Washout coefficient

Fig. 18-6. Typical values of the washout coefficient as a function of rainfall rate and particle diameter. Source After Engelmann (13).

Models to Allow for the Effects of Coastal Sites, Plume Rise, and Buildings on Dispersion of Radionuclides and Guidance on the Value of Deposition Velocity and Washout Coefficients, Fifth Report of a Working Group on Atmospheric Dispersion, National Radiological Protection Board, NRPB-R157, 1983. 

As an approximation, the rate of wet deposition of a pollutant is sometimes taken as AC, where C is the pollutant concentration and A is known as a washout coefficient which is proportional to the precipitation intensity (Shaw, 1984). 

Heterogeneous advective transport in air occurs primarily through the absorption of chemicals into falling water droplets (wet deposition) or the sorption of chemicals into solid particles that fall to earth s surface (dry deposition). Under certain conditions both processes can be treated as simple first-order advective transport using a flow rate and concentration in the advecting medium. For example, wet deposition is usually characterized by a washout coefficient that is proportional to rainfall intensity. 

Chamberlain, 1960 Engelmann, 1968). The quantity A(r2) is called the washout coefficient. It depends on r2 in much the same fashion as Ec. Figure 8-7 shows sample calculations for two drop size spectra with maxima at radii of 0.2 and 1 mm, respectively, according to Zimin (1964) and Slinn and Hales (1971). For a given particle size, the washout coefficient is a constant only if the rain drop spectrum does not change with time. This ideal situation is rarely met in nature, due to the usual variation of the rainfall rate. If this assumption is nevertheless made, the contribution of below-cloud scavenging to the total concentration of particulate matter in rainwater is... 

Fig. 8-7. Washout coefficients according to Slinn and Hales (1971) are shown in curves A and B (left-hand scale). They are based on rain drop size spectra of Zimin (1964) with r,max = 0.2 and 1 mm, respectively, and a precipitation rate of 10 mm/h (10 kg/m2 h). Curve C represents the first term and curves D and E the second term in the bracket of Eq. (8-6) in nonintegrated form (right-hand scale applies). These latter three curves are based on the mass-size distribution for the rural continental aerosol in Fig. 7-3. Curve C was calculated with eA(r2)=l for r2>0.5 ra and eA < I for r2<0.5(im, decreasing linearly toward zero at r2 = 0.06 p.m. This leads to eA = 0.8. Curves D and E were obtained by using the washout coefficients of curves A and B, respectively. Note that below-cloud scavenging (curves D and E) affect only giant particles, whereas nucleation scavenging (curve C) incorporates also submicrometer particles.

Kerker, M. and V. Hampel (1974). Scavenging of aerosol particles by a falling water drop and calculation of washout coefficients. J. Almos. Sci. 31, 1368-1376. 

The older literature is full of experimental estimations of X, also called the washout coefficient, by the measurement of the gas and rainwater concentration of soluble gases. However, that approach is wrong because a) A is a function of height (it should measured as the vertical gas phase concentration profile and not the surface concentration) and b) a dominant part of the dissolved matter arises from in-cloud scavenging. For sub-cloud scavenging, assuming the washout process to be a first-order process (rfc/rft) = Ac, we can describe the sub-cloud process for gases as well as particles indexes g and p denote the gas and particle, respeetively ... 

Jones, J.A. (1983). Models to allow for the effects of coastal sites, plume rise and buildings on dispersion of radionuclides and guidance on the value of deposition velocity and washout coefficients. National Radiological Protection Board, Harwell Report NRPB-R157. 

The interesting features are (1) X goes to zero and S reaches as D approaches [1 (2) S is not a function of when D is less than (3) the maintenance coefficient is very important at low dilution rate but has httle effect afterwards and (4) is never so high that [L can be reached, thus washout always occurs before [L and is a function of S. ... 

Inhaled anesthetics that are relatively insoluble in blood (ie, possess low blood gas partition coefficients) and brain are eliminated at faster rates than the more soluble anesthetics. The washout of nitrous oxide, desflurane, and sevoflurane occurs at a rapid rate, leading to a more rapid recovery from their anesthetic effects compared with halothane and isoflurane. Halothane is approximately twice as soluble in brain tissue and five times more soluble in blood than nitrous oxide and desflurane its elimination therefore takes place more slowly, and recovery from halothane- and isoflurane-based anesthesia is predictably less rapid. 

Inhaled anesthetics that are relatively insoluble in blood (low blood gas partition coefficient) and brain are eliminated at faster rates than more soluble anesthetics. The washout of nitrous oxide, desflurane, and sevoflurane occurs at a rapid rate, which leads to a more rapid recovery from their anesthetic effects compared to halothane and isoflurane. Halothane is approximately twice as soluble in brain tissue and five times more soluble in blood than nitrous oxide and desflurane its elimination therefore takes place more slowly, and recovery from halothane anesthesia is predictably less rapid. The duration of exposure to the anesthetic can also have a marked effect on the time of recovery, especially in the case of more soluble anesthetics. Accumulation of anesthetics in tissues, including muscle, skin, and fat, increases with continuous inhalation (especially in obese patients), and blood tension may decline slowly during recovery as the anesthetic is gradually eliminated from these tissues. Thus, if exposure to the anesthetic is short, recovery may be rapid even with the more soluble agents. However, after prolonged anesthesia, recovery may be delayed even with anesthetics of moderate solubility such as isoflurane. 

Several special terms are used to describe traditional reaction engineering concepts. Examples include yield coefficients for the generally fermentation environment-dependent stoichiometric coefficients, metabolic network for reaction network, substrate for feed, metabolite for secreted bioreaction products, biomass for cells, broth for the fermenter medium, aeration rate for the rate of air addition, vvm for volumetric airflow rate per broth volume, OUR for 02 uptake rate per broth volume, and CER for C02 evolution rate per broth volume. For continuous fermentation, dilution rate stands for feed or effluent rate (equal at steady state), washout for a condition where the feed rate exceeds the cell growth rate, resulting in washout of cells from the reactor. Section 7 discusses a simple model of a CSTR reactor (called a chemostat) using empirical kinetics. 

The S is the input concentration of nutrient (to the leftmost vessel), and D is the washout rate. These two parameters are under the control of the experimenter. The terms 7 and y, are the yield coefficients. For convenience, one can scale substrate concentrations S, by S , time by /D (making m, nondimensional and D = 1), and microorganism concentrations by and to obtain the less cluttered system... 

In continuous reactors, the threshold coefficient is identical with the steady state substrate concentration (17,18). For increasing temperatures, it has been observed to fall (17,18) and show a minimum (18). These responses are consistent with the d > 0 curves shown in Figure 6. It has also been observed to Increase nonllnearly with dilution rate until washout occurred (17.18). In both Instances, the slope at low dilution rates decreased with rising temperature. The observed responses to increasing dilution rate are also consistent with equation (27). 

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