Film flow of a suspension down an inclined plane

2003 ◽  
Vol 361 (1806) ◽  
pp. 847-869 ◽  
Author(s):  
Xiaofan Li ◽  
C. Pozrikidis
Keyword(s):  
Film Flow ◽  
Inclined Plane

Instability of a liquid film flow over a vibrating inclined plane

1995 ◽  
Vol 294 ◽  
pp. 391-407 ◽  
Author(s):  
David R. Woods ◽  
S. P. Lin
Keyword(s):  
Gravity Waves ◽  
Film Flow ◽  
Shear Waves ◽  
Faraday Waves ◽  
Critical Amplitude ◽  
Inclined Plane ◽  
Flow Parameters ◽  
Chebychev Polynomials ◽  
Liquid Film Flow ◽  
Faraday Wave

The problem of the onset of instability in a liquid layer flowing down a vibrating inclined plane is formulated. For the solution of the problem, the Fourier components of the disturbance are expanded in Chebychev polynomials with time-dependent coefficients. The reduced system of ordinary differential equations is analysed with the aid of Floquet theory. The interaction of the long gravity waves, the relatively short shear waves and the parametrically resonated Faraday waves occurring in the film flow is studied. Numerical results show that the long gravity waves can be significantly suppressed, but cannot be completely eliminated by use of the externally imposed oscillation on the incline. At small angles of inclination, the short shear waves may be exploited to enhance the Faraday waves. For a given set of relevant flow parameters, there exists a critical amplitude of the plane vibration below which the Faraday wave cannot be generated. At a given amplitude above this critical one, there also exists a cutoff wavenumber above which the Faraday wave cannot be excited. In general the critical amplitude increases, but the cutoff wavenumber decreases, with increasing viscosity. The cutoff wavenumber also decreases with increasing surface tension. The application of the theory to a novel method of film atomization is discussed.

Developing Film Flow on an Inclined Plane With a Critical Point

2001 ◽  
Vol 123 (3) ◽  
pp. 698-702 ◽  
Author(s):  
Kenneth J. Ruschak ◽  
Steven J. Weinstein ◽  
Kam Ng
Keyword(s):  
Velocity Profile ◽  
Critical Point ◽  
Film Flow ◽  
Boundary Layer Equation ◽  
Critical Conditions ◽  
Integral Approach ◽  
Inclined Plane ◽  
Navier Stokes Equation ◽  
Moderate Reynolds Number ◽  
Momentum Integral

Viscous, laminar, gravitationally-driven flow of a thin film on an inclined plane is analyzed for moderate Reynolds number under critical conditions. A previous analysis of film flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an ordinary differential equation for the film thickness for flow over a round-crested weir, and the singularity associated with the critical point for a subcritical-to-supercritical transition was removable. For developing flow on a plane with a supercritical-to-subcritical transition, however, the same approach leads to a nonremovable singularity. To eliminate the singularity, the film equations are modified for a velocity profile of changing shape. The resulting predictions compare favorably with those from the two-dimensional boundary-layer equation obtained by finite differences and with those from the Navier-Stokes equation obtained by finite elements.

Multi-layer film flow down an inclined plane: experimental investigation

2014 ◽  
Vol 55 (12) ◽  
Author(s):  
D. Henry ◽  
J. Uddin ◽  
J. Thompson ◽  
M. G. Blyth ◽  
S. T. Thoroddsen ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Film Flow ◽  
Inclined Plane ◽  
Layer Film ◽  
Multi Layer Film

Three-dimensional thin film flow over and around an obstacle on an inclined plane

2009 ◽  
Vol 21 (3) ◽  
pp. 032102 ◽  
Author(s):  
S. J. Baxter ◽  
H. Power ◽  
K. A. Cliffe ◽  
S. Hibberd
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
Inclined Plane

Exact solutions for thin film flow of a third grade fluid down an inclined plane

2008 ◽  
Vol 38 (5) ◽  
pp. 1336-1341 ◽  
Author(s):  
T. Hayat ◽  
R. Ellahi ◽  
F.M. Mahomed
Keyword(s):  
Thin Film ◽  
Exact Solutions ◽  
Film Flow ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Inclined Plane ◽  
Grade Fluid
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