Study of Shiny Film Coating on Multi-Fluid Flows of a Rotating Disk Suspended with Nano-Sized Silver and Gold Particles: A Comparative Analysis

: The current effort is devoted to investigate the shiny thin ﬁlm with a metallic tactile covering of nanoparticles over the surface of a rotating disk. To decorate, glowing silver and gold particles were chosen. Four illustrative base liquids, namely (i) ethanol, (ii) methanol, (iii) ethylene-glycol, and (iv) water were considered with different geometries, which have great importance in industrial usage. An emphasis on comparative multi nanoﬂuid analysis was used to make a sound judgment on which one of the ﬂuids best suited the metallic glittering process of spin coating. The ﬁlm thickness process highly depends on the process of evaporation, which takes some time to settle on the disk’s surface. It was found that of the base ﬂuids, the best choices were ethanol alloys with silver. Hence, one can conclude that from an experimental point of view, if silver alloy is used for coating, then only those liquids can be considered that exhibit ethanol-like properties. The impact of pertinent parameters with different aspects are graphically illustrated in each case.


Introduction
The mechanical process of covering the surface of an object/substrate with the help of a very thin layer is known as "Coating". This layer can be of some sort of paint, lacquer or a thin polymer sheet, which may be used for protective or decorative purposes. Nowadays, most of the engineered products go through the process of coating to prevent corrosion and to make them attractive [1,2]. From an industrial point of view, coating involves the development of a thin film layer (which can be polymeric or lacquer) on a substrate or fabric etc. If the substrate starts and ends the process wound up in a roll, the process may be termed "roll-to-roll" or "web-based" coating. Apart from a process of simple coating, developing a uniform and thin film or covering to a spinning sample or substrate, is called "spin coating". In the latter sort of coating, a small amount of liquid solution is placed at the center of the highly rotating disk, with the help of a pipette or syringe, resulting in the solution spreading uniformly and evenly in all directions as elaborated in [3]. This is all because of centrifugal forces, which cause liquid solution to spread across the surface uniformly. Application of spin coating is mainly used to fabricate tiny structures, usually of micrometer size or even much smaller, known as the microfabrication process. Manufacturing of solar cells, integrated circuits, insulators, nanomaterials, The layer of nanofluid across the surface is evenly spread out; thus, appropriate assumptions can be enlisted as: i.
The nanofluid is assumed to be diluted and an impact of evaporation of a thin layer of the liquid is negligible as the solution is behaving "non-volatile". ii. The nanoparticles and the base fluid are in equilibrium, therefore, no slip condition is considered.
The governing equations in components form are: Initial and boundary conditions associated with Equations (1)- (5) are defined in the following sub sections:
The nanofluid is assumed to be diluted and an impact of evaporation of a thin layer of the liquid is negligible as the solution is behaving "non-volatile". ii.
The nanoparticles and the base fluid are in equilibrium, therefore, no slip condition is considered.
The governing equations in components form are: ∂u ∂t Initial and boundary conditions associated with Equations (1)- (5) are defined in the following sub sections:

Initial Conditions
here, h, h 0 and T 0 represent thickness of the film, initial thickness of the film and room temperature respectively.

Boundary Conditions
• At the surface of the rotating disk (i). u = 0, (ii). v = r Ψ, (iii). w = 0, • At the free surface of the rotating disk where L denotes heat transfer coefficient and σ stands for surface tension.
By using suitable transformations [40], the governing equations can be obtained as: here, Re is the Reynolds number and Pr denotes the Prandtl number, whereas ∅ 1 and ∅ 2 represent dimensionless constants.

Thermophysical Properties
The present investigation is concerned with the development of a thin film of liquid on a rotating disk with different metallic particles that require effective thermo-physical properties of nanofluids and nanoparticles. Two distinctive models proposed by Khanafer and Vafai [41] were chosen to analyze the density and specific heat of the nanofluids; whereas to estimate the thermal conductivity and viscosity of fluids, the thermophysical model [42] is utilized. In view of the thermophysical model in the presence of multi fluids containing two different types of nano-sized metallic particles, the realistic properties were developed as follows:

For Water as the Base Fluid
The most significant and highly utilized fluid on this planet is water that contains 997.1 kg·m −3 , density, 0.89 mPa·S. viscosity, 4179 J/Kg m heat capacity and 0.569 W·m −1 ·K −1 thermal conductivity.

