# Mechanism and Modeling of Contaminant Accumulation on Hot-Film Air Flow Sensor

Authors: Changrong Yuan; Zhongsheng Sun; Xiaoning Li
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

Hot-film air flow sensors are now widely applied in many industrial fields. Their accuracy can be seriously affected when there are contaminants accumulated on the sensor chip. To predict the decrease of accuracy caused by contamination, the accumulation mechanism of contaminant particles on the surface of the sensor chip is studied in this paper. The adsorption process of particle is analyzed and a theoretical model of the cumulative thickness of the particles over time is established. A test platform for the particle accumulation is built and a long-term cumulative test is conducted. According to the tests, cumulative thickness of the particles increases while the growth rate slows over time. The results of the test fit those of the theoretical model. Various factors affecting the accumulation of contaminants are analyzed. The results indicate that the cumulative thickness of the particles increases along with the increase of the particle concentration, the particle charge, and the electric field strength on the chip surface but decreases along with the increase of the particle radius. The test results also show that the electrical force is the dominant reason of particle adsorption accumulation. By decreasing the electric field strength on the sensor surface, the cumulative thickness of the particles can be effectively reduced.


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## Body

## 1. Introduction

In recent years, MEMS hot-film air flow sensor has been widely used in the fields of aerospace, automotive, biomedical, environmental monitoring, semiconductor, and domestic appliances due to its ability of indirect measurement of air mass flow via measurements of temperature changes and the characteristics of high accuracy, fast response, and low power consumption [1–3]. However, in practical applications, it is found that if the gas to be measured contains aerosol particles, oil mist, etc., the surface of the sensor chip will be contaminated, which affects the accuracy of the sensor. For example, one of the typical applications of MEMS hot-film flow sensor is in the field of automotive engines [4–6]. It is an important sensor for controlling the air-fuel ratio in the electronic control fuel injection device of the automobile. It is used to measure the air flow inhaled into the engine as a basic signal for determining the fuel injection, which directly affects the performance of the power, cost, emission, and stable operation of the automobile engine [7]. As the automotive engine usually works in a dirty air environment, the measurement area of the sensor would be contaminated by the prevalent pollutants [8, 9]. A heat insulating layer is generated to make the sensor difficult to dissipate, which would produce an air-fuel ratio error of 30%-45% [10]. When the sensor is contaminated, it would cause the problems such as difficulty in starting the engine, unstable idle speed, power reduction, and increased fuel consumption [11, 12].Xu [13] used the Workbench Fluent module of ANSYS to analyze the flow field of the sensor chip in the presence of air contamination. It was found that the diameter of the particles and the amount of contaminants in the air are the main factors affecting the temperature distribution of the sensor chip. Komorska [14] studied the effect of partial choking on the intake manifold. The air cannot flow through the part of the channel blocked by the contaminants, which affects the distribution of the airflow over the entire channel area, thus causing the flow rate calculated by the sampling part to be out of alignment. Hecht et al. [15, 16] studied the effect of thermophoretic force on the accumulation of contaminants. The thermophoretic force was used to reduce the accumulation of tiny particles such as dust and oil mist by adding heating resistance on the surface of the hot film. In [17], the influence of electric field and sensor chip position on the accumulation of particles was studied through experiments. The results show that the accumulation of particles is exacerbated due to the presence of the electric field, and the gravity of the particles has no significant effect on the accumulation of particles.As MEMS hot-film gas flow sensors have been widely used in the past decade, the problem of contamination in its application is just exposed, resulting in a lack of targeted research work. In addition, the sensor chip is relatively small, and the research of the contamination on the surface of the chip is difficult, so that there are few related literatures on practical operation. In this paper, the accumulation mechanism of contaminant particles on the surface of the sensor chip is studied. The particle motion is analyzed and a theoretical model of the cumulative thickness of the particles over time is established. The factors affecting the accumulation of particles are analyzed by the model. It is proposed to reduce the contaminants by decreasing the electrical force on the surface of the chip.


