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Oil dispersants are a mixture of surfactants and solvents that break up an oil slick into droplets. By breaking up the oil slick into droplets, microbes and the environment can biodegrade the oil easier. A mixture of oil and water is normally unstable, but can be stabilized by the addition of surfactants. Surfactants improve their interactions by standing at the oil-water interface thereby decreasing the surface energy. Dispersants have had negative effects in the environment due to their toxicity, however reformulated dispersants have been accepted by the U.S. Environmental Protection Agency (EPA).

= History= In 1967, the ship, Torrey Canyon, leaked oil into the English Coast. Primarily, alkylphenol surfactant were used to break up the oil. However, the use of this proved to be very toxic to the environment. All types of marine life were killed. This lead to a reformulation of new dispersants to be more environmentally sensitive. After the Torrey Canyon incident, new boat spraying systems were developed. Later reformulations allowed for more dispersant to be contained at a higher concentration to be aerosolized.

= Theory =

Requirements
There are five general requirements for surfactants to successfully disperse oil.
 * 1) Dispersant must be on the oil's surface in proper concentration.
 * 2) Dispersant must penetrate/mix with oil.
 * 3) Surfactant molecules must orient at the oil-water interface (hydrophobic in oil and hydrophillic in water).
 * 4) Oil-water interfacial surface tension must be lowered (so the oil can be broken up).
 * 5) Energy must be applied to mix (i.e. by wave).

Hydrophilic-lipophilic balance (HLB) is a coding scale that ranges from 0 to 20 for nonionic surfactants and takes into account the chemical structure of surfactant molecule. A zero value corresponds to the most lipophillic and a twenty value is the most hydrophilic for a non-ionic surfactant.

Dispersion Models
Developing well constructed models that take into account variables such oil type, salinity, surfactant, etc. are necessary to select the appropriate dispersant for the given situation. Two models exist that integrate the use of dispersants, Mackay's Model and Johansen's Model. There are several parameters that must be considered when creating a dispersion model. These include: Slick thickness, advection, resurfacing, and wave action. The general issue with dispersants in modeling 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 also increase the amount of breakup caused by wave action. This causes the oil slick's behavior to be more dominated by vertical diffusion rather than horizontal advection.

One equation for the modeling of oil spills is :

$$(\frac {\partial h}{\partial t})\bigtriangledown (h(\vec {U} + (\frac {\vec {t}}{f}) - \bigtriangledown(E\bigtriangledown h) = R $$

where
 * h is the oil slick thickness
 * $$\vec {U}$$ is the velocity of ocean currents in the mixing layer of the water column(where oil and water mix together)
 * $$\vec {t}$$ is the wind-driven shear stress
 * f is the oil-water friction coefficeint
 * 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: First, 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
 * Calibrated based on data from experimental spills

Mackay's model is lacking in several areas, including the fact that it does not account for evaporation and does not account for the topography of the ocean floor or the geography of the spill zone.

Johansen's model is more complex than Mackay's model in that 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 that particle is in. This means that an particle in the vapor state will travel much further than a particle on the surface or under the surface of the ocean. The model makes improvement 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 emperical data

Oil dispersants are modeled by Johansen by using a different set of entrainment and resurfacing parameters for treated vs untreated oil. This allows areas of the oil slick to be modeled differently to get a better understanding of how oil spreads along the surface of the water.

Non-Ionic Surfactants
In order to determine the Gibbs free energy of micellization, the change in chemical potential for the surfactant going from a single solvated molecule to a micelle. There are many approaches to this, one of which is called the phase separation model. This model takes advantage of the fact that micellization is much like two distinct phases separated by a monolayer, however, the model does not take into account the changes in energy associated with the interactions of charges and thus makes it suitable only for descibing nonionic surfactants. In the phase separation model, there are two distinct phases, the alpha(α) and beta(β). The interfacial tension between the two phases is described by the Laplace Equation, which relates the change in pressure across two phases to the curvature and interfacial tension.

$$ \Delta P= \gamma (C_1 +C_2)$$

Where:

$$ \Delta P$$ is the change in pressure across the interface

$$\gamma$$ is the interfacial tension

$$C_1 $$and $$C_2$$ are the curvatures of the selected interface

The chemical potential, μ, at low concentrations can be described by the equation :

$$\mu _{sur} (micelle) = \mu ^0 _{sur} + RTln[S]$$

When [S], the concentration of surfactant reaches the critical micelle concentration, the chemical potenial of the surfactant in the micelle is equal to the chemical potential of the surfactant when it is solvated. Thus, the molar Gibbs free energy of micelle formation is described by the equation:

$$\Delta G^{mic} _m = \mu_{micelle} - \mu^{0} _{sur} = RTlnCMC$$

The main factor that drives the formation of micelles is the movement of the hydrocarbon chains out of water and into an environment where they can interact with other non-polar groups is driven by entropy. Although there is ordering occurring by creating a phase separation, the entropy gained by the water molecules interacting with other water molecules is far greater in magnitude.