• For gold nanoparticles
The mathematical expressions that describe the thermophysical properties of water and gold nanofluids are given as: µ n f water/gold = 0.89 1.013 + 0.092φ − 0.015φ 2 (20) where the gold density is 19,300 kg·m −3 and heat capacity and thermal conductivity are 126 J/kg m and 317 W·m −1 ·K −1 , respectively.

For Ethanol as the Base Fluid
The features displayed by ethanol at room temperature have a density of 789 kg·m −3 . The viscosity is 1.074 mPa·S, heat capacity is 2500 J/Kg m and thermal conductivity is 0.0235 W·m −1 ·K −1 .

For Ethylene-Glycol as the Base Fluid
The density of ethylene-glycol at room temperature by System International (SI) units system is 1101 kg·m −3 . The viscosity takes the numerical value 0.0162 mPa·S, heat capacity and thermal conductivity are respectively 2400 J/Kg m and 0.256 W·m −1 ·K −1 .

• For gold nanoparticles
For an Ethylene-glycol and Gold nanofluids suspension, the physical property of gold density is 19,300 kg·m −3 , heat capacity is 126 J/Kg m and thermal conductivity is 317 W·m −1 ·K −1 . Accordingly, the mathematical expression can be written as: • For silver nanoparticles For the suspension of ethylene-glycol and silver nanofluids the physical property of silver density is 10,490 kg·m −3 . The heat capacity and thermal conductivity are 233 J/Kg m and 429 W·m −1 ·K −1 , respectively. On the previous contrast, mathematical expression can be attained as: For the best understating of readers, the realistic physical properties of base fluids and nanoparticles are offered in Tables 1 and 2.

Discussion
The process of coating heavily depends upon the time taken by any fluid to settle down on the surface of the material; a fluid can only be considered more suitable for the coating if it takes less time to leave its effects on the surface. Moreover, the engaged nanoparticles are of very small size and of a concentration of at most 2%. The effects on viscosity, thermal conductivity, density and heat capacity are evaluated experimentally in many communications. It is now a well-established fact that in the presence of such a small quantity of nanosized particles, the nature of fluid does not change but changes in physical properties are evident. For that, many correlations are presented for different situations and particles. To serve the purpose of this study, four different kinds of Newtonian fluids having diverse physical and chemical properties are considered instead of non-Newtonian fluids because coatings with such types of fluids would have a tremendous impact on the cost, volume, weight, and mechanical properties of electronic, optoelectronic, and photovoltaic devices; thus, this portion is dedicated to the parametric study of the proposed model in which four kinds of Newtonian fluids, such as water, ethanol, methanol and ethylene-glycol are opted for as the base fluids. The gold and silver nanoparticles are used to furnish the thin metallic and shiny coating on the surface of the rotating disk. The main reason to carry out this graphical work is to confirm whether or not the obtained mathematical results are in complete coherence with the physical expectation of the spin coatings. Moreover, the graphic illustrations will help to make a sound judgement about the role and contribution of field variables. Major parameters which have been comprehensively focused on are the concentration of the metallic particles and the thermocapillary parameter. Furthermore, the presented parametric study unlike the customary results and discussion have been delicately divided into three following sub sections to make this comparative analysis more clear and fathomable.

Thickness of the Film
The key emphasis in this article is on furnishing a shiny metallic layer of nanoparticles, suspended with different base fluids displaying distinct physical and chemical features altogether. Here, the sole aim is to decide which one of the base fluids is the best suitable choice for this metallic covering over the disk with spin coatings that can quickly spread on the disk in a short span of time. As shown in Figure 2, it can clearly be seen that ethanol is the sole liquid which shows a rapid action with both metals as compared to the other base fluids. It is in accordance with their physical prospects, due to their densities, which help them evaporate quickly and results in a shiny metallic nanoliquids coating on the disk. On the other hand, silver particles' coating is much faster than gold, as Figure 3 shows. rotating disk. The main reason to carry out this graphical work is to confirm whether or not the obtained mathematical results are in complete coherence with the physical expectation of the spin coatings. Moreover, the graphic illustrations will help to make a sound judgement about the role and contribution of field variables. Major parameters which have been comprehensively focused on are the concentration of the metallic particles and the thermocapillary parameter. Furthermore, the presented parametric study unlike the customary results and discussion have been delicately divided into three following sub sections to make this comparative analysis more clear and fathomable.

