The convection-diffusion equation for a finite domain with time varying boundaries

A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at the ends. When the input concentration is arbitrary, the problem is underdetermined because of an unknown exit concentration. We resolve this by defining the exit concentration as a solution to a similar diffusion equation which satisfies a Dirichlet condition at the left end of the half line. This problem does not appear to have been solved in the literature, and the resulting representation should be useful for problems of practical interest. Authors of previous works on problems of this type have eliminated the unknown exit concentration by assuming a continuous concentration at the outflow boundary. This yields a well-posed problem by forcing a homogeneous Neumann exit, widely known as the Danckwerts [1] condition. We provide a solution to the Neumann problem and use it to produce an estimate which demonstrates that the Danckwerts condition implies a zero concentration at the outflow boundary, even for a long flow domain and a large time.Comment: W. J. Golz and J. R. Dorroh. 2001. The Convection-diffusion equation for a finite domain with time varying boundaries. Applied Mathematics Letters 14 : 983-988 (received by AML September 2000; accepted by AML October 2000

The HPx software for multicomponent reactive transport during variably-saturated flow: Recent developments and applications

Abstract HPx is a multicomponent reactive transport model which uses HYDRUS as the flow and transport solver and PHREEQC-3 as the biogeochemical solver. Some recent adaptations have significantly increased the flexibility of the software for different environmental and engineering applications. This paper gives an overview of the most significant changes of HPx, such as coupling transport properties to geochemical state variables, gas diffusion, and transport in two and three dimensions. OpenMP allows for parallel computing using shared memory. Enhancements for scripting may eventually simplify input definitions and create possibilities for defining templates for generic (sub)problems. We included a discussion of root solute uptake and colloid-affected solute transport to show that most or all of the comprehensive features of HYDRUS can be extended with geochemical information. Finally, an example is used to demonstrate how HPx, and similar reactive transport models, can be helpful in implementing different factors relevant for soil organic matter dynamics in soils. HPx offers a unique framework to couple spatial-temporal variations in water contents, temperatures, and water fluxes, with dissolved organic matter and CO2 transport, as well as bioturbation processes

Long-term electrode behavior during treatment of arsenic contaminated groundwater by a pilot-scale iron electrocoagulation system.

Iron electrocoagulation (Fe-EC) is an effective technology to remove arsenic (As) from groundwater used for drinking. A commonly noted limitation of Fe-EC is fouling or passivation of electrode surfaces via rust accumulation over long-term use. In this study, we examined the effect of removing electrode surface layers on the performance of a large-scale (10,000 L/d capacity) Fe-EC plant in West Bengal, India. We also characterized the layers formed on the electrodes in active use for over 2 years at this plant. The electrode surfaces developed three distinct horizontal sections of layers that consisted of different minerals: calcite, Fe(III) precipitates and magnetite near the top, magnetite in the middle, and Fe(III) precipitates and magnetite near the bottom. The interior of all surface layers adjacent to the Fe(0) metal was dominated by magnetite. We determined the impact of surface layer removal by mechanical abrasion on Fe-EC performance by measuring solution composition (As, Fe, P, Si, Mn, Ca, pH, DO) and electrochemical parameters (total cell voltage and electrode interface potentials) during electrolysis. After electrode cleaning, the Fe concentration in the bulk solution increased substantially from 15.2 to 41.5 mg/L. This higher Fe concentration led to increased removal of a number of solutes. For As, the concentration reached below the 10 μg/L WHO MCL more rapidly and with less total Fe consumed (i.e. less electrical energy) after cleaning (128.4 μg/L As removed per kWh) compared to before cleaning (72.9 μg/L As removed per kWh). Similarly, the removal of P and Si improved after cleaning by 0.3 mg/L/kWh and 1.1 mg/L/kWh, respectively. Our results show that mechanically removing the surface layers that accumulate on electrodes over extended periods of Fe-EC operation can restore Fe-EC system efficiency (concentration of solute removed/kWh delivered). Since Fe release into the bulk solution substantially increased upon electrode cleaning, our results also suggest that routine electrode maintenance can ensure robust and reliable Fe-EC performance over year-long timescales

Fiber Optical Sensing of Bearing Performance and Pump Conditions

Lectur

A model of dispersive transport across sharp interfaces between porous materials

Recent laboratory experiments on solute migration in composite porous columns have shown an asymmetry in the solute arrival time upon reversal of the flow direction, which is not explained by current paradigms of transport. In this work, we propose a definition for the solute flux across sharp interfaces and explore the underlying microscopic particle dynamics by applying Monte Carlo simulation. Our results are consistent with previous experimental findings and explain the observed transport asymmetry. An interpretation of the proposed physical mechanism in terms of a flux rectification is also provided. The approach is quite general and can be extended to other situations involving transport across sharp interfaces.Comment: 4 pages, 4 figure