A BURGERS CONCENTRATION DISPERSION-EQUATION

In a non-vertical borehole light particles tend to rise towards the upper side of the borehole. The resulting non-uniform density distribution tends to induce an upwards contribution to the longitudinal flow along that upper side of the flow, with a compensating downflow elsewhere. On average the particles experience an extra upflow proportional to the cross-sectionally averaged concentration of particles. Mathematically this concentration-related change of speed corresponds to the nonlinearity of the Burgers equation. Such is the strength of the buoyancy effect that in realistic flow conditions the Burgers nonlinearity can be significant for particle volume fractions of only one part per thousand.