). In this equation, d is the thickness of the film.…”

Section: Methodsmentioning

confidence: 99%

Polyelectrolyte Multilayers as Nanocontainers for Functional Hydrophilic Molecules

2003

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We report on the introduction of small organic hydrophilic molecules (fluorescein, rhodamine B, and two coumarin-based dyes) in multilayers of strong polyelectrolytes, studied by X-ray reflectometry, UV/visible spectroscopy, and fluorescence measurements. Very low diffusion coefficients (about 10 -17 cm 2 ‚s -1 ) were found for the inward diffusion of fluorescein in preformed multilayers. In addition, diffusion was accompanied by substantial variations of the thickness of the multilayer (up to 300%), ruling out the practical significance of inward diffusion as a tool to dope multilayers. We then attempted to coadsorb the fluorophores simultaneously with the polyions during the construction of the multilayer. However, displacement of small molecules by polyions of identical charge and outward diffusion of the fluorophores during the rinsing step resulted in very limited inclusion of the dye by this procedure. This issue was solved by introducing the fluorophore in all baths, including the rinsing ones. Then, the concentration of the multilayers in dye is directly related to the concentration of the dipping solutions and is dependent on the nature of the dye and of the multilayer. The outward diffusion of the fluorophores from these multilayers was studied, and very low diffusion coefficients were again determined, depending on the net charge of the dye. The ability to load rapidly polyelectrolyte multilayers with a variety of hydrophilic organic molecules of small molar mass, in tunable concentration, is a major outcome of the present study. It offers new opportunities to use these multilayers as templates for the confinement of active molecules in functional devices.

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Section: Methodsmentioning

confidence: 99%

Polyelectrolyte Multilayers as Nanocontainers for Functional Hydrophilic Molecules

2003

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“…where z is the coordinate measured in the direction of pesticide release (Figure 4), C (kg/cm 3 ), as a function of t and z, is the pesticide concentration in the concrete subject to washing by overland flow. An analytical solution can be derived for the washoff load, M W (t d ,t), as fraction of washoff potential (F), 38,39 τ π π π τ…”

Section: ■ Experimental Sectionmentioning

confidence: 99%

Insecticide Washoff from Concrete Surfaces: Characterization and Prediction

Luo

Jorgenson

Thuyet

et al. 2013

Environ. Sci. Technol.

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Pesticide runoff from impervious surfaces is a significant cause of aquatic contamination and ecologic toxicity in urban waterways. Effective mitigation requires better understanding and prediction of off-site transport processes. Presented here is a comprehensive study on pesticide washoff from concrete surfaces, including washoff tests, experimental data analysis, model development, and application. Controlled rainfall experiments were conducted to characterize washoff loads of commercially formulated insecticides with eight different active ingredients. On the basis of the analysis of experimental results, a semimechanistic model was developed to predict pesticide buildup and washoff processes on concrete surfaces. Three pesticide product specific parameters and their time dependences were introduced with empirical functions to simulate the persistence, transferability, and exponential characteristics of the pesticide washoff mechanism. The parameters were incorporated using first-order kinetics and Fick's second law to describe pesticide buildup and washoff processes, respectively. The model was applied to data from 21 data sets collected during 38 rainfall events, with parameters calibrated to pesticide products and environmental conditions. The model satisfactorily captured pesticide mass loads and their temporal variations for pesticides with a wide range of chemical properties (log KOW = 0.6-6.9) under both single and repeated (1-7 times) rainfall events after varying set times (1.5 h∼238 days after application). Results of this study suggested that, in addition to commonly reported physicochemical properties for the active ingredient of a pesticide product, additional parameters determined from washoff experiments are required for risk assessments of pesticide applications on urban impervious surfaces.

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“…Some of the models published in the literature predict the transfer phenomena occurring inside the foods during drying. However, many are solved fixing the geometric characteristics of the food (that is, neglecting shrinkage) and considering constant the transfer properties, thus leading only to approximate solutions [11]. Indeed, drying models that describe more accurately the process are difficult to obtain, mostly because transport properties (like for instance, the moisture diffusivity) are not constant, and their variation throughout the process is not available.…”

Section: Introductionmentioning

confidence: 99%

Modelling and simulation of pear drying

Guiné

Rodrigues

Figueiredo

2007

Applied Mathematics and Computation

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In the present work a diffusion based model was adopted to represent the drying behaviour of pears in a continuous convective drier, taking into consideration the variation of the properties of the pears along drying.The program developed simulated a significant number of situations resultant from the variation of some of the operating conditions. The temperatures tested were 30, 40 and 50°C, the air velocities were 0.5, 1.0 and 1.5 m/s, and the relative humidity of the drying air was 40%, 50% and 60%.From the situations analyzed, and considering the specifications required for the final product, it was concluded that the drying should be carried out at 40°C, with a drying air velocity of 1.5 m/s and containing 60% RH.

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Solutions of Diffusion Equation With Constant Diffusion and Surface Emission Coefficients

Cited by 42 publications

References 10 publications

Polyelectrolyte Multilayers as Nanocontainers for Functional Hydrophilic Molecules

Polyelectrolyte Multilayers as Nanocontainers for Functional Hydrophilic Molecules

Insecticide Washoff from Concrete Surfaces: Characterization and Prediction

Modelling and simulation of pear drying

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