Boiling of Argon flow in a microchannel by considering the spherical geometry for roughness barriers

Journal of Molecular Liquids 321 (2021) 114462

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Boiling of Argon flow in a microchannel by considering the spherical geometry for roughness barriers using molecular dynamics simulation Amirhosein Mosavi a,b, Majid Zarringhalam c, Davood Toghraie d, Amin Rahmani e, Aliakbar Karimipour f,⁎ a

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran d Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran e Department Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran f Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam b c

a r t i c l e

i n f o

Article history: Received 11 June 2020 Received in revised form 31 August 2020 Accepted 27 September 2020 Available online 12 October 2020 Keywords: Microchannel Boiling Spherical roughness Molecular dynamic simulation

a b s t r a c t In this research, the method of molecular dynamic (MD) is used to consider the influences of the spherical roughness barrier on the boiling flow regime of Argon particles, flowing into microchannel with a square cross-section.

To prepare boiling conditions, different constant temperatures from 84 K to 133 K are applied on the walls of microchannels. Results show that roughness elements help boiling thermal forces to the distribution of fluid atoms in central layers of a microchannel, especially at high time steps between 750,000 and 1,000,000. This phenomenon is noticeable under applied high wall temperatures of 114 K and 133 K. Also, a summation of velocity values indicated that increasing boundary wall temperatures of rough microchannels results in a small reduction of the velocity of fluid flow, whereas; it is almost unchanged in the smooth microchannel. The statistical approach shows that the presence of spherical roughness does not have a destructive influence on the boiling flow properties of Argon into the microchannel. Also, they are useful to enhance effective surfaces of heat transfer, which empower the boiling process. Therefore, investing in polishing microchannel surfaces and removing the spherical shape of roughness components can even be a serious mistake for some of the practical applications. © 2020 Elsevier B.V. All rights reserved.

1. Introduction Nowadays, the application of Argon fluid is increasing in some medical surgeries due to its boiling capability in very low temperatures which brings rapid coagulation in tissues and blood [1,2]. Employing Argon fluid in this method reduces damage area in tears and bleeding of body tissues. On the other side, it increases improvement speed due to decreasing perforation depth in the patient's body and reduces the risk of infection. Also, this method is even employed to destroy cancers and tumors cells in micro-scale by medical microprobes which are not easily analyzed especially by in small scale of microchannels and membranes[3–8].

For very small scales of systems, the continuum model is not reliable [9]. The alternative is to employ the Molecular Dynamic Simulation (MDS) method [10]. This method is one of the best to consider the physical movements of particles. In the MDS method, atoms and molecules are allowed to interact for a fixed period to give a dynamic visual description of the system. Before emerging possibility to simulate the ⁎ Corresponding author.

E-mail addresses: amirhosein.mosavi@tdtu.edu.vn (A. Mosavi), aliakbarkarimipour@duytan.edu.vn (A. Karimipour).

https://doi.org/10.1016/j.molliq.2020.114462 0167-7322/© 2020 Elsevier B.V. All rights reserved.

molecular dynamics with computers, it was the idea to use experimental physical models such as macroscopic spheres. The idea was to sort them out to repeat the fluid properties, but fortunately, today computers keep track of the lines [11,12]. Therefore, it is presently only applicable to small systems. Molecular dynamics simulation was initially carried out in 1957 for a system composed of hard spheres by Alder and Wainwright [13]. In their system, particles were moving with a completely constant speed, and the collision between particles was quite elastic. Therefore, it was possible to solve a dynamic problem without any approximation. Next, in 1964, Rahman [14] employed this method for Lennard-Jones particles. Then, this potential function was commonly used by other researchers. Afterward, Craig et al. [15], Zhu and Granick [16], and Tretheway and Meinhart [17], experimentally showed that flow slippage in a nanoscale depends strongly to the interaction between wall-fluid and surface roughness effects. Generally, most of the papers by molecular dynamic simulation method present investigation of nanoflows [18–26]. The majority of presented channels in the mentioned references are in nanoscale [18–22], and others are related to surface phenomenon [23–26]. Moreover, previous papers contain a simulation domain with a small number of particles. Therefore, presenting a molecular dynamics simulation study on the fluid flow inside microchannels with a large number of Argon atoms under phase

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

lower wall of the nanochannel was in superheated conditions and the upper wall was at saturation temperature. They reported increasing heat transfer with increasing temperature in both states of saturation and superheat. It was found that in the state of phase change, the surface tension profiles fluctuate. Also, they reported that with increasing temperature in the superheated region, the surface tension is weakened. Afterward, these researchers [41] enlarged the previous study with a simulation of the boiling flow of 70,000 atoms of Argon fluid in a nanochannel. Fluid flow was enforced under different external forces and it was reported that the role of driving forces in the ranges of 2 to 12 Pico-Newton does not affect density profiles of argon flow inside nanochannel.