Ionic Surfactants
Describing the formation of micelles mathematically for ionic surfactants is far more difficult because of the repulsion that occurs between the head groups as the micelle is formed. In addition, the surfactant molecules must be dehydrated prior to micelle formation, which decreases the shielding of each head group and thus increases the repulsion between two molecules. For this reason, the CMC of ionic surfactants tends to be higher than that of nonionic surfactants. . When addressing ionic surfactants, one must consider the electric double layer that forms at the surface of the micelle. The electric double layer has the effect of stabilizing the micelle by sheilding the like charges from each head group. Addign salt to ionic surfactants has the effect of drastically reducing the CMC. The salt increases the concentration of ions available to screen the charge of the ionic head groups and thus will make it easier for aggregation to occur. Another method to reduce the CMC of an ionic micelle is to increase the length of the alkyl chain, increasing the amount of dispersion interactions and thus making micelle formation more energetically favorable.

Ionic micelles are very difficult to describe mathematically due to the repulsion that occurs between all head groups. Due to the sheer number of variables as well as the fact that the electric potential felt by each headgroup is dependent on each other group.

= Types of Surfactants = There are four main types of surfactants, each with different properties and applications. They are: Anionic, Cationic, Nonionic, and Zwitterionic or amphoteric. Anionic surfactants are compounds that contain an anionic polar group. Examples of anionic surfactants include sodium dodeccyl sulfate and sodium dioctyl sulfosuccinate. Included in this class of surfactants are sodium alkylcarboxylates, which are also known as soaps. Cationic surfactats are similar in nature to anionic surfactants except the surfactant molecules carry a positive charge at the hydrophilic portion. Many of these compounds are quaternary ammonium salts, as well as cetyl ammonium bromide CTAB. Non-ionic surfactants are non-charged and together with anionic surfactants make up the majority of oil dispersant formulations. The hydrophilic portion of the surfactant contains polar functional groups, such as -OH or -NH. Zwitterionic surfactants are the most expensive and are therefore used for specific applications. These compounds have both positively and negatively charge components to them. An example of a zwitterionic compound is phosphatidylcholine, which is a lipid and is not soluble in water on a meaningful level.

HLB Values
Surfactant behavior is highly dependent on the HLB value. In general, compounds with an HLB of 1 to 4 will not mix with water. Compounds that have an HLB value above 13 will form a clear solution with water. Oil dispersants tend to have HLB values ranging from 8-18.

Comparative Industrial Formulations
Two formulations of different dispersing agents for oil spills: DISPERSIT™ and Omni-Clean® are shown below. A key difference between the two is that Omni-Clean® uses ionic surfactants whereas DISPERSIT™ uses entirely non-ionic surfactants. Omni-Clean® was formulated for little to no toxicity toward the environment. DISPERSIT™ however was designed as a direct competitor to COREXIT. DISPERSIT™ contains non-ionic surfactants which allows for primarily oil soluble surfactants as well as primarily water soluble surfactants. The partitioning of surfactants between the phases allows for a very effective dispersant.

= Degradation and Toxicity = Both the degradation and the toxicity of dispersants depend on the chemicals chosen within the formulation. Compounds that interact too harshly with Oil dispersants should be tested to ensure that they meet three further criteria:


 * 1) They should be biodegradable
 * 2) In the presence of oil, they must not be preferentially utilized as carbon source
 * 3) They must be nontoxic to indigenous bacteria.

= Applications =

Oil Treatment
Effectiveness of the dispersant depends on weathering of the oil, sea energy (waves), salinity of water, temperature and the type of the oil itself. Dispersion is unlikely to occur if the oil spreads into a thin layer because the dispersant requires a certain thickness in order to work, otherwise the dispersant will interact with the water and not just the oil. More dispersant may be required if the sea energy is low. The salinity of the water is more important for dispersants that use ionic surfactants as they will preferentially interact with the water layer more so than with the oil. Viscosity of the oil is another important factor, viscosity can retard dispersant migration to oil-water interface and also can increase the energy required to sheer off a drop from the slick. Viscosities below 2,000 centipoise are optimal for dispersants. If the viscosity is above 10,000 centipoise, no dispersion will be able to occur.

Methods of Use
Dispersants are delivered in concentrated-dilute solutions and are aerosolized via aerial spraying typically using an aircraft or boat. Enough dispersant with droplets in the proper size are necessary, which can be achieved by the rate of pumping the dispersant. Droplets larger than 1,000 µm is preferred to ensure they are heavy enough to not be blown away by the wind. The ratio of dispersant to oil is typically 1:20.

Deep Water Horizion
During the Deepwater Horizon oil spill, an estimated 1.84 million gallons of oil dispersants were used in an attempt to reduce the amount of surface oil and thus mitigate the damage to wildlife. Additionally, almost half(771,000 gallons) of the dispersants were applied directly at the wellhead. The primary dispersant used was corexit, which was controversial due to its toxicity relative to other dispersants.

Exxon Valdez
Dispersants were also used during the Exxon Valdez oil spill, although their use was far less effective. Alaska had fewer than 4,000 gallons of dispersants available at the time of the incident and no aircraft to dispense them with. The dispersants that were introduced were relatively ineffective due to insufficent wave action to mix the oil and water and so their use was abandoned shortly after. = References =