Influence of surface roughness on the fluid flow in microchannel

Surface roughness is a crucial factor of fluid flow in microfluidic channels. Most of the existing studies focus on the effect of regular microstructured surfaces on fluid flow, while researchs about the impact of random rough surfaces on fluid flow remains limited. Therefore, in this study, a random rough surface model and two microstructured surface models were established, and the effects surface roughness on the fluid flow at Wenzel state and Cassie-Baxter state were studied using COMSOL multi-physics simulation software. Our findings reveal that both the flow velocity and the fluid flow rate at the microchannel outlet decreases with the surface roughness increases. Notably, the flow rate and velocity of the fluid flow at Cassie-Baxter state is higher than that of fluid flow at Wenzel state.


Intorduction
Micro/nano-scale electromechanical systems (MEMS/NEMS) with micro/nano-scaled channels have gained widespread applications in diverse fields such as physics, chemistry, aerospace, environmental monitoring, biological detection, targeted drug delivery, DNA manipulation, and biomedicine.[1][2][3] The efficient transfer of fluids in microchannels is a prerequisite for the smooth operation of these microfluidic systems.[4] Due to the larger surface-to-volume ratio, micro/nano-scaled channels render the flow of the fluid more susceptible to surface properties such as roughness, hydrophobicity, and surface forces than in macro-scaled channels.[5][6] Currently, the control of fluid flow resistance at micro/nano scales stands as a key limiting factor in the development of micro/nano fluid systems.Therefore, how to reduce and control fluid flow resistance at these scales has become a hot topic in the field of microfluidics, which has important practical implications for enhancing the performance and long-term development of microfluidic systems.This also provides a theoretical basis for the design and manufacture of micro/nano fluid devices.
Surface roughness alters the wetting states of the fluid at the solid-liquid interface.For hydrophilic surface, the fluid completely wets the solid surface, called the Wenzel state; while on hydrophobic surfaces, studies have shown that when fluid flows over rough solid surfaces, gas molecules can be trapped within the microstructure of the solid surface, forming stable bubbles on its surface known as the Cassie state.[7] Actually, the Cassie state exists only under ideal conditions, and the fluid often flows over surfaces at Cassie-Baxter state which stands between the Wenzel state and the Cassie state.Up to now, although numerous studies have examined the influence of mesoscopic and nano-scale surface roughness on fluid flow, most have focused on regular microstructured surfaces [8][9][10][11][12], and very few studies have investigated the impact of random rough surfaces on the liquid flow through the microchannel.Therefore, the effects of surface roughness on fluid flow in different wetting states, namely Wenzel state and Cassie-Baxter state, were investigated in this study.A random rough surface model and two regular microstructured models (triangular groove and cone) were established using COMSOL multi-physics simulation software to explore how surface roughness affects the fluid flow in both Wenzel and Cassie-Baxter states.

Modeling and simulation Settings
In this work, COMSOL multi-physics simulation software is used to build three microchannel models which have lower walls with random surface roughness, triangular groove structures and conical structures respectively (as shown in Figure 1).The surface roughness Rq of the lower wall with a random rough surface is dimensionless.According to Ref [13], the height h of the triangular groove structure and the conical structure is proportional to Rq, i.e., htri =3.2Rq,and hcone=3.8Rq.This study focuses on laminar flow physics field (The Reynolds number is approximately between 13.2-24.9).The dimensions, lengths, widths and heights of the microchannels are 25um, 25um and 40um, respectively.The upper wall of the microchannel is smooth, and the lower wall is set to be rough surface.Water was used as the working fluid in the simulation, with an external reference pressure of 1 standard atmosphere (1.01325x10 5 Pa) and a temperature of 293.15K.As the slip length on the solid-liquid contact surface is very small and can be neglected.Therefore, when setting the boundary conditions, the solid-liquid interface was assigned as no-slip condition, while the gas-liquid interface was assigned as slip condition.Pressure driven flow with inlet pressure of 100 Pa and outlet pressure of 0 Pa was used .The fluid flows from the inlet to outlet and backflow at the outlet is inhibited.Additionally, both the side walls of the fluid flow are set as symmetric planes.To simplify the model, the shap of the meniscus at liquid-gas interface is ignored.The grid is set to be controlled by the physical field, and the cell size is refined.A two-dimensional cross section at the outlet is set, and the outlet flow is calculated by integrating the two-dimensional cross section.