Also, published papers as references [42–47] studied nanoflow of Argon fluid into different nanochannels. Also, some of the researchers as in references [48–63] studied the influences of fluid model parameters and suspending nanoparticles into fluids on the flow. The other literature reviews [64–68] showed that all the above works have focused on the small scale of fluid flow with a limited number of atoms. Thus, previous molecular dynamic studies presented the behavior of fluid flows in very small scales of channels which were mostly under single-phase condition. Hence, the novelty of this work is related to filling out the lack of previous studies on the influences of spherical roughness on the boiling flows in phase change domain with different thermal energy supports. Moreover, this research presents the large scale simulations of molecular dynamics which are computationally expensive. In this research, results of simulations of 10 million particles of Argon fluid within a cubic microchannel are presented and analyzed by employing a new statistical approach in the MD method.

change conditions can be attractive for researchers to extend this work.

Nevertheless, the following literature presents the results of some researchers have focused on the phase change and surfaces roughness on a small scale.

Baricik et al. [27] using the molecular dynamics method investigated the effect of wall force on the fluid flow and compared it with the predictions based on kinetic theory. Their results showed that passing through the influence domain of wall force, the gas velocity profile is linear and the density is completely uniform in the channel. Niavarani and Priezjev [28] presented the influence of roughness on the slip flow by MDS. They concluded that the effective slip length and its slope are significantly decreased due to the presence of surface roughness alternatively. Toghraie and Azimian [29] published the Poiseuille flow using molecular dynamics simulation. They concluded that the velocity profile, length of slip, and slip velocity depend on the propulsion force. Sofos et al. [30] studied the heat transfer coefficient and shear energy of Argon in nanochannel by non-equilibrium molecular dynamics simulation. Their results showed that the local heat transfer coefficient is significantly decreased in the layers near the surface roughness.

Barisik and Beskok [31] studied the flow of Argon gas in transient and molecular free regimes inside nanochannels using MDS. Their outputs revealed that in all cases, the numerical value of Tangential Momentum Accommodation Coefficient (TMAC) between the fluid and the solid is independent of Knudsen's number and fluid properties. Aminfar and Razmara [32] employed molecular dynamics simulation to study the Poiseuille flow of Argon fluid in a nanochannel. They applied external force on fluid particles under various potential functions and concluded that the characteristics of flow hydrodynamic behavior depend on the interaction type of potential between atoms. Nourian et al. [33] studied molecular dynamics simulation of the effects of the roughness of the chess surface on the flow of Argon in a nanochannel which was contained roughness on its lower wall. Their results indicated that with increasing energy absorption or increasing roughness, density layering is enhanced near the wall. Wen and Jiang [34] investigated the nanoflows of the water. They succeeded in building a series of nature-inspired nanochannels. They also found that the inner surfaces of these types of nanochannels play a major role in fluid transmission into nanochannels. Rezaei et al. [35] using molecular dynamics simulations studied electro-osmotic flow in electrolyte fluid, adjacent to parallel load walls. They concluded that the electro-osmotic flow acts as a uniform flow with a non-slip condition on the walls. In other words, the flow velocity starts from zero on walls, then increases in a relatively large electric dipole region to reach constant value in the middle region of fluid flow. Sahebi and Azimian [36] investigated the mechanisms of thermal creep flow of nanotubes by MDS. They reported that the distribution of fluid density is formed layering under the wall force effect.

Then, the temperature gradient creeps through layers along the nanotube which causes fluid to flow from the cold side to the warm side.

Faraji et al. [37] obtained the temperature profile for the flow of Argon fluid in nano dimensions using two methods. The first method was of molecular dynamical and the second method was applying a temperature jump model on the boundaries in the Navier-Stokes equations. Finally, they concluded that the Navier-Stokes modified model presents accurate results in comparison with the molecular dynamics method.

Sotoudeh et al. [38] used the MDS method to investigate the diffusion of a shock waves in Argon solids. They measured some thermodynamic properties of density, temperature, and pressure during the shock wave diffusion to show the effect of passing shock wave on increasing the mentioned thermodynamic properties significantly.

Heydarinejad et al. [39] using the MD method investigated the influences of wall force on the temperature distribution of fluid flowing into nanochannels. They concluded that channel dimensions have to be as least as large as the Mean Free Path (MFP) of Argon gas fluid flow in periodic directions.

Toghraie and Azimian [40] used the MDS method to study the boiling flow of liquid argon inside the nanochannel. In this study, the

2. Simulation method 2.1. Simulation tools The present work was simulated with LAMMPS code. It can model ensembles of atoms in different phases of liquid, solid, or gaseous.

Also, it can model even the multi-phase flows of systems with only a few numbers of atoms up to millions or billions, using a variety of interatomic potentials (force fields) and boundary conditions.

2.2. Simulation domain The platinum microchannel was simulated in size of 10,000∗ 5000 ∗ 5000 (A°)3 in X, Y, and Z directions orderly as shown in Fig. 1.

Firstly, the internal surfaces of this microchannel were completely smooth. Then, to simulate the rough microchannel, the spherical geometry of roughness components was simulated on the internal surfaces of a copy of the simulated smooth microchannel. Therefore, both microchannels were exactly in the same shape, except their only difference which was the presence of roughness components.