## 2. Accumulation Mechanism and Model

### 2.1. Analysis of Accumulation Mechanism of Contaminant Particles

MEMS hot-film gas flow sensors are often used in harsh working environments where contaminants are contained. Contaminants can be accumulated on the surface of the sensor chip, affecting the accuracy of the sensor [18]. There are many forces that affect the accumulation of contaminant particles, such as air adhesion, air buoyancy, gravity of the particles themselves, Saffman lift force, electrical force, etc. [19, 20]. When the particles move inside the pipe, most of them get charged due to the collisions and frictions. Since an electric field is generated by the energized thin film resistors, the particles passing through the surface of the chip experience the electrical force. As the electric field decreases along with the increase of the distance, the influence of the electrical force on the particle accumulation also decreases along with the increase of the distance. Therefore, particles in a certain range of the flow channel above the surface of the chip will be accumulated by the electrical force generated on the chip surface, as shown in Figure 1. The particle motion is specifically considered in two stages: (1) the particles in the region I are transported horizontally in the pipe at a certain speed before entering the surface of the sensor chip, and the applied forces are in a balanced state; (2) when the particles flowing from the region I into the region II pass through the surface of the sensor chip, the original force balance of the particles is broken due to the new electrical force, resulting in the adsorption and accumulation on the surface of the chip. The particles far away from the surface of the chip (region III) are less affected by the electrical force and the particles will not be adsorbed.Figure 1
Schematic diagram of accumulation of contaminant particles on the surface of the chip.


### 2.2. Single Particle Adsorption Process Description

#### 2.2.1. Basic Force and Motion Analysis of Particles in the Pipe

The contaminant particles in the pipe experience the basic force and motion [21, 22] before being affected by the electrical force on the surface of the chip. The flow process can be approximately described by a free and uniform suspension flow model that ignores the friction and collision between particles and between the particles and the pipe, and studies the motion discipline of single particle to investigate the situation of the entire flow channel. The particles moving in the horizontal pipe are mainly forced by drag forceFd of the gas to the particles, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs, as shown in Figure 2. In the horizontal direction, the particles move forward along the pipe for a long time or distance, reach a certain final velocity, and then maintain a uniform motion by the horizontal component forceFdx of drag forceFd and pressure gradient forceFp. In the vertical direction, the particles are transported in suspension by the vertical component forceFdy of drag forceFd, buoyancyFb, gravity Fg, and Saffman lift forceFs.Figure 2
Schematic diagram of the forces of particles in the pipe before approaching the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force; ugx: velocity of the gas in x-axis direction.According to Newton’s second law, in thex-axis direction, the particles experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(1)mpdupxdt=Fdx+FpIn they-axis direction, the particles are under the vertical component forceFdy of drag force, buoyancyFb, gravity Fg, and Saffman lift forceFs, which can be given by(2)mpdupydt=Fdy+Fb-Fg-FsThe expressions of drag forceFd, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs [19, 23] are substituted into (1) and (2):(3)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(4)mpdupydt=6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2wheremp is the mass of particle,upx is the velocity of particle in thex-axis direction,μ is the aerodynamic viscosity coefficient,rp is the radius of particle, ugx is the velocity of gas in thex-axis direction,Vp is the volume of particle,p is the pressure in the flow channel,upy is the velocity of particle in they-axis direction, ugy is the velocity of gas in they-axis direction, ρg is the density of gas, and g is gravity acceleration.In thex-axis direction, when the particles are accelerated to the maximum speed, the horizontal acceleration will be 0 and the particles maintain a constant velocity:(5)dupxdt=0Substituting (5) into (3)(6)6πμrpugx-upx-Vp∂p∂x=0In they-axis direction, when the particles are in equilibrium state, the vertical acceleration is 0:(7)dupydt=0Substituting (7) into (4)(8)6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2=0The particles move in the pipe for a long time and gradually reach a steady state.upx andupy in (6) and (8) are thex-direction andy-direction velocity when the contaminant particles reach the steady state and also are the initial velocity of particles entering the sensor chip.


