text: Developing well-constructed models (accounting for variables such as oil type, salinity and surfactant) are necessary to select the appropriate dispersant in a given situation. Two models exist which integrate the use of dispersants: Mackays model and Johansens model. There are several parameters which must be considered when creating a dispersion model, including oil-slick thickness, advection, resurfacing and wave action. A general problem in modeling dispersants is that they change several of these parameters; surfactants lower the thickness of the film, increase the amount of diffusion into the water column and increase the amount of breakup caused by wave action. This causes the oil slick's behavior to be more dominated by vertical diffusion than horizontal advection.
  One equation for the modeling of oil spills is:
  where
  * h is the oil-slick thickness
  *  is the velocity of ocean currents in the mixing layer of the water column (where oil and water mix together)
  *  is the wind-driven shear stress
  * f is the oil-water friction coefficient
  * E is the relative difference in densities between the oil and water
  * R is the rate of spill propagation
  Mackay's model predicts an increasing dispersion rate, as the slick becomes thinner in one dimension. The model predicts that thin slicks will disperse faster than thick slicks for several reasons. Thin slicks are less effective at dampening waves and other sources of turbidity. Additionally, droplets formed upon dispersion are expected to be smaller in a thin slick and thus easier to disperse in water.
  The model also includes:
  * An expression for the diameter of the oil drop
  * Temperature dependence of oil movement
  * An expression for the resurfacing of oil
  * Calibrations based on data from experimental spills
  The model is lacking in several areas: it does not account for evaporation, the topography of the ocean floor or the geography of the spill zone.
  Johansens model is more complex than Mackays model. It considers particles to be in one of three states: at the surface, entrained in the water column or evaporated. The empirically based model uses probabilistic variables to determine where the dispersant will move and where it will go after it breaks up oil slicks. The drift of each particle is determined by the state of that particle; this means that a particle in the vapor state will travel much further than a particle on the surface (or under the surface) of the ocean. This model improves on Mackay's model in several key areas, including terms for:
  * Probability of entrainment – depends on wind
  * Probability of resurfacing – depends on density, droplet size, time submerged and wind
  * Probability of evaporation – matched with empirical data
  Oil dispersants are modeled by Johansen using a different set of entrainment and resurfacing parameters for treated versus untreated oil. This allows areas of the oil slick to be modeled differently, to better understand how oil spreads along the water's surface.