2.3. Simulation detail According to Fig. 1, 10,000,000 of Argon fluid atoms were arranged on the lateral regions of microchannels and central region were completely empty. Then, in order to draw results of density, velocity and temperature, channel height was layered into 2200 bins in z- direction. Structure of atoms was Face Center Cubic with lattice constant of 5.26 A°. Barriers were simulated in peculiarities of X: 2000, 4000, 6000 and 8000 A°. Therefore, interval distance between barriers was 4000 A°.

The dimensions of each of element were 500 and 50 A3 in order of diameter and height.

2.4. Boundary condition To move the fluid flow, a force of 0.002 eV/Angstrom was exerted on atoms at the inlet of smooth and roughened microchannels in x2

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

Fig. 1. Shape of the roughened microchannel in front & perspective views.

direction as shown schematically in the front view of the microchannel in Fig. 1. Also, boundary temperatures in the order of 84 K, 96 K, 108 K, 114 K, and 133 Kelvin were applied on the walls of microchannels to provide the required energy for the boiling condition of Argon fluid flow.

2.6. Equilibrium state Atomic oscillations in the neighborhood of the walls were fixed with temperatures of 84 K, 96 K, 108 K, 114 K, and 133 K. Also, the initial Argon velocity was balanced with constant wall temperatures. Afterward, a propulsion force of 0.002 eV/Angstrom was exerted. The equilibrium state of the system was about a 200,000-time step, while running was performed until 1,000,000-time step.

2.5. Force field The interaction of fluids atoms are introduced as below [41]:

ϕ r ij ¼ 4ε

" 6 # σ 12 σ − rij ≤r c r ij r ij

3. Results & discussion ð1Þ

This paper studies the effect of the spherical shape of barriers on the boiling flow of Argon into the microchannel. Walls of microchannel were affected by temperatures of 84 K, 96, 108, 114 K, and 133 K and an exerted force of 0.002 eV/Angstrom at the inlet of the microchannel.

Afterward, results of density, velocity & temperature of flow on the roughened and smooth surfaces of microchannels were compared to draw influences of roughness components. This work is also validated by references [40, 41].

Figs. 2 to 11 present profiles of the density of Argon flow into cubic microchannels. The vertical axis shows density values per gram/cm3 unit versus bin numbers as shown in the horizontal axe. According to these figures, density values of fluid flow were plotted at 4-time steps in order of 250,000, 500,000, 750,000, and 1,000,000 to exhibit completion of the boiling process under different fixed temperatures in walls.

Figs. 2, 4, 6, 8 and 10 are belonged to channel with roughened surfaces with constant boundary temperatures of 84 K, 96 K, 108 K, 114 K, and 133 K respectively and Figs. 3, 5, 7, 9 & 11 have belonged to the ideal microchannel under the order of pre-mentioned boundary wall temperatures.

As a general view, it is seen from the above figures that rising wall temperature from 84 K to 114 K and 133 K can reduce instability which is valid in all mentioned time steps. In fact, with increasing the boundary temperatures of microchannels, the power of the boiling process is increased. Consequently, it accelerates the translocation of atoms to get sooner equivalency. Also, at time steps of 1,000,000, calculation of density values under boundary wall temperature of 114 K and 133 K, shows that the summation of density values in 800 layers in the central section of the roughened channel is higher than that of the ideal channel. On the other side; the comparison of Figs. 2, 4, 6, 8, 10 with Figs. 3, 5, 7, 9, 11 shows that growth of density profiles in the central region of rough microchannels is mostly weaker than that of smooth microchannel at low time steps of 250,000, 500,000 and 750,000, whereas; it is vice versa at a time step of 1,000,000. Because, growth in density profiles from time step 750,000 to 1,000,000, in central layers of the rough microchannel is more than that of a smooth one. It means that roughness elements play a reducer role in density profiles at low time steps (before 750,000) and a booster role at high time steps after

which rij, defines the interatomic space between atoms i & j, and the energy parameter is defined byεas the depth of the potential well and parameter r c introduces cut-off radios which is accounted as much as 8.5125 Angstrom [34]. The atomic mass, diameter, and potential depth of Argon particles are defined in the following order: m = mf = mAr = 39.95 g/mol, σ = σf = σAr = 3.405 A° and ε = εf = εAr = 1.67 ∗ 10−21 J. Next, for platinum particles, values are indicated as following order of atomic mass ms = mpt = 195.08 g/mol, diameterσ s = σpt = 2.475A°, and potential depth εs = εpt = 1.67 ∗ 1021 J. Also, for the interaction of solid-fluid particles, the modified LJ equation is used, pairing with Lorentz–Berthelot as following equations [40,41]:

ϕw r ij ¼ 4εsf

ε sf ¼

" 6 # σ sf 12 σ sf r ij ≤r c − r ij r ij

pffiffiffiffiffiffiffiffiffi σs þ σ f εs εs σ sf ¼ 2

ð2Þ

ð3Þ

Also, Newton's law is introduced in MD as the gradient of the potential equation according to the following [40].

X i≠ j

2

F ij ¼ mi

d ri dv ¼ mi i dt dt 2

!