#### 2.2.2. Force and Motion Analysis of Particles Adsorbed on the Surface of the Chip

When the particles move inside the pipe, most of them get charged due to the collisions and frictions [24]. The charged particles additionally experience the electrical force from the sensor chip and the adhesion resistance from the gas. The electric field strength around the chip decreases along with the increase of distance, so most of the particles far away from the surface of the chip move normally in the pipe. Only the charged particles close to the chip are adsorbed by the electrical force generated on the sensor chip to overcome the gas adhesion resistance and accumulate on the surface of the chip. Particles far away from the surface of the chip are still forced byFd,Fb, Fg,Fp, andFs and flow horizontally along the pipe. The charged particles near the surface of the chip are affected by the electrical forceFe and the gas adhesion resistanceFr in addition to the effects ofFd,Fb, Fg,Fp, andFs, as shown in Figure 3. The electrical forceFe causes the particles to accumulate on the surface of the chip, and the adhesion resistanceFr prevents the particles from moving toward the surface of the chip.Figure 3
Schematic diagram of the forces when the particles are adsorbed to the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force;Fe: electrical force;Fr: adhesion resistance;d: distance between particle and chip; ugx: velocity of the gas inx-axis direction.The hot-film flow sensor consists of a heating resistor, an upstream temperature measuring resistor and a downstream temperature measuring resistor. When the sensor is energized, an electric field is generated around the heating resistor and the temperature measuring resistors in the middle of the chip. The heating resistor and the temperature measuring resistors are fabricated on the chip surface with the metal arrays. Although the total lateral extension of the metal arrays is significantly larger than those of the particles passing by, the width of a single metal wire (lateral extension) is small (only a few microns), which is similar to the particle size. So the electric field of a uniformly charged line source is utilized to estimate the electric force acting on the particles passing by. Assuming that the charge line density isλe and the particle charge isqp, the electrical forceFe of the charged particles [25] is expressed as(9)Fe=qpλe2πε0R-ywhereε0 is the vacuum dielectric constant andR is the radius of pipe.The particles additionally experience the adhesion resistance of the gas when they are adsorbed to the surface of the chip [26], which can be given by(10)Fr=πrp22CDρgupx2whereCD is the coefficient of resistance.According to Newton’s second law, in thex-axis direction, the particles still experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(11)mpdupxdt=Fdx+FpIn they-axis direction, the particles experience the electrical forceFe, adhesion resistanceFr, the vertical component forceFdy of drag force and Saffman lift forceFs, buoyancyFb, and gravity Fg are ignored [17], which can be given by(12)mpdupydt=Fe-Fr+Fdy-FsThe expressions of drag forceFd, pressure gradient forceFp, electrical forceFe, adhesion resistanceFr, and Saffman lift forceFs are substituted into (11) and (12):(13)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(14)mpdupydt=qpλe2πε0R-y-πrp22CDρgupx2+6πμrpugy-upy-6.44μρg1/2rp2ugx-upxdugxdy1/2The charged particles near the chip can be adsorbed on the surface of the chip in the situation that the resultant force of the electrical force and the vertical component force of drag force must be greater than or equal to the resultant force of the adhesion resistance and the Saffman lift force. The equation can be given by(15)Fe+Fdy≥Fr+FsThe electrical force of the particles increases along with the decrease of the distance. When the distance between the particle and the surface of the chip is less than a certain value,Fe+Fdy>Fr+Fs, the particle accelerates toward the surface of the chip. When the distance between the particle and the surface of the chip is larger than a certain value, Fe+Fdy<Fr+Fs, the particle cannot be adsorbed on the surface of the chip. Therefore, a critical distancedc exists at which the particle will be absorbed to the surface of the chip when the distance between the particle and the chip is less than the critical distance; otherwise, the particle will not be adsorbed, as shown in Figure 4.Figure 4
Schematic diagram of particles adsorbed to the surface of the chip.The force equation of the particles at the critical distancedc can be considered as(16)Fec+Fdy=Fr+FswhereFec is the electrical force of the particles at the critical distancedc.The expressions of electrical forceFe, the vertical component forceFdy of drag force, adhesion resistanceFr, and Saffman lift forceFs are substituted into (16):(17)qpλe2πε0dc+6πμrpugy-upy=πrp22CDρgupx2+6.44μρg1/2rp2ugx-upxdugxdy1/2wheredc is the critical distance between the particle and the surface of the chip.


