# Three flow regimes of viscous jet falling onto a moving surface

A.V. Hlod, A.C.T. Aarts, A.A.F. Ven, van de, M.A. Peletier

5 Citations (Scopus)

### Abstract

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied theoretically. The fluid is modelled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. We distinguish three flow regimes, called inertial, viscous-inertial and viscous, according to which effect is dominant in the momentum transfer through the jet cross section. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. The parameter regions of the three flow regimes, and their boundaries, are confirmed experimentally. Influences of surface tension, bending stiffness and air drag are presented.
Original language English 196-219 IMA Journal of Applied Mathematics 77 2 https://doi.org/10.1093/imamat/hxr017 Published - 2012

### Fingerprint

Fluids
Momentum transfer
Momentum
Viscous flow
Drag
Surface tension
Nozzles
Conservation
Gravitation
Newtonian Fluid
Viscous Flow
Nozzle
Stiffness
Surface Tension
Boundary conditions
Algebraic Equation
Inertia
Gravity
Cross section
Air

### Cite this

title = "Three flow regimes of viscous jet falling onto a moving surface",
abstract = "A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied theoretically. The fluid is modelled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. We distinguish three flow regimes, called inertial, viscous-inertial and viscous, according to which effect is dominant in the momentum transfer through the jet cross section. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. The parameter regions of the three flow regimes, and their boundaries, are confirmed experimentally. Influences of surface tension, bending stiffness and air drag are presented.",
author = "A.V. Hlod and A.C.T. Aarts and {Ven, van de}, A.A.F. and M.A. Peletier",
year = "2012",
doi = "10.1093/imamat/hxr017",
language = "English",
volume = "77",
pages = "196--219",
journal = "IMA Journal of Applied Mathematics",
issn = "0272-4960",
publisher = "Oxford University Press",
number = "2",

}

Three flow regimes of viscous jet falling onto a moving surface. / Hlod, A.V.; Aarts, A.C.T.; Ven, van de, A.A.F.; Peletier, M.A.

In: IMA Journal of Applied Mathematics, Vol. 77, No. 2, 2012, p. 196-219.

TY - JOUR

T1 - Three flow regimes of viscous jet falling onto a moving surface

AU - Hlod, A.V.

AU - Aarts, A.C.T.

AU - Ven, van de, A.A.F.

AU - Peletier, M.A.

PY - 2012

Y1 - 2012

N2 - A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied theoretically. The fluid is modelled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. We distinguish three flow regimes, called inertial, viscous-inertial and viscous, according to which effect is dominant in the momentum transfer through the jet cross section. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. The parameter regions of the three flow regimes, and their boundaries, are confirmed experimentally. Influences of surface tension, bending stiffness and air drag are presented.

AB - A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied theoretically. The fluid is modelled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. We distinguish three flow regimes, called inertial, viscous-inertial and viscous, according to which effect is dominant in the momentum transfer through the jet cross section. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. The parameter regions of the three flow regimes, and their boundaries, are confirmed experimentally. Influences of surface tension, bending stiffness and air drag are presented.

U2 - 10.1093/imamat/hxr017

DO - 10.1093/imamat/hxr017

M3 - Article

VL - 77

SP - 196

EP - 219

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 2

ER -