F ij ¼ − ∇ ðϕ þ ϕw Þ

ð4Þ

ð5Þ

Afterward, the relation of velocity and temperature is linked to the Gaussian distribution to compute temperature as below formula [41]: Natm 1 X 1 3 m j vi 2 j¼ kB T Natm i¼1 2 2

ð6Þ 3

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

2000

0

Bin Number Fig. 2. Density profile for roughened channel under 84 K.

wall temperature to Argon fluid atoms due to increasing effective contact surfaces for thermal energy transfer. Their first effect (trapping atoms) prevents easy movement of Argon atoms from the vicinity of microchannel surfaces to the middle region of the channel which causes

750,000. In fact, the spherical geometry of roughness barriers has two types of influence on the boiling flow of Argon. First, they trap Argon atoms in their interval distance and their second effect is related to their influence on the increasing rate of energy transfer from boundary

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

Bin Number Fig. 3. Density profile for ideal channel under 84 K. 4

2000

0

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

2000

0

Bin Number Fig. 4. Density profile for the roughened channel under 96 K.

raised with time step progress, whereas; wall temperature is unchanged. The direction of energy transfer from microchannel walls to fluid flow is perpendicular to the direction of external force. Hence,

to reduce density in central layers. But, their second effect (increasing energy transfer) accelerates the translocation of fluid atoms from lateral layers to central layers. Theoretically, temperatures of flow could be

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

Bin Number Fig. 5. Density profile for the ideal channel under 96 K. 5

2000

0

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

2000

0

Bin Number Fig. 6. Density profile for the roughened channel under 108 K.

the enhancement of wall temperature does not push fluid flow to move forward parallel with external force direction. As a result, it can be concluded that at low time steps (before 750,000), the first effect of the

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

0.025

Density (gram/cm^dim)

roughness component can overcome to the second effect while; the second effect overcomes to the first effect at high time steps (after 750,000) due to the completion of the boiling process and emerging significant

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

Bin Number Fig. 7. Density profile for the ideal channel under 108 K. 6

2000

0

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

2000

0

Bin Number Fig. 8. Density profile for the roughened channel under 114 K.

kinetic energy of atoms. Thus, the criteria of empowering and weakening thermal behavior of fluid flow are important for cost and benefit analysis for further experimental investigations and manufacturing

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

0.025

Density (gram/cm^dim)

channels for practical applications. Therefore, a study on the effect of spherical geometry of barriers from a density viewpoint, indicates that using a roughened surface can be useful for better distribution of

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

Bin Number Fig. 9. Density profile for the ideal channel under 114 K. 7

2000

0

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

2000

0

Bin Number Fig. 10. Density profile for the roughened channel under 133 K.

Figs. 12 and 13 present velocity profiles of flow into microchannels with roughened and smooth surfaces at time step 1,000,000. Each figure contains 5 profiles concerning 5 different boundary wall temperatures of 84 K, 96 K, 108 K, 114 K, and 133 Kelvin as guided in symbol boxes

atoms in the high temperature of 114 K to 133 K at high time steps (after 750,000). Hence, investing in polishing the microchannel surfaces and removing the spherical shape of the roughness component can even be vain for some of the practical applications.

250000 Time Step 500000 Time Step 750000 Time Step 1000000 Time Step

Density (gram/cm^dim)

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

500

1000

1500

Bin Number Fig. 11. Density profile for the ideal channel under 133 K. 8

2000

0

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

Velocity of argon fluid (angstroms/picoseconds)

4 T=84 K T=96 K T=108 K T=114 K T=133 K

3.5 3 2.5 2 1.5 1 0.5 0

500

1000

1500

2000

Number of bin

Fig. 12. Velocity profile for rough microchannel.

microchannel both profiles have fluctuated irregularly. Also, the amplitude of fluctuation of velocity profiles in the central region of the roughened channel is approximately higher than that of the ideal channel.

Velocity values in 2200 bins indicated that increasing boundary wall temperatures cause to decrease the velocity value of fluid flow inside a roughened microchannel while; it is almost unchanged in a smooth microchannel. Because summation of density value of 2200 bins of

of both figures. Also, to produce velocity value in the X-direction, an external driving force 0.002 eV/Angstrom is enforced at the entrance region of the microchannel. It is clear that the trend of velocity graphs of roughened surfaces is mostly similar to those of smooth surfaces with a little difference in the layers are in exposure of roughness barriers. Because, velocity values of layers in the vicinity of microchannel walls are lower than those of smooth surfaces, while; in the central region of the

Velocity of argon fluid (angstroms/picoseconds)

4 T=84 K T=96 K T=108 K T=114 K T=133 K

3.5 3 2.5 2 1.5 1 0.5 0

500

1000

1500

Number of bin

Fig. 13. Velocity profile for smooth microchannel.