### 2.3. Mathematical Model of Accumulation of Particles on Sensor Chip

The charged particles can be adsorbed and accumulated within the critical distancedc from the chip surface (o’ point) when they move in the pipe, as shown in Figure 5. They will be adsorbed by the electric field in the range of arc ‘MGN’. It means that the charged particles passing through arc ‘MGN’ will be adsorbed in thex-o-y plane. Seen from thez-o-y plane, the particles in the rectangular ‘ABCD’ will be adsorbed to accumulate on the surface of the chip.Figure 5
Schematic diagram of range of particles absorbed to the surface of the chip.The total mass of charged particles that can be adsorbed to the surface of the chip during timet is as follows [27]:(18)Mall=ηψVall=ηψlrdcupx-twhereηis the proportion of unipolar charged particles,Ψis the average mass concentration of particles,lr is the length of charged straight line, and upx- is the average velocity of the particles in the area ‘ABCD’.The velocity of the particles in thex-axis direction is solved by (6). Following from the Hagen–Poiseuille equation, ∂p/∂x and ugx can be given by(19)∂p∂x=ΔpL=8μqvπR4(20)ugx=Δp4μLR2-y2=2qvπR4R2-y2where Δp is the gas pressure difference,qv is the volumetric flow rate, andL is the length of pipe.Therefore, the expression of the particle velocity in thex-axis direction is as follows:(21)upx=ugx-Vp6πμrp∂p∂x=2qvπR4R2-y2-4qvVp3π2R4rpThe average particle velocity in the area ‘ABCD’ is given by(22)upx-=1dc∫R-dcRupxdy=qvπR4-23dc2+2Rdc-169rp2Substituting (22) into (18), the expression ofMall is(23)Mall=ηψlrdcupx¯t=ηψlrqvtπR4-23dc3+2Rdc2-169rp2dcA regularity is formed in the process of particle accumulation on the surface of the chip. The charged particles are mainly accumulated around the central region (the thin film resistance arrangement region) and keep a ‘U’-shaped distribution due to the electric field generated around the thin film resistor, as shown in Figure6. As the electric field in the edges of the electrodes is significantly increased, the cumulative thickness of the particles in the edge of the thin film resistor is larger than that in the middle of the thin film resistor in region A. The cumulative thickness of the particles in regions B, C, and D can be ignored because it is much smaller than that in region A. Assuming that the particles are equal-diameter spheres and the particles are accumulated regularly on the surface of the chip with positive italic rule. The cumulative state diagram is shown in Figure 7.Figure 6
Physical diagram of contaminant particles accumulated on the surface of the chip.Figure 7
Schematic diagram of the accumulation state of contaminant particles on the surface.The number of A-A cross-section particles is(24)N=i+i-1+⋯+i-j-1=ij-12j2+12jThe geometric relationship is(25)ht=2rpjsin⁡θ(26)b=a+2htcot⁡θ=2rpiThen the total number of particles accumulated on the surface of the chip is(27)Nall=lp2rpN=lp2rpaht+2ht2cot⁡θ4rp2sin⁡θ-ht28rp2sin2⁡θ+ht4rpsin⁡θwhereN is the number of A-A cross-section particles,lp is the particle ‘U’-shaped cumulative length,θis the bottom angle,a,b are the side lengths, andht is the cumulative thickness of the particles over time.According to the qualitative relationship of the particles themselves, the total number of particles (Nall) can also be expressed as(28)Nall=MallρpVpSubstituting (27) into (28)(29)ht2+2asin⁡θ+2rpsin⁡θ4cos⁡θ-1ht-16Mallrp3sin2⁡θ4cos⁡θ-1lpρpVp=0Solving (29)(30)ht=12Mallsin2⁡θ4cos⁡θ-1πlpρp+a+rp2sin2⁡θ4cos⁡θ-12-a+rpsin⁡θ4cos⁡θ-1Substituting (23) into (30)(31)ht=12ηψlrqvt-2/3dc3+2Rdc2-16/9rp2dcsin2⁡θ4cos⁡θ-1π2lpρpR4+a+rp2sin2⁡θ4cos⁡θ-12-a+rpsin⁡θ4cos⁡θ-1


## 2.1. Analysis of Accumulation Mechanism of Contaminant Particles

MEMS hot-film gas flow sensors are often used in harsh working environments where contaminants are contained. Contaminants can be accumulated on the surface of the sensor chip, affecting the accuracy of the sensor [18]. There are many forces that affect the accumulation of contaminant particles, such as air adhesion, air buoyancy, gravity of the particles themselves, Saffman lift force, electrical force, etc. [19, 20]. When the particles move inside the pipe, most of them get charged due to the collisions and frictions. Since an electric field is generated by the energized thin film resistors, the particles passing through the surface of the chip experience the electrical force. As the electric field decreases along with the increase of the distance, the influence of the electrical force on the particle accumulation also decreases along with the increase of the distance. Therefore, particles in a certain range of the flow channel above the surface of the chip will be accumulated by the electrical force generated on the chip surface, as shown in Figure 1. The particle motion is specifically considered in two stages: (1) the particles in the region I are transported horizontally in the pipe at a certain speed before entering the surface of the sensor chip, and the applied forces are in a balanced state; (2) when the particles flowing from the region I into the region II pass through the surface of the sensor chip, the original force balance of the particles is broken due to the new electrical force, resulting in the adsorption and accumulation on the surface of the chip. The particles far away from the surface of the chip (region III) are less affected by the electrical force and the particles will not be adsorbed.Figure 1
Schematic diagram of accumulation of contaminant particles on the surface of the chip.


