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Thin film coating is a process of making liquid film cover and deposit base body surface by the way of dipping, spraying, sliding or spin coating, which is a kind of modern surface engineering. It plays an important role in the actual processing, such as improving the surface properties, fine processing, and new surface properties. Analysis of the influence of substrating morphology and fluid flow properties itself on coating fluid motion has an important significance to optimize the thin film coating and improve the quality of the final film. The influence from uneven substrate surface’s geometry configuration on internal motion of the flow field in slip-coating is analyzed by using the FLUENT software as a calculation platform. A two-dimension model of slip coating under isosceles triangle and isosceles trapezoid substrate was established, and thin film coating fluid motions under different configuration parameters were simulated. It is pointed out that the key factor determining the turbulence generation and evolution is the parameter of substrating surface nature. The effects of the change of Reynolds number on turbulent appearance and action area are studied. The velocity contours of fluid field on different substrate surfaces are shown, and the impact of substrate geometry on the backwater region is analyzed.

Thin film coating is a kind of modern surface engineering, which generally refers to the process of covering substrate surface with a layer of liquid film. At present, coating technology including electroplating, painting, thermal spraying and vapor deposition, compared with the heat treatment, bead welding and other surface engineering, has several advantages such as less constraint conditions, large space of selection technology and material type and so on, and is used in practical engineering more and more widely. It can play out in three ways such as fine processing, optimization of surface properties, and making new surface properties [

With the development of material science, liquid thin film begins to take a more and more important role, and consequential quality requirements of the coated thin film are more and more high. In modern industrial applications, thin film coating process needs to meet some special requirements such as: the shape of thin film flow surface is complicated, the fluid coating needs to be carried out in a great disturbance; problem of the actual flow of the film is nonlinear; rheological properties of thin film flow cannot be changed arbitrarily; it should meet the demand of high speed coating industrial production. According to the form of thin film defect, it could be divided into two types, discontinuity and continuity [

In the actual production, due to factors of mechanical equipment, operation, production process and fluid properties, coating film maybe have some defects which cannot be completely eliminated such as folds, ripple and bubble [

In fluid dynamics foreign scholars have carried out much research work on the film flow. However, in this field, most previous studies about the flow of the film focused on the flat surface problem. In recent years, research of the liquid film flow characteristics on surface of basal with specific geometry morphology begins. The reason for this study is the surface of the thin film coating substrate is never perfectly flat but quite complex in the actual production.

The film flow on smooth surface can be approximated as a shear flow between two infinite flat plates with rigid surface and specific geometry morphology, which is called the Couette flow. This is a basic research model of the thin film coating.

Two-dimension Couette model is shown in

u = 1 2 μ d p d x y 2 + c 1 y + c 2 (1-1)

The boundary conditions are as follows:

{ y = 0 , u = 0 y = h , u = v (1-2)

where u is the distribution velocity, μ is fluid viscosity, p is the pressure, h is the distance between the parallel plates, x, y represents the spatial coordinates respectively, and v is a constant velocity along the x direction.

The velocity distribution can be generated by substituting Formula (1-2) into Formula (1-1) as follows:

u = v h y + 1 2 μ d p d x ( y 2 − b y ) (1-3)

The velocity distribution of dimensionless form is expressed as

u v = y h + D ( 1 − y h ) y h (1-4)

In the above formula, D is the dimensionless pressure gradient

D = − b 2 2 μ v d p d x

Thin film coating fluid mechanics problems studied in this paper are based on the improvement of the Couette flow model, in which the bottom surface is undulate substrate. The change of the internal structure of the flow field caused by the uneven geometry is studied. Physical models of the shear drag flow by the

approximate Couette model are shown in

Under the hypothesis that the roof and floor are infinite and the base plate geometry is periodic, one circle can be selected for calculation, as shown in

∂ u ∂ t + u ⋅ ∇ u = f − 1 ρ ∇ p + 1 ρ ∇ ( λ ∇ ⋅ u ) + 1 ρ ∇ ⋅ ( 2 μ S ) (1-5)

∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 (1-6)

∂ ( ρ T ) ∂ t + ∇ ⋅ ( ρ u T ) = ∇ ⋅ ( k c p g r a d T ) + S T (1-7)

In the formula, u is the velocity vector, ρ is the density, t is the time, T is the temperature, k is heat conduction coefficient, c p is specific heat capacity, and S T is viscous dissipation.

In

energy conservation equation. Those formulas constitute equations of Newton fluid motion and are also known as the Navier-Stokes equations. Reference to Couette flow model, on the roof to be applied moving wall boundary condition, the floor uses the solid wall boundary condition.

From the calculation results, compared with Couette flow on the flat base plate, with a fixed plate distance H = 1.6 and constant initial Reynolds number Re = 10, substrate irregularity degree is a key factor affecting the formation of eddy current. Seen from

phenomenon of thin film coating fluid occurs, accompanied by the vortices. Increasing unevenness r will make the eddy current phenomenon more and more obvious, and effect the location of vortex generation. Here defined unflatness of the basal plate with triangular groove is r = ( H − h ) / W .

Thin-film coating flow on trapezoidal base board and triangular basal floor are analogous. Similar with the approximate Couette flow on triangular basal plate, as seen from

increasing the roughness of R will expand the scope of the vortex. Here the definition of basal plate roughness with isosceles trapezoid is r = ( H − h ) / ( W − D ) .

In theory, film coating fluid should maintain in the laminar or nearly laminar flow state, which means that the flow must be carried out as far as possible at a low Reynolds number range [

of them is chosen to study.

As can be seen from

Velocity contours of film coating fluid on the triangle basal plate and trapezoid substrate at the same low Reynolds number are respectively shown as

We proposed a two-dimension model of slip coating under isosceles triangle and isosceles trapezoid substrate, and thin film coating fluid motions under different configuration parameters were simulated. It is pointed out that the key factor determining the turbulence generation and evolution is the parameter of substratum surface nature, with the increase of basal plate roughness, flow separation phenomenon of thin film coating fluid occurs, accompanied by the vortices. Increasing unevenness r will make the eddy current phenomenon more and more obvious, and effect the location of vortex generation. The effects of the change of Reynolds number on turbulent appearance and action area are studied, compared with the unevenness, the Reynolds number for the eddy current generation and development is not the dominant factor. The velocity contours of fluid field on different substrate surfaces are shown, and the impact of substrate geometry on the backwater region is analyzed. The center dead zones exists can be taken as a reference to judge whether the vortex exists.

This work was partly supported by the Chang Jiang Youth Scholars Program of China and grants (51373033 and 11172064) from the National Natural Science Foundation of China to Prof. Xiaohong Qin. As well as “The Fundamental Research Funds for the Central Universities” and “DHU Distinguished Young Professor Program” to her. It also has the support of the Key grant Project of Chinese Ministry of Education (No 113027A). This work has also been supported by “Sailing Project” from Science and Technology Commission of Shanghai Municipality (14YF1405100) to Dr. Hongnan Zhang.

Liang, Z.Y. and Zhou, H. (2017) Numerical Simulation of the Thin Film Coating Flow in Two-Dimension. Open Journal of Fluid Dynamics, 7, 330-339. https://doi.org/10.4236/ojfd.2017.73021