9

2000

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

550 500

T=84 K T=96 K T=108 K T=114 K T=133 K

Temprature of argon fluid (K)

450 400 350 300 250 200 150 100 50 0

500

1000

1500

2000

Number of bin

Fig. 14. Velocity profile for rough microchannel.

roughness components empower boiling force which intends to move atoms from the lateral region to the middle section of the microchannel in Z-direction and contradicted with external force direction. Nevertheless, differences in velocity values between roughened and ideal microchannels are so small that the influence of spherical geometry of roughness components on the velocity of fluid flow can be ignorable for practical application.

rough microchannel for temperatures of 84 K, 96 K, 108 K, 114 K, and 133 K are 3693, 3672, 3654, 3622, and 3649 Angstrom/ps whereas; they are 3689, 3709, 3708, 3706, and 3702 Angstrom/ps for the smooth microchannel. The statistical approach by the above values shows that roughness plays 2 different roles against an external force. First, they trap atoms in lateral regions and prevent their movement in X-axis, parallel with external force direction. Second,

550 500

T=84 K T=96 K T=108 K T=114 K T=133 K

Temprature of argon fluid (K)

450 400 350 300 250 200 150 100 50 0

500

1000

1500

Number of bin

Fig. 15. Velocity profile for smooth microchannel.

10

2000

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462

Figs. 14 and 15 exhibit temperature profiles of Argon flow into rough and smooth channels, which are affected by applying wall temperatures in the range of 84 K to 133 K. These profiles were drawn at 1,000,000time steps. The vertical axe shows temperature values versus bin numbers in the horizontal axe. As can be seen from these figures, Minimum values are at the lateral region and the maximum is in the central layers of microchannels. Therefore, the tread of temperature profiles of both microchannels is similar. The statistical approach by computation of temperature values in all layers of microchannels shows that roughness elements with spherical geometry do not strongly affect the temperature value of Argon fluid when boundary wall temperature is in the range of 114 K to 133 K. Also, the summation of temperature value of 800 layers in the middle section of microchannels shows that roughened microchannel has higher temperature values than smooth microchannel as much as 2.6%, 2.7%, 4.3%, 1%, and 0.7% in order of temperatures 84 K, 96 K, 108 K, 114 K, and 133 K. Hence, rising boundary temperature can eliminate roll of roughness components with spherical geometry on the temperature profiles of Argon flow into the microchannel.

[2] A.S. Goldanlou, M. Zarringhalam, N. Shirani, A.A. Alizadeh, D. Toghraie, S. Rostami, Investigation the effects of an external driving force and cone shape of roughness on the phase change behavior of Argon fluid within a microchannel by molecular dynamic simulation, J. Mol. Liq. (2020) 113503 Jun 3.

[3] S. Rostami, M. Zarringhalam, A.A. Alizadeh, D. Toghraie, A.S. Goldanlou, Molecular dynamic simulation of Argon boiling flow inside smooth and rough microchannels by considering the effects of cubic barriers, J. Mol. Liq. (2020) 113130 May 11.

[4] E. Shirani, A. Razmjou, H. Tavassoli, A. Landarani-Isfahan, S. Rezaei, A.A. Kajani, M. Asadnia, J.W. Hou, M.E. Warkiani, Strategically Designing a Pumpless Microfluidic Device on an “Inert” Polypropylene Substrate with Potential Application in Biosensing and Diagnostics, Langmuir 33 (22) (2017) 5565–5576.

[5] Z. Mehrabi, A. Taheri-Kafrani, M. Asadnia, A. Razmjou, Bienzymatic Modification of Polymeric Membranes to Mitigate Biofouling, Sep. Purif. Technol. 237 (2020), 116464.

[6] M. Zarringhalam, H. Ahmadi-Danesh-Ashtiani, D. Toghraie, R. Fazaeli, Molecular dynamic simulation to study the effects of roughness elements with cone geometry on the boiling flow inside a microchannel, Int. J. Heat Mass Transf.

141 (2019) 1–8 Oct 1.

[7] N. Emami, A. Razmjou, F. Noorisafa, A. Habibnejad Korayem, A. Zarrabi, Ch. Ji, Fabrication of Smart Magnetic Nanocomposite Asymmetric Membrane Capsules for the Controlled Release of Nitratesimulation, Environ. Nanotechnol. Monit. Manag. 8 (2017) 233–243.

[8] M. Zarringhalam, H. Ahmadi-Danesh-Ashtiani, D. Toghraie, R. Fazaeli, The effects of suspending copper nanoparticles into Argon base fluid inside a microchannel under boiling flow condition by using of molecular dynamic simulation, J. Mol. Liq. 293 (2019) 111474 Nov 1.

[9] M. Kalweit, D. Drikakis, Coupling strategies for hybrid molecular—continuum simulation methods, Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 222 (5) (2008) 797–806 May 1.

[10] Allen MP. Tildesley DJ Computer Simulation of Liquids.

[11] K. Kadau, T.C. Germann, P.S. Lomdahl, Large-scale molecular-dynamics simulation of 19 billion particles, International Journal of Modern Physics C 15 (01) (2004) 193–201 Jan. [12] D.C. Rapaport, D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge university press, 2004.

[13] B.J. Alder, T.E. Wainwright, Studies in molecular dynamics. I. General method, J. Chem. Phys. 31 (2) (1959) 459–466 Aug. [14] A. Rahman, Correlations in the motion of atoms in liquid argon, Phys. Rev. 136 (2A) (1964) A405 Oct 19.

