Diffusion through ordered force fields: a case-study problem. The classical Fick or Einstein model for diffusion is based on the assumption that the diffusing molecule is exposed to a random force field arising from molecular motion. The assumption is reasonable and predicts phenomena such as Knudsen diffusion for small-sized pores but might not be true for nanopores, where there may be a directional force field. This variation is due to local concentration differences, the presence of surface charge, etc. Such systems can be simulated by using the Fokker–Planck equation and the Smoluchowski equation, and an illustrative study has been presented by Wang et al. (2009). Your goal is to review this paper, write a computational model that permits incorporation of a prescribed force field, and calculate the additional….
Soil dewatering by electro-osmosis: a case-study problem. The phenomenon of electroosmosis can be used for dewatering and consolidation of soils and mine tailing and waste ludges. The idea is that by appropriate placement of electrodes the flow can be diverted away from a contaminated site in a controlled fashion. In a reverse manner, a flow of a suitable chemical sealant can also be directed towards the spill site. Porous soils such as clays have a negative surface charge and hence the salt-bearing ground water flows from the anode to the cathode, thereby lowering the water table near the contaminated site. Simple models can be based on the equations presented in this chapter and models of increasing levels of complexity may be developed using a 2D or 3D geometry….
A waste stream is to be treated by holding it for some time in a surge tank prior to discharging it into a river. The waste stream has a dissolved toxic species A, which is unstable and undergoes a first-order chemical reaction. The purpose of the surge tank is to allow enough residence time for some decomposition of A to occur in order to reduce the concentration of the pollutant. Derive an expression for the exit concentration as a function of time and the final steady-state concentration in the system. Assume that the tank is well stirred and use the backmixed assumption. The problem is sketched in Fig. 2.2.
The simplified case of Eq. (2.8) with no reaction (Da = 0) is important and provides a very useful experimental method to determine whether and to what extent a reactor is backmixed. The method is known as tracer analysis, also known as stimulus–response experiments. The stimulus represents a change in the inlet conditions, and the change in concentration in the outlet as a function of time is measured and represents the response curve of the system. The exit response can be predicted from the above analysis and matched with the experimental data to test some of the model assumptions, for example, whether the assumption that the system is well mixed holds or not. Two types of tracer injection are common: (i) step injection and (ii) pulse or bolus….
Calculate the performance of the heat exchanger specified below for both cocurrent and countercurrent flows. The hot fluid flow rate is 3 kg/s, and the fluid is to be cooled from 400 K. The cold stream is cooling water at the rate of 4 kg/s available at 300 K. The overall heat transfer coefficient is 800 W/m2 · K. The heat transfer area is 30 m2. The specific heat for both fluids is taken as that of water, 4180 J/kg · K. Also find what the temperatures of the fluids leaving the system would be if the heat exchanger were infinitely long.