Stability analysis of rimming flow inside a horizontally rotating cylinder in the presence of an insoluble surfactant

2017 ◽  
Vol 29 (12) ◽  
pp. 122102 ◽  
Author(s):  
Tara Chand Kumawat ◽  
Naveen Tiwari
Keyword(s):  
Stability Analysis ◽  
Rotating Cylinder ◽  
Rimming Flow ◽  
Insoluble Surfactant

Stability analysis of a thin film on a rotating cylinder with low airflow

2019 ◽  
Vol 31 (3) ◽  
pp. 034106
Author(s):  
Heather Newell ◽  
Hendrik Viljoen
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Rotating Cylinder

The influence of a small upstream wire on transition in a rotating cylinder wake

2015 ◽  
Vol 769 ◽  
Author(s):  
Anirudh Rao ◽  
Alexander Radi ◽  
Justin S. Leontini ◽  
Mark C. Thompson ◽  
John Sheridan ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Hydrogen Bubble ◽  
Instability Mode ◽  
Cylinder Wake ◽  
Rotation Rates ◽  
Mode Transitions

Recent experimental research on rotating cylinder wakes has found that a previously numerically predicted subharmonic instability mode, mode C, occurs for considerably lower rotation rates than predicted through stability analysis, yet other mode transitions occur closer to the predicted onset. One difference between the theoretical and experimental set-ups is the use of a small-diameter hydrogen bubble visualisation wire placed upstream of the rotating cylinder. The current paper tests the hypothesis that a wire, of only $1/100$th of the cylinder diameter, placed five diameters upstream of the cylinder, sufficiently perturbs the flow to substantially affect certain wake transitions, including the onset of mode C. This is achieved using stability analysis of a flow that includes the upstream wire. The results indeed show that the wire of a tiny diameter induces a non-negligible asymmetry in the flow, triggering the subharmonic mode at substantially lower rotation rates. Furthermore, at higher rotation rates, the onset of two other three-dimensional modes are delayed to higher Reynolds numbers. These results make the point that even seemingly minute perturbations caused by minimally intrusive methods may result in substantially altered experimental flow behaviour.

Mathematical Modeling of the Polymer Rotational Molding

2007 ◽  
Author(s):  
Sergei A. Fomin ◽  
Konstantin G. Kornev ◽  
Chris Wolter ◽  
Jon Young ◽  
Tyler Brandenburg
Keyword(s):  
Rotating Cylinder ◽  
Lubrication Approximation ◽  
Steady State Flow ◽  
Viscous Liquids ◽  
First Order ◽  
Rimming Flow ◽  
Ucm Fluid ◽  
Inner Surface ◽  
Viscoelastic Liquids ◽  
The Mathematical Model

We study the rimming flow of a viscoelastic film on the inner surface of a horizontal rotating cylinder. Simple lubrication theory is applied assuming that the Reynolds number is small and the liquid film is thin. For the steady-state flow of the Upper-Convected Maxwell (UCM) fluid the mathematical model reduces to a first order nonlinear ODE for the film thickness. We show that the liquid viscoelasticity changes the flow structure. In particular, the singularity observed for viscous liquids within the same lubrication approximation can be eliminated due liquid elasticity. We performed a detailed numeric analysis of the model and revealed some criticality regimes which are specific only for viscoelastic liquids.

Experimental investigation of continuous single-phase rimming flow in a horizontal rotating cylinder

AIChE Journal ◽  
2014 ◽  
Vol 60 (11) ◽  
pp. 3939-3950 ◽  
Author(s):  
Saravanan Suppiah Singaram ◽  
Himanshu Lodha ◽  
Roshan J. Jachuck
Keyword(s):  
Experimental Investigation ◽  
Single Phase ◽  
Rotating Cylinder ◽  
Rimming Flow

The run-off condition for coating and rimming flows

1988 ◽  
Vol 187 ◽  
pp. 99-113 ◽  
Author(s):  
Luigi Preziosi ◽  
Daniel D. Joseph
Keyword(s):  
Critical Condition ◽  
Rotating Cylinder ◽  
Critical Value ◽  
Centripetal Acceleration ◽  
Coating Flows ◽  
Viscous Forces ◽  
Rimming Flow ◽  
Run Off ◽  
Coating Layers ◽  
The Given

A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylinder where the thickness of the layer is larger than a critical value, the excess fluid will run off. For a given maximum thickness the critical condition may be expressed as the minimum speed at which the given layer can be maintained. An approximation of the critical condition using lubrication theory was given by Wallis (1969) and by Deiber & Cerro (1976) for rimming flow and by Moffatt (1977) for coating and rimming flow. Here we address the question of the axial variations of the free surface on the coating layers, and show that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity. The main results of this paper are the experiments which establish the validity of approximations used to describe the underlying fluid mechanics involved in rimming and coating flows.

scholarly journals Stability analysis of non-Newtonian rimming flow

2016 ◽  
Vol 40 (4) ◽  
pp. 2999-3010 ◽  
Author(s):  
Sergei Fomin ◽  
Ravi Shankar ◽  
Peter Haine ◽  
Vladimir Chugunov
Keyword(s):  
Stability Analysis ◽  
Rimming Flow

scholarly journals Instabilities at a sheared interface over a liquid laden with soluble surfactant

2021 ◽  
Vol 129 (1) ◽  
Author(s):  
A. Kalogirou ◽  
M. G. Blyth
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Layer ◽  
Threshold Value ◽  
Long Wavelength ◽  
Budget Analysis ◽  
Insoluble Surfactant ◽  
Bounded Below ◽  
Soluble Surfactant

AbstractThe linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising effect on the flow. As the solubility increases, large-wavelength perturbations are stabilised first, leaving open the possibility of mid-wave instability for moderate surfactant solubilities, and the flow is fully stabilised when the solubility exceeds a threshold value. The predictions of the linear stability analysis are supported by an energy budget analysis which is also used to determine the key physical effects responsible for the (de)stabilisation. Asymptotic expansions performed for long-wavelength perturbations turn out to be non-uniform in the insoluble surfactant limit. In keeping with the findings for insoluble surfactant obtained by Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011), the presence of the wall is found to be a crucial factor in the instability.

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