[15] V.S. Craig, C. Neto, D.R. Williams, Shear-dependent boundary slip in an aqueous Newtonian liquid, Phys. Rev. Lett. 87 (5) (2001) 054504 Jul 17.

[16] Y. Zhu, S. Granick, Rate-dependent slip of Newtonian liquid at smooth surfaces, Phys. Rev. Lett. 87 (9) (2001) 096105 Aug 10.

[17] D.C. Tretheway, C.D. Meinhart, Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids 14 (3) (2002) L9–12 Mar. [18] P. Alipour, D. Toghraie, A. Karimipour, M. Hajian, Molecular dynamics simulation of fluid flow passing through a nanochannel: effects of geometric shape of roughnesses, J. Mol. Liq. 275 (2019) 192–203 Feb 1.

[19] M. Tohidi, D. Toghraie, The effect of geometrical parameters, roughness and the number of nanoparticles on the self-diffusion coefficient in Couette flow in a nanochannel by using of molecular dynamics simulation, Phys. B Condens. Matter 518 (2017) 20–32 Aug 1.

[20] A. Rostami, A. Hemmati-Sarapardeh, A. Karkevandi-Talkhooncheh, M.M. Husein, Sh. Shamshirband, T. Rabczuk, Modeling heat capacity of ionic liquids using group method of data handling: A hybrid and structure-based approach, Int. J. Heat Mass Transf. 129 (2019) 7–17.

[21] A. Toghaniyan, M. Zarringhalam, O.A. Akbari, G.A. Shabani, D. Toghraie, Application of lattice Boltzmann method and spinodal decomposition phenomenon for simulating two-phase thermal flows, Physica A: Statistical Mechanics and its Applications 509 (2018) 673–689 Nov 1.

[22] D.T. Semiromi, A.R. Azimian, Molecular dynamics simulation of nonodroplets with the modified Lennard-Jones potential function, Heat Mass Transf. 47 (5) (2011) 579–588 May 1.

[23] M. Papanikolaou, M. Frank, D. Drikakis, Effects of surface roughness on shear viscosity, Phys. Rev. E 95 (3) (2017) 033108 Mar 13.

[24] M. Papanikolaou, M. Frank, D. Drikakis, Nanoflow over a fractal surface, Phys. Fluids 28 (8) (2016) 082001 Aug 1.

[25] N. Asproulis, D. Drikakis, Wall-mass effects on hydrodynamic boundary slip, Phys.

Rev. E 84 (3) (2011) 031504 Sep 23.

[26] N. Asproulis, D. Drikakis, Boundary slip dependency on surface stiffness, Phys. Rev. E 81 (6) (2010) 061503 Jun 24.

[27] M. Barisik, B. Kim, A. Beskok, Smart wall model for molecular dynamics simulations of nanoscale gas flows, Communications in Computational Physics 7 (5) (2010) 977 May 1.

[28] A. Niavarani, N.V. Priezjev, Modeling the combined effect of surface roughness and shear rate on slip flow of simple fluids, Phys. Rev. E 81 (1) (2010) 011606 Jan 25.

[29] D.T. Semiromi, A.R. Azimian, Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function, Heat Mass Transf. 46 (7) (2010) 791–801 Aug 1.

[30] F. Sofos, T.E. Karakasidis, A. Liakopoulos, Effect of wall roughness on shear viscosity and diffusion in nanochannels, Int. J. Heat Mass Transf. 53 (19–20) (2010) 3839–3846 Sep 1.

[31] M. Barisik, A. Beskok, Molecular dynamics simulations of shear-driven gas flows in nano-channels, Microfluid. Nanofluid. 11 (5) (2011) 611–622 Nov 1.

[32] N. Razmara, Molecular dynamics simulation of liquid argon flow in nanochannels using different potential functions, Modares Mechanical Engineering 13 (6) (2013) 114–125 Sep 15.

4. Conclusion The present work studied the molecular dynamic simulation of Argon fluid flow inside microchannels with ideal & roughened surfaces.

Fluid flows were affected by boundary temperatures of 84 K, 96 K, 108 K, 108 K, and 133 K to prepare boiling flow conditions. Also, a force of 0.002 eV/Angstrom was exerted on the Argon atoms at the inlet region of microchannels. Results were as following: 1) Despite the undesirable consequences of the spherical geometry of roughness in trapping atoms, they can be beneficial to improve the boiling process and stronger distribution of Argon atoms in the middle region of the microchannel.

2) Influences of spherical roughness barriers in reducing the velocity of Argon atoms were so small that can be ignorable. Also, spherical barriers reduce the temperature of fluid flow in the central region of the microchannel as much as 2.6%, 2.7%, 4.3%, 1%, and 0.7% concerning wall temperatures of 84 K, 96 K, 108 K, 114 K, and 133 Kelvin. Therefore, increasing boundary wall temperature can decrease the consequence of barriers.

3) The optimum condition of using spherical roughness belonged to wall temperature in the range of 114 K to 133 Kelvin. Because the positive role of roughness in the acceleration of the boiling process was approximately equal with its negative role as obstacles to prevent from movements of Argon atoms.

