Stability of a Shear-Thinning Film on a Porous Substrate

2010 ◽  
Author(s):  
R. Usha ◽  
S. Millet ◽  
H. BenHadid ◽  
F. Rousset
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Shear Rate ◽  
Film Flow ◽  
Shear Thinning ◽  
Free Surface Flows ◽  
Significant Feature ◽  
Porous Substrate ◽  
Carreau Model ◽  
Porous Substrates

A significant feature of gravity-driven film flows of Newtonian and rheologically complex fluids down an inclined/vertical substrate is the instability of the free surface which manifests as surface waves having wavelengths much larger than the film thickness. There are a number of applications which can be modeled as thin film flow systems on porous substrates. Pascal [1] investigated the stability of a falling power-law film on an inclined porous substrate. This model for the fluid predicts a viscosity that goes to infinity as the shear rate approaches zero. There is a need to employ a more appropriate model to examine the effects of non-Newtonian rheology on the dynamics and stability of thin film free surface flows down inclined or vertical rigid/porous substrates. The four-parameter Carreau model predicts a viscosity that remains finite as the shear rate approaches zero and is given by η−η∞η0−η∞=[1+(δγ)˙2]n−12.(1) Weinstein [2] and Rousset et al. [3] have considered the Carreau model and have examined the temporal stability of a film flow down an impermeable rigid inclined substrate. The authors show that a shear-thinning Carreau fluid film on a rigid impermeable substrate is more unstable than a Newtonian film. This calls for an analysis that includes both the effects of Carreau non-Newtonian rheology and bottom permeability and the present study reports such an investigation of a Carreau non-Newtonian film on a porous inclined substrate.

Thin-Film Flow at Moderate Reynolds Number

2000 ◽  
Vol 122 (4) ◽  
pp. 774-778 ◽  
Author(s):  
Kenneth J. Ruschak ◽  
Steven J. Weinstein
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Free Surface ◽  
Film Flow ◽  
Previous Analysis ◽  
Vertical Wall ◽  
Integral Approach ◽  
Internal Boundary ◽  
Thin Film Flow ◽  
Moderate Reynolds Number

Viscous, laminar, gravitationally-driven flow of a thin film over a round-crested weir is analyzed for moderate Reynolds numbers. A previous analysis of this flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an equation for the film thickness (Ruschak, K. J., and Weinstein, S. J., 1999, “Viscous Thin-Film Flow Over a Round-Crested Weir,” ASME J. Fluids Eng., 121, pp. 673–677). In this work, a viscous boundary layer is introduced in the manner of Haugen (Haugen, R., 1968, “Laminar Flow Around a Vertical Wall,” ASME J. Appl. Mech. 35, pp. 631–633). As in the previous analysis of Ruschak and Weinstein, the approximate equations have a critical point that provides an internal boundary condition for a bounded solution. The complication of a boundary layer is found to have little effect on the thickness profile while introducing a weak singularity at its beginning. The thickness of the boundary layer grows rapidly, and there is little cumulative effect of the increased wall friction. Regardless of whether a boundary layer is incorporated, the approximate free-surface profiles are close to profiles from finite-element solutions of the Navier-Stokes equation. Similar results are obtained for the related problem of developing flow on a vertical wall (Cerro, R. L., and Whitaker, S., 1971, “Entrance Region Flows With a Free Surface: the Falling Liquid Film,” Chem. Eng. Sci., 26, pp. 785–798). Less accurate results are obtained for decelerating flow on a horizontal wall (Watson, E. J., 1964, “The Radial Spread of a Liquid Jet Over a Horizontal Plane,” J. Fluid Mech. 20, pp. 481–499) where the flow is not gravitationally driven. [S0098-2202(00)01904-0]

scholarly journals Free Surface Thin Film Flow of a Sisko’s Fluid over a Surface Topography

2017 ◽  
Vol 10 (1) ◽  
pp. 307-317 ◽  
Author(s):  
R. A. Shah ◽  
P. Gaskel ◽  
S. Veremieiev ◽  
◽  
◽  
...  
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Surface Topography ◽  
Film Flow ◽  
Thin Film Flow

