An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

An analytical model for contaminant transport in multilayered capped contaminated sediments including the degradation of organic contaminant is presented. The effect of benthic boundary layer was treated as a Robin‐type boundary condition. The results of the proposed analytical model agree well with experimental data. The biodegradation of contaminant in bioturbation layer shows a significant influence on the flux at the surface of system. The maximum flux for the case with t1/2,bio = 0.07 year can be 4.5 times less than that of the case without considering the effect of biodegradation. The thickness of bioturbation layer has a significant effect on the performance of the capped contaminated sediment. The maximum flux for the case with lbio = 15 cm can be 17 times larger than that of the case without bioturbation layer. This may be because the effective diffusion coefficient of sand cap can be 28 times lower than Dbio. The mass transfer coefficient should be considered for the design of the capping system as the contaminant concentration at the top of system for the case with kbl = 2.5 × 10−5 cm/s can be 13 times greater than that of the case with kbl = 10−4 cm/s. The proposed analytical model can be used for verification of complicated numerical methods, evaluation of experimental data, and design of the capping contaminated sediment systems with reactive cap layers

Radial Diffusion and Penetration of Gas Molecules and Aerosol Particles through Laminar Flow Reactors, Denuders, and Sampling Tubes

Flow reactors, denuders, and sampling tubes are essential tools for many applications in analytical and physical chemistry and engineering. We derive a new method for determining radial diffusion effects and the penetration or transmission of gas molecules and aerosol particles through cylindrical tubes under laminar flow conditions using explicit analytical equations. In contrast to the traditional Brown method [Brown, R. L. J. Res. Natl. Bur. Stand. (U. S.) 1978, 83, 1-8] and CKD method (Cooney, D. O.; Kim, S. S.; Davis, E. J. Chem. Eng. Sci. 1974, 29, 1731-1738), the new approximation developed in this study (known as the KPS method) does not require interpolation or numerical techniques. The KPS method agrees well with the CKD method under all experimental conditions and also with the Brown method at low Sherwood numbers. At high Sherwood numbers corresponding to high uptake on the wall, flow entry effects become relevant and are considered in the KPS and CKD methods but not in the Brown method. The practical applicability of the KPS method is demonstrated by analysis of measurement data from experimental studies of rapid OH, intermediate NO3, and slow O3 uptake on various organic substrates. The KPS method also allows determination of the penetration of aerosol particles through a tube, using a single equation to cover both the limiting cases of high and low deposition described by Gormley and Kennedy ( Proc. R. Ir. Acad., Sect. A. 1949, 52A, 163-169). We demonstrate that the treatment of gas and particle diffusion converges in the KPS method, thus facilitating prediction of diffusional loss and penetration of gases and particles, analysis of chemical kinetics data, and design of fluid reactors, denuders, and sampling lines

Source parameters of the left ventricle related to the physiological characteristics of the cardiac muscle.

An attempt is made here to correlate the physiological muscle parameters with the dynamic source parameters of the left ventricle (LV), i.e. the source (isovolumic) pressure Po and the source (internal) resistance, Rs. The internal resistance is described here as a time-dependent parameter, corresponding to the pressure drop (from the theoretical instantaneous isovolumic pressure) associated with the instantaneous ejection flow rate. The source pressure, which relates to the muscle stress and the ventricular volume, is represented by the time-varying elastance concept and a spheroidal model relating the average wall stress to LV pressure. Linear and exponential force-velocity relationships (FVR), expressed in stress-strain rate terms, are compared. Two possible characteristics of the dynamic FVR in the partially active state, based on either a parallel or a fanlike shift of the stress-strain rate curve, are studied by utilizing simple analytical models as well as a computer simulation model. Comparing the calculated results with experimental data indicates that the dynamic FVR shift occurs in a fanlike pattern in which the maximum strain rate remains constant throughout the cycle. This pattern of the FVR shift is consistent with experimental data that show that the internal resistance is linearly related to the instantaneous isovolumic pressure. The analysis also indicates that the difference between the hyperbolic and linear FVR is rather minor, and in spite of some effects on the ejection pattern and the value of Rs, the functional shape has no effect on the global LV characteristics, such as the ejection fraction and stroke volume

Model for left ventricular contraction combining the force length velocity relationship with the time varying elastance theory.

A model for the contraction of the left ventricle (LV) is developed for a spheroidal geometry. The classical force-length-velocity relationship for a single muscle fiber is assumed. The linear maximum pressure volume relationship (maximum elastance), a measure of muscle contractility, is further extended into a time-varying function. This is achieved by utilizing a mechanical activation function, assumed as half a sinusoidal wave, to describe the time-dependent isometric stress for the activated cardiac muscle. This, in turn, results in the time-varying elastance function and represents the instantaneous activity of the muscle contractile proteins. The model is tested for a set of boundary conditions that determine preload, afterload, and the inherent properties of the muscle, i.e., the contractility. The computed results of the isovolumic contraction, auxotonic contraction, and isovolumic relaxation are in agreement with the expected behavior of the LV. The relations between the simulated variations on preload, afterload, and contractility, and the set of performance indexes of the LV, are presented and discussed