Author statement Methodology, Software and Validation: Majid Zarringhalam3, Davood Toghraie4⁎, Amin Rahmani5, Writing - Review & Editing: Amirhosein Mosavi1,2, Amin Rahmani5, Aliakbar Karimipour6.

Writing - Original Draft: Amirhosein Mosavi1,2, Majid Zarringhalam3, Davood Toghraie4⁎, Aliakbar Karimipour6.

Investigation: Davood Toghraie4⁎, Aliakbar Karimipour6.

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References [1] S. Rostami, H. Ahmadi-Danesh-Ashtiani, D. Toghraie, R. Fazaeli, A statistical method for simulation of boiling flow inside a platinum microchannel, Physica A: Statistical Mechanics and its Applications 548 (2020) 123879 Jun 15.

11

A. Mosavi, M. Zarringhalam, D. Toghraie et al.

Journal of Molecular Liquids 321 (2021) 114462 [52] P. Mehdizadeh, Y. Orooji, O. Amiri, M. Salavati-Niasari, H. Moayedi, Green synthesis using cherry and orange juice and characterization of TbFeO3 ceramic nanostructures and their application as photocatalysts under UV light for removal of organic dyes in water, J. Clean. Prod. 252 (2020), 119765.

[53] H. Karimi-Maleh, et al., The role of magnetite/graphene oxide nano-composite as a high-efficiency adsorbent for removal of phenazopyridine residues from water samples, an experimental/theoretical investigation, J. Mol. Liq. 298 (2020), 112040.

[54] A.A. Alrashed, O.A. Akbari, A. Heydari, D. Toghraie, M. Zarringhalam, G.A. Shabani, A.R. Seifi, M. Goodarzi, The numerical modeling of water/FMWCNT nanofluid flow and heat transfer in a backward-facing contracting channel, Phys. B Condens. Matter 537 (2018) 176–183 May 15.

[55] M.R. Gholami, O.A. Akbari, A. Marzban, D. Toghraie, G.A. Shabani, M. Zarringhalam, The effect of rib shape on the behavior of laminar flow of oil/MWCNT nanofluid in a rectangular microchannel, J. Therm. Anal. Calorim. 134 (3) (2018) 1611–1628 Dec 1.

[56] M. Naderi, G. Ahmadi, M. Zarringhalam, O. Akbari, E. Khalili, Application of water reheating system for waste heat recovery in NG pressure reduction stations, with experimental verification, Energy 162 (2018) 1183–1192 Nov 1.

[57] M. Zarringhalam, A. Karimipour, D. Toghraie, Experimental study of the effect of solid volume fraction and Reynolds number on heat transfer coefficient and pressure drop of CuO–water nanofluid, Exp. Thermal Fluid Sci. 76 (2016) 342–351 Sep 1.

[58] D. Toghraie, N.N. Esfahani, M. Zarringhalam, N. Shirani, S. Rostami, Blood flow analysis inside different arteries using non-Newtonian Sisko model for application in biomedical engineering, Comput. Methods Prog. Biomed. 190 (2020) 105338 Jul 1.

[59] A. Hemmati-Sarapardeh, F. Ameli, A. Varamesh, Sh. Shamshirband, A.H. Mohammadi, B. Dabir, Toward generalized models for estimating molecular weights and acentric factors of pure chemical compounds, Int. J. Hydrog. Energy 43 (5) (2018) 2699–2717.

[60] L.K. Foong, N. Shirani, D. Toghraie, M. Zarringhalam, M. Afrand, Numerical simulation of blood flow inside an artery under applying constant heat flux using Newtonian and non-Newtonian approaches for biomedical engineering, Comput. Methods Prog. Biomed. 190 (2020) 105375 Jul 1.

[61] S.R. Yan, M. Zarringhalam, D. Toghraie, L.K. Foong, P. Talebizadehsardari, Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles, Comput. Methods Prog. Biomed. (2020) 105434 Mar 4.

[62] L.K. Foong, M. Zarringhalam, D. Toghraie, N. Izadpanahi, S.R. Yan, S. Rostami, Numerical study for blood rheology inside an artery: the effects of stenosis and radius on the flow behavior, Comput. Methods Prog. Biomed. 193 (2020) 105457 Sep 1.

[63] A. Karimipour, D. Toghraie, L.A. Abdulkareem, A.A. Alizadeh, M. Zarringhalam, A. Karimipour, Roll of stenosis severity, artery radius and blood fluid behavior on the flow velocity in the arteries: application in biomedical engineering, Med. Hypotheses (2020) 109864 May 23.

[64] Orooji, et al., Effects of ZrB2 reinforcement on microstructure and mechanical properties of a spark plasma sintered mullite-CNT composite, Ceram. Int. 45 (2019) 16015–16021.

[65] Y. Orooji, et al., Preparation of mullite-TiB2-CNTs hybrid composite through spark plasma sintering, Ceram. Int. 45 (2019) 16288–16296.