Results and Discussion
As shown in Figure 2, the relationship between the roughness of low wall for three different models and the average outlet velocity (Figure 2a) and outlet flow rate (Figure 2b) is presented.With the increase of surface roughness, both the average outlet velocity and outlet flow rate show an obviously lineardecrease.forall three models.However, it should be noted that the outlet flow of Cassie-Baxter state is higher than that of Wenzel state.One reason for this phenomenon is that in the Wenzel state, with the increase of surface roughness, the solid-liquid contact area also increases, resulting in an increase in fluid flow resistance.Another reason is that due to the existence of surface roughness, vortex will be formed in the trough of the rough surface when the fluid flows through the rough surface.The greater the surface roughness, the more obvious this phenomenon will be, leading to energy loss and a subsequent decrease in outlet flow rate and velocity.This can be observed in the flow field diagram and flow diagram of Wenzel state in Figure 3-Figure 5.In the Cassie-Baxter state, as the surface roughness increases from 0.1 to 0.9, the flow velocity and flow rate at the outlet of the microchannel with conical microstructure decrease from approximately 0.77m/s (0.75m3/s) to approximately 0.60m/s (0.55m3/s), which is significantly higher than the flow velocity and flow rate at the exit of other two models.The outlet velocity and flow rate of models for the random rough low wall and that with triangular groove microstructures are 0.56m/s (0.45m3/s) and 0.57m/s (0.48m3/s), respectively.For the fluid at Wenzel state, the outlet velocity and flow rate for the three microchannel models remain relatively consistent with the changes in roughness.The reason for the higher flow rate at Cassie-Baxter state as compared to the Wenzel state is that, gas bubbles will form on the rough surface at Cassie-Baxter state and which will make the boundray condition be transfered from no-slip condition to slip condition, thus promoting the fluid flow.This should be the main reason that the flow velocity and flow rate at the outlet of the three models in Cassie-Baxter state are obvious higher than those in Wenzel state.However, due to the promotion from the slippage is still less than the impediment from surface roughness, although the flow rate of Cassie-Baxter state is higher than that of Wenzel state, the outlet flow rate and flow velocity still show a downward trend.

Conclusion
The effects of surface roughness of microchannels on fluid flow are studied in this paper.The results show that: (1) On micro and nano scale, with the increase of surface roughness, both the outlet velocity and the average velocity show obvious decrease.This is due to two primary factors.First, the increase of surface roughness leads to the increase of the solid-liquid contact area, which in turn increases the fluid flow resistance.Secondly, when the fluid flows on the rough surface, vortex are formed in the trough of the rough surface, leading to energy loss, and thus resulting in a decrease for both the outlet flow and the outlet average velocity with the increase of surface roughness.(2) The outlet flow rate and average velocity for the fluid at Cassie-Baxter state are higher than those obtained at Wenzel state.This is due to the presence of gas in the Cassie-Baxter state, which introduces slip at the gas-liquid interface and promotes the fluid flow.However, the promotion is still less than the resistance caused by surface roughness.Therefore, the outlet flow rate and the flow velocity also showed a downward trend in Cassie-Baxter state.Our research will provide a better understanding for the prediction and control of the fluid behavior in microchannels, and which has important implications for a range of applications, including nanofabrication, biotechnology, and microelectromechanical systems (MEMS).

Figure 1 .
Figure 1.Microchannel models with different types of lower wall, the lower walls are with (a) random surface roughness (b) conical microstructures and (c) triangular groove microstructures.

Figure 2 .
Figure 2. Relationships between different types of surface roughness and (a) average outlet flow rate and (b) outlet flow rate (working fluid is water)In the Cassie-Baxter state, as the surface roughness increases from 0.1 to 0.9, the flow velocity and flow rate at the outlet of the microchannel with conical microstructure decrease from approximately 0.77m/s (0.75m3/s) to approximately 0.60m/s (0.55m3/s), which is significantly higher than the flow

Figure. 3
Figure. 3 Flow field and stream line map for the partial area of random rough surface (a) and (c) show the flow velocity field and flow line field when the surface roughness is 0.5; (b) and (d) refer to the flow rate field and streamline field when the surface roughness is 0.9.

Figure. 4 9 Figure. 5
Figure. 4 Flow field and stream line map of partial area for the lower wall with conical structures (a) and (c) show the flow velocity field and flow line field when the surface roughness is 0.5; (b) and (d) refer to the flow rate field and streamline field when the surface roughness is 0.9