On rotationally driven nonlinear inclined polymeric jet with gravity effect

Daniel N. Riahi; Saulo Orizaga; Daniel N. Riahi; Saulo Orizaga

doi:10.3934/mine.2022014

Mathematics in Engineering

2022, Volume 4, Issue 2: 1-18. doi: 10.3934/mine.2022014

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Research article

On rotationally driven nonlinear inclined polymeric jet with gravity effect

Daniel N. Riahi ¹,
Saulo Orizaga ^{2
,
,}

1.
Mechanical Science and Engineering, UIUC, 1206 W. Green St. MC 244, Urbana, IL 61801, USA
2.
Department of Mathematics, New Mexico Tech, 801 Leroy Place, Socorro, NM 87801, USA

Received: 12 February 2021 Accepted: 22 June 2021 Published: 13 July 2021

We consider rotationally driven nonlinear polymeric fiber jet, whose centerline is in an inclined plane, in the presence of gravity force. An empirical viscosity model is used for the polymeric fluid flow to investigate properties of the rotating inclined polymeric fiber jet. The aim of the study is to understand properties of such inclined fiber jet shape, which can be due to orientation change of an orifice in a rotating spinneret that generates such jet. Perturbation, asymptotic, scaling and numerical techniques are used to determine the nonlinear steady solutions for the jet quantities for different values of the parameters due to gravity, rotation, viscosity, surface tension and relaxation time. In contrast to the horizontal jet case, presence of gravity and jet inclination increase values of the jet speed, strain rate, stretching rate and the centerline curvature and decrease the value of the jet radius and more so with increasing the arc length, gravity, rotation rate and the relaxation time. However, a non-inclined jet with no imposed restriction on its shape and in presence of gravity leads to smaller fiber radius and larger speed as compared to the ones for inclined jet case.
- jet flow,
- rotating jet,
- gravity force,
- inclined jet,
- polymeric fluid
Citation: Daniel N. Riahi, Saulo Orizaga. On rotationally driven nonlinear inclined polymeric jet with gravity effect[J]. Mathematics in Engineering, 2022, 4(2): 1-18. doi: 10.3934/mine.2022014

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Abstract

We consider rotationally driven nonlinear polymeric fiber jet, whose centerline is in an inclined plane, in the presence of gravity force. An empirical viscosity model is used for the polymeric fluid flow to investigate properties of the rotating inclined polymeric fiber jet. The aim of the study is to understand properties of such inclined fiber jet shape, which can be due to orientation change of an orifice in a rotating spinneret that generates such jet. Perturbation, asymptotic, scaling and numerical techniques are used to determine the nonlinear steady solutions for the jet quantities for different values of the parameters due to gravity, rotation, viscosity, surface tension and relaxation time. In contrast to the horizontal jet case, presence of gravity and jet inclination increase values of the jet speed, strain rate, stretching rate and the centerline curvature and decrease the value of the jet radius and more so with increasing the arc length, gravity, rotation rate and the relaxation time. However, a non-inclined jet with no imposed restriction on its shape and in presence of gravity leads to smaller fiber radius and larger speed as compared to the ones for inclined jet case.

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