This work describes a method to obtain a complete description of a spray flow by computing the evolution of its probability, density function (PDF) simultaneously with the gas flow in which it is embedded. Given an ensemble of spray flows, it is possible to develop a PDF for the drops that gives the expected number of drops per unit volume of spray space, where the phase space is defined as the space of characteristics that describe each drop. We can then derive an evolution equation for that function, called the spray equation.; If we assume that a set of low-order moments, such as the means and variances, of the PDF carry the greatest amount of information about the function, then the PDF can be integrated to derive transport equations for these moments the solution of which will allow us to approximate the shape of the PDF and achieve closure of the system of equations. To accomplish this closure, we employ a maximum entropy model. By maximizing Shannon's entropy subject to given moment constraints, it is possible to obtain the most unbiased PDF within the imposed constraints. This PDF now represents the distribution of drops across the ensemble at each point in the spray flow. By integrating it over its domain, we can close any higher-order terms appearing within the moment transport equations.; To explore its usefulness, the approach is tested on a quasi-one-dimensional spray flow. There is no mean velocity in the transverse direction and gradients of averaged quantities in the transverse direction vanish. Submodels which account for the effects of the gas on the drops, including turbulence modification and the correlation between the gas and drop velocities, are employed. Three test cases are explored to see the effects of velocity slip on the moments as the drops are decelerated, accelerated, and injected at the same mean velocity as the gas. There is also a discussion on extending the approach to a more general problem.
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