Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 130, pp. 1-15.

Title: Method of straight lines for a Bingham problem as 
       a model for the flow of waxy crude oils
       
Authors: German Ariel Torres (Univ. Nacional de Cordoba, Argentina)
         Cristina Turner     (Univ. Nacional de Cordoba, Argentina)

Abstract: 
 In this work, we develop a method of straight lines for
 solving a Bingham problem that models the flow of waxy crude oils.
 The  model describes the flow of mineral oils with a high content
 of paraffin at temperatures below the cloud point
 (i.e. the crystallization temperature of paraffin)
 and more specifically below the pour point at which the crystals
 aggregate themselves and the oil takes a jell-like structure.
 From the rheological point of view such a system can be modelled
 as a Bingham fluid whose parameters evolve according to the
 volume fractions of crystallized paraffin and the aggregation
 degree of crystals. We prove that the method is well defined
 for all times, a monotone property, qualitative behaviour
 of the solution, and a convergence theorem. The results are
 compared with numerical experiments at the end of this article.
 
Submitted April 15, 2005. Published November 24, 2005.
Math Subject Classifications: 35A40, 35B40, 35R35, 65M20, 65N40.
Key Words: Bingham fluid; straight lines; non-newtonian fluids.