Developing flow of a power-law liquid film on an inclined plane

2003 ◽  
Vol 15 (10) ◽  
pp. 2973 ◽  
Author(s):  
Steven J. Weinstein ◽  
Kenneth J. Ruschak ◽  
Kam C. Ng
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Inclined Plane ◽  
Developing Flow

scholarly journals Effect of Wind Stress on the Dynamics and Stability of Nonisothermal Power-Law Film down an Inclined Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-31 ◽  
Author(s):  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Multiple Scales ◽  
Critical Value ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Nonlinear Stability Analysis ◽  
Inclined Plane ◽  
Condensate Film ◽  
Power Law Index

Dynamics and stability of a nonisothermal power-law liquid film down an inclined plane is considered in the presence of interfacial shear. Linear stability characteristics of the power-law liquid film using normal mode approach reveal that isothermal and evaporating films are unstable for any value of power-law index while there exists a critical value of power-law index for the case of condensate film above which condensate film ow system is always stable. This critical value of power-law index increases with the increase in shear stress at the interface. Weakly nonlinear stability analysis using method of multiple scales divulges the existence of zones due to supercritical stability and subcritical instability. The nonlinear evolution equation is solved numerically in a periodic domain. The results reveal that (1) for an isothermal dilatant (pseudoplastic) liquids, the maximum wave amplitude is always smaller (larger) than that for a Newtonian liquid and the amplitude of permanent wave increases with the increase in interfacial shear; (2) condensation of pseudoplastic film happens for the earlier instant of time when the phase change parameter increases and the effect of interfacial shear makes the film more corrugated; (3) dilatant (pseudoplastic) evaporating liquid film attains rupture faster (slower) than that of Newtonian liquid film, and the interfacial shear does not influence the time at which rupture occurs.

Linear stability of power law liquid film flows down an inclined plane

1994 ◽  
Vol 27 (11) ◽  
pp. 2297-2301 ◽  
Author(s):  
Chi-Chuan Hwang ◽  
Jun-Liang Chen ◽  
Jaw-Shi Wang ◽  
Jenn-Sen Lin
Keyword(s):  
Liquid Film ◽  
Linear Stability ◽  
Power Law ◽  
Inclined Plane ◽  
Film Flows

Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane

2003 ◽  
Vol 70 (6) ◽  
pp. 915-923 ◽  
Author(s):  
R. Usha ◽  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Nonlinear Stability ◽  
Flow System ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Inclined Plane ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Power Law Index

Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.

Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

1978 ◽  
Vol 45 (1) ◽  
pp. 19-24 ◽  
Author(s):  
V. Narayanamurthy ◽  
P. K. Sarma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Mathematical Formulation ◽  
Liquid Films ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Falling Liquid Film ◽  
Falling Liquid Films ◽  
Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

scholarly journals Considerations on finding the rolling and spinning friction coefficients

2018 ◽  
Vol 184 ◽  
pp. 01009
Author(s):  
Florina-Carmen Ciornei ◽  
Stelian Alaci ◽  
Sorinel-Toderas Siretean ◽  
Mariana-Catalina Ciornei ◽  
Ioan-Bogdan Dragoi ◽  
...  
Keyword(s):  
Power Law ◽  
Normal Force ◽  
Point Contact ◽  
Rolling Friction ◽  
Friction Torque ◽  
Complex Motion ◽  
Inclined Plane ◽  
Friction Coefficients ◽  
Detailed Procedure ◽  
Tilting Angle

The complex motion from a point contact has as consequence the occurrence of a friction torsor within both spinning and rolling friction exist. Additionally, recent researches showed that the two friction moments, spinning and rolling torques, are not proportional to the normal force. Here, the power law dependency is accepted and therefore, besides the coefficients of spinning and rolling friction, the exponents from the relations friction torque-normal force should be first determined. The paper proposes as method for finding the four parameters the use of the inclined plane principle. The acceleration of a revolution body in descending motion on the inclined plane is found for four different values of the tilting angle and a system of four equations is obtained. The detailed procedure of finding the solutions of the system is presented in the present paper.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Viscous damping and instabilities in stratified liquid film flowing down a slightly inclined plane

1997 ◽  
Vol 9 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Igor L. Kliakhandler ◽  
Gregory I. Sivashinsky
Keyword(s):  
Liquid Film ◽  
Viscous Damping ◽  
Inclined Plane ◽  
Stratified Liquid
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