Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

2014 ◽  
Vol 30 (5) ◽  
pp. 505-513 ◽  
Author(s):  
C.-I. Chen ◽  
M.-C. Lin ◽  
C.-K. Chen
Keyword(s):  
Power Law ◽  
Spin Coating ◽  
Film Flow ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Landau Equation ◽  
Shear Thickening ◽  
Vital Role ◽  
Power Law Fluid ◽  
Power Law Index

AbstractThe phenomena of surface instabilities in a thin power-law fluid during spin coating are investigated. The set of Navier-Stokes equations with non-Newtonian behavior in the region of low Reynolds number serves as a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolution equation of the Ostwald de-Waele type fluid to govern the propagation of surface waves. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The amplitude of instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of power-law index plays a vital role in stabilizing the film flow. The shear-thinning fluid is more unstable than the shear-thickening fluid in the stability analysis. Further, the nonlinear wave speed in the supercritical stability region decreases with increasing values of power-law index.

scholarly journals Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1959
Author(s):  
Adrian S. Halifi ◽  
Sharidan Shafie ◽  
Norsarahaida S. Amin
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Power Law ◽  
Vortex Formation ◽  
Shear Thickening ◽  
Power Law Model ◽  
Governing Equations ◽  
Power Law Fluid ◽  
Transfer Parameters ◽  
Power Law Index

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Tandem Arrangement ◽  
Square Cylinders ◽  
Shear Thickening Fluids ◽  
Power Law Index

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

scholarly journals Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Cha'o-Kuang Chen ◽  
Dong-Yu Lai
Keyword(s):  
Spin Coating ◽  
Film Flow ◽  
Multiple Scales ◽  
Landau Equation ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Magnetic Filed

This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Weakly Nonlinear Stability Analysis of a Thin Power-Law Fluid during Spin Coating

2013 ◽  
Vol 319 ◽  
pp. 90-95
Author(s):  
Ming Che Lin ◽  
Chun I Chen ◽  
Shou Jen Huang
Keyword(s):  
Power Law ◽  
Nonlinear Stability ◽  
Spin Coating ◽  
Kinematic Model ◽  
Vital Role ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Pseudoplastic Fluid ◽  
Weakly Nonlinear ◽  
Dilatant Fluid

The weakly nonlinear stability of a thin Ostwald de-Waele power-law fluid during spin coating is investigated. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The study reveals that the rotation number generates a destabilizing effect either in pseudoplastic fluid or in dilatant fluid. Further, it is shown that the degree of power-law index n plays a vital role in stabilizing the film flow.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

A Numerical Model for Edge Effect Correction of the Mooney Rheometer

2009 ◽  
Vol 82 (4) ◽  
pp. 401-417
Author(s):  
Sergio A. Montes
Keyword(s):  
Experimental Data ◽  
Edge Effect ◽  
Power Law ◽  
Power Law Fluid ◽  
One Dimensional ◽  
Complex Shear ◽  
Theoretical Predictions ◽  
Power Law Index ◽  
Significant Concentration ◽  
Finite Difference Techniques

Abstract The flow of a power law fluid within the cavity of a multi-speed Mooney rheometer is studied by means of finite difference techniques with the aim of quantifying the edge effects that occur in the vicinity of the rotor corner. As expected, a significant concentration of shear stress occurs near the rotor edge. As the power law index varies, significant stagnation zones are found within the cavity, which combined with thin-shearing behavior near the moving surfaces, yield complex shear rate distributions. However, when torque is calculated, the edge effect can be described by a factor which is numerically very similar to a factor obtained from one-dimensional models described in the literature. Comparison of theoretical predictions and experimental data was found to be satisfactory.

Developing and Fully Developed Non-Newtonian Fluid Flow and Heat Transfer Through Concentric Annuli

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Mohammad Sefid ◽  
Ehsan Izadpanah
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Convection Heat Transfer ◽  
Channel Length ◽  
Laminar Flows ◽  
Rheological Parameter ◽  
Power Law Fluid ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Power Law Index

Developing and fully developed laminar flows of power law fluid with forced convection heat transfer through a concentric annular duct are numerically analyzed. The results are presented for the following ranges: 0.2 ≤ n ≤ 1.8 (power law index), 10 ≤ Re ≤ 1000 (Reynolds number), and r* = 0.2, 0.5, 0.8 (aspect ratio). In addition, the influences of different thermal boundary conditions on the thermal performance are delineated. The effects of rheological parameter on the developing length, friction factor, temperature distribution, velocity profile, and Nusselt number along the channel length are investigated. The results are compared with earlier research and excellent agreement was observed.

Unsteady Flow of a Power–Law Fluid past a Shrinking Sheet with Mass Transfer

2012 ◽  
Vol 67 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Nor Azizah Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Power Law ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Shrinking Sheet ◽  
Power Law Fluid ◽  
Suction Parameter ◽  
Shooting Technique ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Power Law Index

The unsteady two-dimensional boundary layer flow past a shrinking sheet in a non-Newtonian power-law fluid is investigated. The governing partial differential equations are transformed into a nonlinear ordinary differential equation using a similarity transformation before being solved numerically by the Runge-Kutta-Fehlberg method and the NAG Fortran library subroutine DO2HAF with shooting technique. The results obtained by both methods are in good agreement. It is found that dual solutions exist for a certain range of the unsteadiness parameter and the suction parameter. Moreover, by increasing the power-law index n, the skin friction coefficient is enhanced.

scholarly journals Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid

2018 ◽  
Vol 7 (2.15) ◽  
pp. 38
Author(s):  
Siti Sabariah Abas ◽  
Yazariah Mohd Yatim ◽  
. .
Keyword(s):  
Power Law ◽  
Similarity Solution ◽  
Travelling Wave ◽  
Global Maximum ◽  
Surface Tension Effect ◽  
Power Law Fluid ◽  
Transverse Profile ◽  
Strong Surface ◽  
Gravity Driven ◽  
Power Law Index

Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time  and position , the rivulet widens or narrows according to , where  is velocity of a rivulet, and the film thickens or thins according to a free parameter , independent of power-law index . The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.  

scholarly journals Instability of the Non-Isothermal Inclined Film Flow of a Power-Law Fluid With Temperature Dependent Consistency

2021 ◽  
Author(s):  
Mohammad Mahmud Hasan
Keyword(s):  
Power Law ◽  
Theoretical Study ◽  
Film Flow ◽  
Small Variation ◽  
Critical Conditions ◽  
Equilibrium Flow ◽  
Temperature Dependent ◽  
Power Law Fluid ◽  
Long Wavelength ◽  
Fluid Properties

In this thesis we undertake a theoretical study of the flow stability of a liquid film with power-law rheology down a heated incline. We develop and implement a mathematical model for the flow that captures the variation with temperature of the rheological aspect of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infintesimal perturbations imposed on the equilibrium flow. We obtain asymptotic solutions based on the assumption of perturbations of long wavelength and small variation in viscosity with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian reheology and the dependence of the fluid properties on temperature

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