The entrainment or dispersion into the water column of substances other than oil which float at the water surface follows the same approach used in earlier Type A models (Reed, 1989), wherein the dispersion rate per second is

Da = K3 (W + 1)²/(1 + 50μ^1/2δSt) 7　(3-5)

with the wind speed, W, expressed in m/sec here (Mackay et al., 1980). K3 is a constant, μ is viscosity (centipoise), δ is slick thickness (m) and st is interfacial tension between the pollutant and water. K3 is set equal to 0.11. In the case of hazardous substances which form a surface slick, Equation (3-5) appears to underestimate entrainment as compared to evaporation. Results developed by Wolff and Poels (1986) have been used to apply a correction factor Db which depends on solubility:

where

　

 For hazardous substances which float, the entrainment rate is then DaDb. Entrained substances are assumed to dissolve, as long as saturation conditions are not exceeded.

 For oils and petroleum products, entrainment and dissolution modeling is based on the laboratory results of Delvigne and Sweeney (1988). The oil is represented by a large number of particles, each of which represents in turn a group of oil droplets of like size and composition (Elliott, 1986; Johansen, 1985). When a particle is on the surface, it behaves as a slick; when in the water column, a particle behaves as a droplet. The extent of the surface slick at any time is the superposition of all the surface particles at that time.

 Transport of oil at the surface is computed simply as 3.6% of the wind speed, plus the current (Reed et al., 1990). Horizontal transport in the water column is computed from the current alone.

 The entrainment of oil from the sea surface into the water column is based on Delvigne and Sweeney (1988):

　

where

　

 The empirical coefficient C^* is a function of the viscosity of the oil. Values for C^* are given by Delvigne and Sweeney (1988) for three oils (Table 3.1).

　

　

The limited data for C^* suggests the approximation

where

 The dissipation wave energy, D, in kg/s² is approximated from the breaking wave height, Hb in m, as

where

　

 The fraction of the sea surface covered by breaking waves per unit time is approximated as

　

for the wind speed W in m/sec (O'Muircheartaigh and Monahan, 1986).

　

 Observed droplet sizes range from 1 to about 1600 μm, with the majority of the oil in the range 50-350 μm. The droplet size distribution was shown by Delvigne and Sweeney (1987) to be related to kinematic viscosity, v, and the energy dissipation rate, e (J/m³ sec), by

　

　

 According to Delvigne and Sweeney, the turbulent energy dissipation rate in breaking waves is on the order of 10³ to 10⁴ J/m³/sec; here we use an intermediate value of 5000. For the mean particle size, d50, the value of C0 is approximately 1400; for the maximum and minimum particle sizes, the coefficient is about 3400 and 500, respectively.

 The initial entrainment depth is taken as

　

 A terminal rise velocity for entrained oil droplets of size class i is given by

　

　

where

　

 The mixing depth, hi, for each particle size class i is taken as

　

　

 The vertical dispersion coefficient, Dv, in m²/sec is estimated from data reported by Thorpe (1984), based on acoustic studies of air bubbles, as

for the wind speed at 10 m height in m/sec.

 The mixing depth for each particle class is allowed to increase to a maximum of 25 m, the observed depth of the pycnocline during these experimental spills. The model assumes uniform distribution of each particle size class over the associated mixing depth, so the resurfacing rate for size class i, mixed over the depth hi, is simply

　

　

 Laboratory flume studies (Delvigne et al., 1987) have shown that the majority of oil droplets formed in breaking wave conditions are in the range 50 ≦ d0 ≦ 350 μm. Table 3.2 suggests that, except for highly emulsified, high viscosity oils which tend to form larger particle sizes (Equation 3-11), most oil entrained in breaking waves will tend to remain subsurface as long as breaking continues to occur at virtually every location at least once per unit rise time. As soon as seas subside, however, any subsurface oil particles over 100 μm in diameter will resurface within an hour, reforming a surface slick.

　

　

 The viscosity μ is allowed to increase for petroleum products according to an emulsification algorithm, also from Mackay et al. (1980). The rate of incorporation of water into the slick is

　

　

　

 Gasoline, kerosene, and light diesel fuel are assumed not to form emulsions with water (Payne and Phillips, 1985). The resultant viscosity μ of the oil in the slick is then computed using the Mooney (1951) equation

μ/μoexp(2.5Fwc/(1.0-0.65Fwc)) 10　(3-18)

in which μo is the viscosity of the parent oil connected for temperature and evaporated fraction. The effect of evaporation on viscosity is modeled

as

μ = μoexp(C4Fevap)11　(3-19)

　

where Fevap is the fraction evaporated from the slick. The model uses C4 = 1 for gasoline, kerosene, and light diesel fuel, and C4 = 10 for other petroleum products. (Mackay et al., 1982).

 The entrainment process is assumed to affect all four modeled fractions of a petroleum product equally. Aromatics are modeled as dissolving from entrained oil droplets and surface slicks using a standard mass-transfer and differential concentration equation (Equation 3-25).

 Entrained "residual" oil is assumed to exist as particulate oil in the water column, and does not enter the toxicological concentration computations. This dispersion/emulsification formulation will eventually drive all residual oil into the water column, giving surface slicks a finite lifetime.