## 2.2. Single Particle Adsorption Process Description

### 2.2.1. Basic Force and Motion Analysis of Particles in the Pipe

The contaminant particles in the pipe experience the basic force and motion [21, 22] before being affected by the electrical force on the surface of the chip. The flow process can be approximately described by a free and uniform suspension flow model that ignores the friction and collision between particles and between the particles and the pipe, and studies the motion discipline of single particle to investigate the situation of the entire flow channel. The particles moving in the horizontal pipe are mainly forced by drag forceFd of the gas to the particles, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs, as shown in Figure 2. In the horizontal direction, the particles move forward along the pipe for a long time or distance, reach a certain final velocity, and then maintain a uniform motion by the horizontal component forceFdx of drag forceFd and pressure gradient forceFp. In the vertical direction, the particles are transported in suspension by the vertical component forceFdy of drag forceFd, buoyancyFb, gravity Fg, and Saffman lift forceFs.Figure 2
Schematic diagram of the forces of particles in the pipe before approaching the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force; ugx: velocity of the gas in x-axis direction.According to Newton’s second law, in thex-axis direction, the particles experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(1)mpdupxdt=Fdx+FpIn they-axis direction, the particles are under the vertical component forceFdy of drag force, buoyancyFb, gravity Fg, and Saffman lift forceFs, which can be given by(2)mpdupydt=Fdy+Fb-Fg-FsThe expressions of drag forceFd, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs [19, 23] are substituted into (1) and (2):(3)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(4)mpdupydt=6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2wheremp is the mass of particle,upx is the velocity of particle in thex-axis direction,μ is the aerodynamic viscosity coefficient,rp is the radius of particle, ugx is the velocity of gas in thex-axis direction,Vp is the volume of particle,p is the pressure in the flow channel,upy is the velocity of particle in they-axis direction, ugy is the velocity of gas in they-axis direction, ρg is the density of gas, and g is gravity acceleration.In thex-axis direction, when the particles are accelerated to the maximum speed, the horizontal acceleration will be 0 and the particles maintain a constant velocity:(5)dupxdt=0Substituting (5) into (3)(6)6πμrpugx-upx-Vp∂p∂x=0In they-axis direction, when the particles are in equilibrium state, the vertical acceleration is 0:(7)dupydt=0Substituting (7) into (4)(8)6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2=0The particles move in the pipe for a long time and gradually reach a steady state.upx andupy in (6) and (8) are thex-direction andy-direction velocity when the contaminant particles reach the steady state and also are the initial velocity of particles entering the sensor chip.


