Extension of a viscous thread with temperature-dependent viscosity and surface tension

2016 ◽  
Vol 800 ◽  
pp. 720-752 ◽  
Author(s):  
Dongdong He ◽  
Jonathan J. Wylie ◽  
Huaxiong Huang ◽  
Robert M. Miura
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Temperature Profile ◽  
Solid Wall ◽  
Analytic Solutions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Initial Shape ◽  
Vertically Aligned ◽  
Dependent Viscosity

We consider the evolution of a long and thin vertically aligned axisymmetric viscous thread that is composed of an incompressible fluid. The thread is attached to a solid wall at its upper end, experiences gravity and is pulled at its lower end by a fixed force. As the thread evolves, it experiences either heating or cooling by its environment. The heating affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We develop a framework that can deal with threads that have arbitrary initial shape, are non-uniformly preheated and experience spatially non-uniform heating or cooling from the environment during the pulling process. When inertia is completely neglected and the temperature of the environment is spatially uniform, we obtain analytic solutions for an arbitrary initial shape and temperature profile. In addition, we determine the criteria for whether the cross-section of a given fluid element will ever become zero and hence determine the minimum stretching force that is required for pinching. We further show that the dynamics can be quite subtle and leads to surprising behaviour, such as non-monotonic behaviour in time and space. We also consider the effects of non-zero Reynolds number. If the temperature of the environment is spatially uniform, we show that the dynamics is subtly influenced by inertia and that the location at which the thread will pinch is selected by a competition between three distinct mechanisms. In particular, for a thread with initially uniform radius and a spatially uniform environment but with a non-uniform initial temperature profile, pinching can occur either at the hottest point, at the points near large thermal gradients or at the pulled end, depending on the Reynolds number. Finally, we show that similar results can be obtained for a thread with initially uniform radius and uniform temperature profile but exposed to a spatially non-uniform environment.

New correlation for the temperature-dependent viscosity for saturated liquids

2016 ◽  
Vol 30 (32n33) ◽  
pp. 1650399 ◽  
Author(s):  
Jianxiang Tian ◽  
Laibin Zhang
Keyword(s):  
Surface Tension ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Average Deviation ◽  
New Correlation ◽  
Multiple Parameter ◽  
The One ◽  
Dependent Viscosity ◽  
Better Than ◽  
Triple Point Temperature

Based on the recent progress on both the temperature dependence of surface tension [H. L. Yi, J. X. Tian, A. Mulero and I. Cachading, J. Therm. Anal. Calorim. 126 (2016) 1603, and the correlation between surface tension and viscosity of liquids [J. X. Tian and A. Mulero, Ind. Eng. Chem. Res. 53 (2014) 9499], we derived a new multiple parameter correlation to describe the temperature-dependent viscosity of liquids. This correlation is verified by comparing with data from NIST Webbook for 35 saturated liquids including refrigerants, hydrocarbons and others, in a wide temperature range from the triple point temperature to the one very near to the critical temperature. Results show that this correlation predicts the NIST data with high accuracy with absolute average deviation (AAD) less than 1% for 21 liquids and more than 3% for only four liquids, and is clearly better than the popularly used Vogel–Fulcher–Tamman (VFT) correlation.

Nonlinear equilibrium solutions for the channel flow of fluid with temperature-dependent viscosity

2000 ◽  
Vol 406 ◽  
pp. 1-26 ◽  
Author(s):  
D. P. WALL ◽  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Critical Reynolds Number ◽  
Isothermal Flow ◽  
Basic Flow ◽  
Secondary Flows ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Viscosity Models ◽  
Dependent Viscosity