Thickness of the Film
The key emphasis in this article is on furnishing a shiny metallic layer of nanoparticles, suspended with different base fluids displaying distinct physical and chemical features altogether. Here, the sole aim is to decide which one of the base fluids is the best suitable choice for this metallic covering over the disk with spin coatings that can quickly spread on the disk in a short span of time. As shown in Figure 2, it can clearly be seen that ethanol is the sole liquid which shows a rapid action with both metals as compared to the other base fluids. It is in accordance with their physical prospects, due to their densities, which help them evaporate quickly and results in a shiny metallic nanoliquids coating on the disk. On the other hand, silver particles' coating is much faster than gold, as Figure 3 shows.
In Figures 4-7, thermocapillary parameters and the concentration of the metallic particles' influence on nanofluid coating have been displayed. It is a well-recognized fact that the thicker solution yields to the thicker layer of the film. The thermocapillary parameter depletes and attenuates this metallic layer as shown in Figures 4 and 5. From the above given facts, it is inferred that ethanol and silver particles share a great deal of mutual compatibility. Thickness of the film increases in size upon the additional supply of metallic particles as shown in Figures 6 and 7. This confirms the above preceding claim that an increase of the particles will enlarge the film thickness in size. Therefore, it can be concluded that any fluids and particles which exhibit different characteristics like ethanol and silver are regarded as the most suitable option for this metallic process of coating. Consequently, to see the effects of thermal, radial and azimuthal velocity, ethanol was chosen as a base fluid.   In Figures 4-7, thermocapillary parameters and the concentration of the metallic particles' influence on nanofluid coating have been displayed. It is a well-recognized fact that the thicker solution yields to the thicker layer of the film. The thermocapillary parameter depletes and attenuates this metallic layer as shown in Figures 4 and 5. From the above given facts, it is inferred that ethanol and silver particles share a great deal of mutual compatibility. Thickness of the film increases in size upon the additional supply of metallic particles as shown in Figures 6 and 7. This confirms the above preceding claim that an increase of the particles will enlarge the film thickness in size. Therefore, it can be concluded that any fluids and particles which exhibit different characteristics like ethanol and silver are regarded as the most suitable option for this metallic process of coating. Consequently, to see the effects of thermal, radial and azimuthal velocity, ethanol was chosen as a base fluid.

Radial Velocity and Azimuthal Velocity
In Figures 8-21, the radial and azimuthal velocities have been sketched for all base fluids, the thermocapillary parameter and the concentration of the particles. In view of suitable transformation, the mathematical expressions take the following final form: In Equations (58) and (59), = ℎ 0 is the initial thickness of the film. A similar trend in the behavior of both types of velocities is observed in the presence of silver and gold particles.

Radial Velocity and Azimuthal Velocity
In Figures 8-21, the radial and azimuthal velocities have been sketched for all base fluids, the thermocapillary parameter and the concentration of the particles. In view of suitable transformation, the mathematical expressions take the following final form: In Equations (58) and (59), = ℎ 0 is the initial thickness of the film. A similar trend in the behavior of both types of velocities is observed in the presence of silver and gold particles.

Radial Velocity and Azimuthal Velocity
In Figures 8-21, the radial and azimuthal velocities have been sketched for all base fluids, the thermocapillary parameter and the concentration of the particles. In view of suitable transformation, the mathematical expressions take the following final form:                                      In Figures 8-19, the behavior of ethanol is quite prominent for all cases. It is observed that the radial velocity and azimuthal velocity increase for silver and gold. However, radial velocity and azimuthal velocity react quite differently for the thermocapillary parameter and the concentration of the particles. It is seen that temperature increases by increasing the values of thermocapillary parameter, as shown in Figures 20 and 21. It is in accordance with the physical expectation because radial velocity does not allow the fluid to move with full strength. However, the radial velocity is supported by the thermocapillary parameter. On the other hand, a complete reverse trend can be noted for the azimuthal velocity by varying both α and φ.