Influence of Upstream Conditions and Gravity on Highly Inertial Thin-Film Flow

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Flow Field ◽  
Film Flow ◽  
Flow Direction ◽  
Vertical Wall ◽  
Galerkin Projection ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Horizontal Wall

Steady two-dimensional thin-film flow of a Newtonian fluid is examined in this theoretical study. The influence of exit conditions and gravity is examined in detail. The considered flow is of moderately high inertia. The flow is dictated by the thin-film equations of boundary layer type, which are solved by expanding the flow field in orthonormal modes in the transverse direction and using Galerkin projection method, combined with integration along the flow direction. Three types of exit conditions are investigated, namely, parabolic, semiparabolic, and uniform flow. It is found that the type of exit conditions has a significant effect on the development of the free surface and flow field near the exit. While for the parabolic velocity profile at the exit, the free surface exhibits a local depression, for semiparabolic and uniform velocity profiles, the height of the film increases monotonically with streamwise position. In order to examine the influence of gravity, the flow is studied down a vertical wall as well as over a horizontal wall. The role of gravity is different for the two types of wall orientation. It is found that for the horizontal wall, a hydraulic-jump-like structure is formed and the flow further downstream exhibits a shock. The influence of exit conditions on shock formation is examined in detail.

Preparation of La1−zSrzCo1−yFeyO3−x thin films, membranes, and coatings on dense and porous substrates

1995 ◽  
Vol 10 (12) ◽  
pp. 3210-3221 ◽  
Author(s):  
Meilin Liu ◽  
Dongsheng Wang
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Metal Ions ◽  
Chelating Agent ◽  
Ceramic Membranes ◽  
High Ratio ◽  
Porous Substrate ◽  
Processing Parameter ◽  
Pechini Process ◽  
Porous Substrates

A modified Pechini process has been successfully developed for preparation of thin films of La1−zSrzCo1−yFeyO3−x (LSCF) on both dense and porous substrates. Results indicatc that the most important processing parameter is the ratio of the polymerization/complexation agent to metal ions. Ceramic films derived from solutions with a relatively low ratio of citric acid to metal ions are usually cracked, while films derived from solutions with a relatively high ratio are crack-free and uniform. The use of ethylenediamine as an additional chelating agent further improves film quality, especially the adhesion and uniformity of the films. A single coating of solution typically yields a ceramic film of thickness about 0.4 μm, and thicker films can be prepared by application of successive coatings. For deposition of thin-film membranes on a porous substrate, however, it is necessary to modify the surface of the porous substrate in order to prevent solution from infiltrating into the pores due to capillary force, and to prevent oxide films from cracking due to surface roughness. The application of an intermediate polymer film to the surfaces of porous substrates has effectively overcome the problems and has resulted in uniform, nonporous membranes of LSCF on porous substrates. Successful deposition of thin-film ceramic membranes on porous substrates is important to fabrication of various ionic and micro-ionic devices based on ceramic thin films.

The impact of different arrangement of molecular chains in term of low and high shear rate’s viscosities on heat and mass flow of Non-Newtonian shear thinning fluids

2021 ◽  
Vol 24 ◽  
Author(s):  
Mohsan Hassan ◽  
Abrar Faisal ◽  
Khurram Javid ◽  
Salah Ud-Din Khan ◽  
Ashfaq Ahmad ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Boundary Layer Flow ◽  
Shear Thinning ◽  
High Shear Rate ◽  
High Shear ◽  
Carreau Model ◽  
Shear Thinning Fluids ◽  
Layer Flow ◽  
The Impact

Background: Non-Newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even in everyday life. The viscosity of shear thinning fluids is sometimes decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems. Objective: So, the effects of viscosities at a low and high shear rate on the heat and mass boundary layer flow of shear thinning fluid over moving belts is investigated in this study. For this proposed, the generalized Carreau model of viscosity relates to shear rate and is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, expression of the thermal conductivity model, similar to the viscosity equation due to the non-Newtonian nature of the fluid, is used in the energy equation. Methods: On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-Shooting Method. The results are compared with existing results for limited cases and good agreement is found. Results : The results are obtained in the form of velocity and temperature profiles under the impact of all the viscosity’s parameters and are displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid. Conclusion: The velocity and temperature of the fluid are decreased and increased respectively by all viscosity’s parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment, but will also help improve the economy and efficiency of the overall process.

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