We investigate three-dimensional nonlinear rotating viscoelastic curved jets in the presence of gravity force. Applying the Giesekus model for the viscoelastic stress parts of the jet flow system and using perturbation methods with a consistent scaling, a relatively simple system of equations with realistic three-dimensional centerlines is developed. We determine numerically the relevant solution quantities of the model in terms of the radius, speed, tensile force, stretching rate, strain rate and the jet centerline versus arc length and for different parameter values associated with gravity, viscosity, rotation, surface tension and viscoelasticity. Considering the jet flow system in full 3-dimensions and in the presence of gravity can be significant, impacting the jet speed, strain rate, tensile force, stretching rate and the centerline curvature are notably increased in magnitude and the jet radius size is reduced and this becomes more dominant with larger values of the arc length, gravity, rotation and viscoelasticity. In particular, for a typical value of the gravity and for an order one value of the arc length, we found that gravity makes jet speed higher by at least a factor of 2 and makes jet radius lower by a factor of 0.6 or smaller as we compare to the corresponding values when gravity is not considered.
Riahi, Daniel N., and Saulo Orizaga. "On three-dimensional rotating viscoelastic jets in the Giesekus model." Partial Differential Equations in Applied Mathematics 5 (2022): 100364. https://doi.org/10.1016/j.padiff.2022.100364
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Partial Differential Equations in Applied Mathematics