Thermal Analysis
In this section, the temperature of nanofluid was examined vertical to the disk. The mathematical relationships for temperature and temperature gradient were respectively denoted by the following relations:  In Figures 8-19, the behavior of ethanol is quite prominent for all cases. It is observed that the radial velocity and azimuthal velocity increase for silver and gold. However, radial velocity and azimuthal velocity react quite differently for the thermocapillary parameter and the concentration of the particles. It is seen that temperature increases by increasing the values of thermocapillary parameter, as shown in Figures 20 and 21. It is in accordance with the physical expectation because radial velocity does not allow the fluid to move with full strength. However, the radial velocity is supported by the thermocapillary parameter. On the other hand, a complete reverse trend can be noted for the azimuthal velocity by varying both α and φ.

Thermal Analysis
In this section, the temperature of nanofluid was examined vertical to the disk. The mathematical relationships for temperature and temperature gradient were respectively denoted by the following relations: In Equations (58) and (59), R = r h 0 is the initial thickness of the film. A similar trend in the behavior of both types of velocities is observed in the presence of silver and gold particles.
In Figures 8-19, the behavior of ethanol is quite prominent for all cases. It is observed that the radial velocity and azimuthal velocity increase for silver and gold. However, radial velocity and azimuthal velocity react quite differently for the thermocapillary parameter and the concentration of the particles. It is seen that temperature increases by increasing the values of thermocapillary parameter, as shown in Figures 20 and 21. It is in accordance with the physical expectation because radial velocity does not allow the fluid to move with full strength. However, the radial velocity is supported by the thermocapillary parameter. On the other hand, a complete reverse trend can be noted for the azimuthal velocity by varying both α and ϕ.

Thermal Analysis
In this section, the temperature of nanofluid was examined vertical to the disk. The mathematical relationships for temperature and temperature gradient were respectively denoted by the following relations: Here smooth and organized curves are drawn in Figures 22-27. It is found that an addition of extra nanoparticles strengthens the drag force between the particles. However, thermocapillary parameter α works altogether differently by reducing the heat of the nanofluid that ultimately affirms the earlier preceding claim regarding the addition of metallic particles to the base fluid ethanol.
Here smooth and organized curves are drawn in Figures 22-27. It is found that an addition of extra nanoparticles strengthens the drag force between the particles. However, thermocapillary parameter α works altogether differently by reducing the heat of the nanofluid that ultimately affirms the earlier preceding claim regarding the addition of metallic particles to the base fluid ethanol.
Here smooth and organized curves are drawn in Figures 22-27. It is found that an addition of extra nanoparticles strengthens the drag force between the particles. However, thermocapillary parameter α works altogether differently by reducing the heat of the nanofluid that ultimately affirms the earlier preceding claim regarding the addition of metallic particles to the base fluid ethanol.

Conclusions
A comparative study for silver and gold nanoparticles was comprehensively carried out to form a thin and shiny metallic layer over the surface of a rotating disk via spin coatings. Moreover, a detailed analysis of nanofluids suspended with four different types of base fluids, namely water, ethanol, methanol and ethylene-glycol has also been examined under the assumptions of nanofluids to be diluted and non-volatile. Finally, a parametric study on the basis of obtained expressions of results was made to apprehend the effects of the main parameters involved. Some significant findings are enlisted below:


Silver metallic coating quickly settles down on the surface of the disk than to develop a gold coating.

Conclusions
A comparative study for silver and gold nanoparticles was comprehensively carried out to form a thin and shiny metallic layer over the surface of a rotating disk via spin coatings. Moreover, a detailed analysis of nanofluids suspended with four different types of base fluids, namely water, ethanol, methanol and ethylene-glycol has also been examined under the assumptions of nanofluids to be diluted and non-volatile. Finally, a parametric study on the basis of obtained expressions of results was made to apprehend the effects of the main parameters involved. Some significant findings are enlisted below: • Silver metallic coating quickly settles down on the surface of the disk than to develop a gold coating. • Thickness of the film increases with the addition of extra metallic particles. • Radial velocity is hampered by adding more nanoparticles. • Increase in the quantity of particles surges the thermal effects of the nanofluid.

•
It is worth investigating that these results will help to choose the optimum base fluid with gold or silver particles.

•
The graphical results show depletion of the fluid layer with time and one can hardly find such an evaluation in the available literature.

•
Finally, it is concluded that the base fluid is the best choice for ethanol alloys with silver in the process of coating. In this way, it can be concluded that from the experimental point of view if silver alloy is used for coating then only such liquids should be considered which exhibit ethanol-like properties. Now, this effort is available for further experimental studies for those who are working in this regime for the validation of their lab results.  ;