[66] H. Karimi-Maleh, et al., A new nickel-based co-crystal complex electrocatalyst amplified by NiO dope Pt nanostructure hybrid; a highly sensitive approach for determination of cysteamine in the presence of serotonin, Sci. Rep. 10 (2020) 11699.

[67] H. Karimi-Maleh, et al., Tuning of metal oxides photocatalytic performance using Ag nanoparticles integration, J. Mol. Liq. 314 (2020) 113588.

[68] H. Karimi-Maleh, et al., An amplified voltammetric sensor based on platinum nanoparticle/polyoxometalate/two-dimensional hexagonal boron nitride nanosheets composite and ionic liquid for determination of N-hydroxysuccinimide in water samples, J. Mol. Liq. 310 (2020) 113185.

[33] H. Noorian, D. Toghraie, A.R. Azimian, Molecular dynamics simulation of Poiseuille flow in a rough nano channel with checker surface roughnesses geometry, Heat Mass Transf. 50 (1) (2014) 105–113 Jan 1.

[34] L. Wen, L. Jiang, Construction of biomimetic smart nanochannels for confined water, Natl. Sci. Rev. 1 (1) (2013) 144–156 Nov 8.

[35] M. Rezaei, A.R. Azimian, D.T. Semiromi, The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study, Heat Mass Transf. 51 (5) (2015) 661–670 May 1.

[36] M. Sahebi, A.R. Azimian, Molecular dynamics investigation of the mechanisms of thermal creep flow in nanotubes, Modares Mechanical Engineering 15 (10) (2015) 225–232 Dec 15.

[37] F. Faraji, A. Rajabpour, F. Kowsary, Temperature profile for nanoscale Poiseuille flow: a multiscale study, J. Mech. Sci. Technol. 30 (2) (2016) 803–807 Feb 1.

[38] F. Sotoudeh, A. Rajabpour, M. Khanaki, Shock wave propagation in the solid argon by molecular dynamics simulation: effect of initial strain, Modares Mechanical Engineering 16 (3) (2016) 364–370 May 15.

[39] G. Heidarinejad, R. Rabani, E. Shirani, The effect of wall force field on temperature distribution in nanochannel contains Lennard-Jones fluid by molecular dynamic simulation, Modares Mechanical Engineering 17 (6) (2017) 23–31 Aug 15.

[40] D.T. Semiromi, A.R. Azimian, Molecular dynamics simulation of annular flow boiling with the modified Lennard-Jones potential function, Heat Mass Transf. 48 (1) (2012) 141–152 Jan 1.

[41] D. Toghraie, A.R. Azimian, Molecular dynamics simulation of annular flow boiling in a microchannel with 70000 atoms, World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering 5 (6) (2011) 831–837 Jun 25.

[42] A. Liakopoulos, F. Sofos, T.E. Karakasidis, Darcy-Weisbach friction factor at the nanoscale: from atomistic calculations to continuum models, Phys. Fluids 29 (5) (2017) 052003 May 4.

[43] A. Liakopoulos, F. Sofos, T.E. Karakasidis, Friction factor in nanochannel flows, Microfluid. Nanofluid. 20 (1) (2016) 24 Jan 1.

[44] S. Zhang, F. Hao, H. Chen, W. Yuan, Y. Tang, X. Chen, Molecular dynamics simulation on explosive boiling of liquid argon film on copper nanochannels, Appl. Therm. Eng. 113 (2017) 208–214 Feb 25.

[45] L. Li, P. Ji, Y. Zhang, Molecular dynamics simulation of condensation on nanostructured surface in a confined space, Applied Physics A 122 (5) (2016) 496 May 1.

[46] C.Y. Ji, Y.Y. Yan, A molecular dynamics simulation of liquid–vapour–solid system near triple-phase contact line of flow boiling in a microchannel, Appl. Therm. Eng. 28 (2–3) (2008) 195–202 Feb 1.

[47] T. Fu, Y. Mao, Y. Tang, Y. Zhang, W. Yuan, Effect of nanostructure on rapid boiling of water on a hot copper plate: a molecular dynamics study, Heat Mass Transf. 52 (8) (2016) 1469–1478 Aug 1.

[48] S. Rostami, M.A. Mozoun, D. Toghraie, M. Zarringhalam, A.S. Goldanlou, Insight into the significance of blood flow inside stenosis coronary jointed with bypass vein: the case of anemic, normal, and hypertensive individuals, Comput. Methods Prog.

Biomed. (2020) 105560 May 22.

[49] Y. Orooji, et al., Co-reinforcing of mullite-TiN-CNT composites with ZrB2 and TiB2 compounds, Ceram. Int. 45 (2019) 20844–20854.

[50] Y. Orooji, M. Ghanbari, O. Amiri, M. Salavati-Niasari, Facile fabrication of silver iodide/graphitic carbon nitride nanocomposites by notable photo-catalytic performance through sunlight and antimicrobial activity, J. Hazard. Mater. 389 (2020), 122079.

[51] Y. Orooji, et al., Cerium doped magnetite nanoparticles for highly sensitive detection of metronidazole via chemiluminescence assay, Spectrochim Acta A Mol Biomol Spectrosc 234 (2020), 118272.

12