Numerical Simulations of Convection Induced by Korteweg Stresses in a Miscible Polymer-Monomer System: Effects of Variable Transport Coefficients, Polymerization Rate and Volume Changes
We modeled a miscible polymer-monomer system with a sharp transition zone separating the two fluids to determine if convection analogous to Marangoni convection in immiscible fluids could occur because of thermal and concentration gradients. We considered three cases: with a temperature gradient along the transition zone, with a variable transition zone width, and one with a gradient in the conversion of polymerization. Using the Navier-Stokes equations with an additional term, the Korteweg stress term arising from non-local interactions in the fluid, we demonstrated with realistic parameters that measurable fluid flow would result in the absence of buoyancy-driven convection for all three cases. We show that even if the Korteweg stress is not a function of temperature, the increase in the diffusion coefficient with temperature can result in convection because a gradient in the transition zone width develops. We also examine the effects of a polymer viscosity that is not only a function of concentration but also temperature. We demonstrate that a constant flux of heat, as would be realistic for a heating element in contact with the side of the reactor, would produce a greater flow than a linear thermal gradient parallel to the transition zone. We demonstrate that qualitatively different flow patterns can be realized by using unusual initial conditions that could be realized with different masks for the photopolymerization. We also demonstrate that the volume change during polymerization and caused by side heating could not cause significant fluid flow that would confound the observation of Korteweg-stress induced flows. To avoid buoyancy-driven convection, the experiment would have to be performed in microgravity.