The nonlinear stability of the channel flow of fluid with temperature-dependent viscosity is considered for the case of vanishing Péclet number for two viscosity models, μ(T), which vary monotonically with temperature, T. In each case the basic state is found to lose stability from the linear critical point in a subcritical Hopf bifurcation. We find two-dimensional nonlinear time-periodic flows that arise from these bifurcations. The disturbance to the basic flow has wavy streamlines meandering between a sequence of triangular-shaped vortices, with this pattern skewing towards the channel wall which the basic flow skews towards. For each of these secondary flows we identify a nonlinear critical Reynolds number (based on half-channel width and viscosity at one of the fixed wall temperatures) which represents the minimum Reynolds number at which a secondary flow may exist. In contrast to the results for the linear critical Reynolds number, the precise form of μ(T) is not found to be qualitatively important in determining the stability of the thermal flow relative to the isothermal flow. For the viscosity models considered here, we find that the secondary flow is destabilized relative to the corresponding isothermal flow when μ(T) decreases and vice versa. However, if we remove the bulk effect of the non-uniform change in viscosity by introducing a Reynolds number based on average viscosity, it is found that the form of μ(T) is important in determining whether the thermal secondary flow is stabilized or destabilized relative to the corresponding isothermal flow. We also consider the linear stability of the secondary flows and find that the most unstable modes are either superharmonic or subharmonic. All secondary disturbance modes are ultimately damped as the Floquet parameter in the spanwise direction increases, and the last mode to be damped is always a phase-locked subharmonic mode. None of the secondary flows is found to be stable to all secondary disturbance modes. Possible bifurcation points for tertiary flows are also identified.

scholarly journals Non-isothermal process of viscoelastic polymer fi lm casting

2019 ◽  
pp. 27-29 ◽  
Author(s):  
A. V. Вaranov
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Polymer Melt ◽  
Maxwell Model ◽  
Air Cooling ◽  
Isothermal Process ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Uniaxial Stretching ◽  
Dependent Viscosity

The steady-state non-isothermal process of viscoelastic fl at polymer fi lm casting is considered. The polymer melt is extruded through a fl at die, subjected to uniaxial stretching and at the same time air cooling, and then fi nally cooled down on a chill roll. It is assumed that the fi lm is wide enough, the distance between the extruder die and the cooling roller is minimal to such an extent that it is possible to neglect change of width of a fi lm in the course of longitudinal stretching. It is also believed that the forces of gravity, inertia and surface tension can be ignored. From a rheological standpoint, polymer melt is the viscoelastic fl uid. The upper-convective Maxwell model with temperature-dependent viscosity is used. The problem is solved by a numerical method of fi nite diff erences.

Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties

2012 ◽  
Vol 697 ◽  
pp. 175-203 ◽  
Author(s):  
Francesco Zonta ◽  
Miguel Onorato ◽  
Alfredo Soldati
Keyword(s):  
Reynolds Number ◽  
Thermal Expansion ◽  
Thermal Expansion Coefficient ◽  
Channel Flow ◽  
Expansion Coefficient ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Effects Of Temperature ◽  
Dependent Viscosity

AbstractDirect numerical simulation (DNS) is used to study the behaviour of stably-stratified turbulent channel flow with temperature-dependent fluid properties: specifically, viscosity ($\ensuremath{\mu} $) and thermal expansion coefficient ($\ensuremath{\beta} $). The governing equations are solved using a pseudo-spectral method for the case of turbulent water flow in a channel. A systematic campaign of simulations is performed in the shear Richardson number parameter space (${\mathit{Ri}}_{\tau } = \mathit{Gr}/ {\mathit{Re}}_{\tau } $, where $\mathit{Gr}$ is the Grashof number and ${\mathit{Re}}_{\tau } $ the shear Reynolds number), imposing constant-temperature boundary conditions. Variations of ${\mathit{Ri}}_{\tau } $ are obtained by changing ${\mathit{Re}}_{\tau } $ and keeping $\mathit{Gr}$ constant. Independently of the value of ${\mathit{Ri}}_{\tau } $, all cases exhibit an initial transition from turbulent to laminar flow. A return transition to turbulence is observed only if ${\mathit{Ri}}_{\tau } $ is below a threshold value (which depends also on the flow Reynolds number). After the transient evolution of the flow, a statistically-stationary condition occurs, in which active turbulence and internal gravity waves (IGW) coexist. In this condition, the transport efficiency of momentum and heat is reduced considerably compared to the condition of non-stratified turbulence. The crucial role of temperature-dependent viscosity and thermal expansion coefficient is directly demonstrated. The most striking feature produced by the temperature dependence of viscosity is flow relaminarization in the cold side of the channel (where viscosity is higher). The opposite behaviour, with flow relaminarization occurring in the hot side of the channel, is observed when a temperature-dependent thermal expansion coefficient is considered. We observe qualitative and quantitative modifications of structure and wall-normal position of internal waves compared to previous results obtained for uniform or quasi-uniform fluid properties. From the trend we observe in the investigated low-Reynolds-number range, we can hypothesize that, whereas the effects of temperature-dependent viscosity may be masked at higher Reynolds number, the effects of temperature-dependent thermal expansion coefficient will persist.

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