### 2.2.2. Force and Motion Analysis of Particles Adsorbed on the Surface of the Chip

When the particles move inside the pipe, most of them get charged due to the collisions and frictions [24]. The charged particles additionally experience the electrical force from the sensor chip and the adhesion resistance from the gas. The electric field strength around the chip decreases along with the increase of distance, so most of the particles far away from the surface of the chip move normally in the pipe. Only the charged particles close to the chip are adsorbed by the electrical force generated on the sensor chip to overcome the gas adhesion resistance and accumulate on the surface of the chip. Particles far away from the surface of the chip are still forced byFd,Fb, Fg,Fp, andFs and flow horizontally along the pipe. The charged particles near the surface of the chip are affected by the electrical forceFe and the gas adhesion resistanceFr in addition to the effects ofFd,Fb, Fg,Fp, andFs, as shown in Figure 3. The electrical forceFe causes the particles to accumulate on the surface of the chip, and the adhesion resistanceFr prevents the particles from moving toward the surface of the chip.Figure 3
Schematic diagram of the forces when the particles are adsorbed to the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force;Fe: electrical force;Fr: adhesion resistance;d: distance between particle and chip; ugx: velocity of the gas inx-axis direction.The hot-film flow sensor consists of a heating resistor, an upstream temperature measuring resistor and a downstream temperature measuring resistor. When the sensor is energized, an electric field is generated around the heating resistor and the temperature measuring resistors in the middle of the chip. The heating resistor and the temperature measuring resistors are fabricated on the chip surface with the metal arrays. Although the total lateral extension of the metal arrays is significantly larger than those of the particles passing by, the width of a single metal wire (lateral extension) is small (only a few microns), which is similar to the particle size. So the electric field of a uniformly charged line source is utilized to estimate the electric force acting on the particles passing by. Assuming that the charge line density isλe and the particle charge isqp, the electrical forceFe of the charged particles [25] is expressed as(9)Fe=qpλe2πε0R-ywhereε0 is the vacuum dielectric constant andR is the radius of pipe.The particles additionally experience the adhesion resistance of the gas when they are adsorbed to the surface of the chip [26], which can be given by(10)Fr=πrp22CDρgupx2whereCD is the coefficient of resistance.According to Newton’s second law, in thex-axis direction, the particles still experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(11)mpdupxdt=Fdx+FpIn they-axis direction, the particles experience the electrical forceFe, adhesion resistanceFr, the vertical component forceFdy of drag force and Saffman lift forceFs, buoyancyFb, and gravity Fg are ignored [17], which can be given by(12)mpdupydt=Fe-Fr+Fdy-FsThe expressions of drag forceFd, pressure gradient forceFp, electrical forceFe, adhesion resistanceFr, and Saffman lift forceFs are substituted into (11) and (12):(13)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(14)mpdupydt=qpλe2πε0R-y-πrp22CDρgupx2+6πμrpugy-upy-6.44μρg1/2rp2ugx-upxdugxdy1/2The charged particles near the chip can be adsorbed on the surface of the chip in the situation that the resultant force of the electrical force and the vertical component force of drag force must be greater than or equal to the resultant force of the adhesion resistance and the Saffman lift force. The equation can be given by(15)Fe+Fdy≥Fr+FsThe electrical force of the particles increases along with the decrease of the distance. When the distance between the particle and the surface of the chip is less than a certain value,Fe+Fdy>Fr+Fs, the particle accelerates toward the surface of the chip. When the distance between the particle and the surface of the chip is larger than a certain value, Fe+Fdy<Fr+Fs, the particle cannot be adsorbed on the surface of the chip. Therefore, a critical distancedc exists at which the particle will be absorbed to the surface of the chip when the distance between the particle and the chip is less than the critical distance; otherwise, the particle will not be adsorbed, as shown in Figure 4.Figure 4
Schematic diagram of particles adsorbed to the surface of the chip.The force equation of the particles at the critical distancedc can be considered as(16)Fec+Fdy=Fr+FswhereFec is the electrical force of the particles at the critical distancedc.The expressions of electrical forceFe, the vertical component forceFdy of drag force, adhesion resistanceFr, and Saffman lift forceFs are substituted into (16):(17)qpλe2πε0dc+6πμrpugy-upy=πrp22CDρgupx2+6.44μρg1/2rp2ugx-upxdugxdy1/2wheredc is the critical distance between the particle and the surface of the chip.


## 2.2.1. Basic Force and Motion Analysis of Particles in the Pipe

The contaminant particles in the pipe experience the basic force and motion [21, 22] before being affected by the electrical force on the surface of the chip. The flow process can be approximately described by a free and uniform suspension flow model that ignores the friction and collision between particles and between the particles and the pipe, and studies the motion discipline of single particle to investigate the situation of the entire flow channel. The particles moving in the horizontal pipe are mainly forced by drag forceFd of the gas to the particles, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs, as shown in Figure 2. In the horizontal direction, the particles move forward along the pipe for a long time or distance, reach a certain final velocity, and then maintain a uniform motion by the horizontal component forceFdx of drag forceFd and pressure gradient forceFp. In the vertical direction, the particles are transported in suspension by the vertical component forceFdy of drag forceFd, buoyancyFb, gravity Fg, and Saffman lift forceFs.Figure 2
Schematic diagram of the forces of particles in the pipe before approaching the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force; ugx: velocity of the gas in x-axis direction.According to Newton’s second law, in thex-axis direction, the particles experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(1)mpdupxdt=Fdx+FpIn they-axis direction, the particles are under the vertical component forceFdy of drag force, buoyancyFb, gravity Fg, and Saffman lift forceFs, which can be given by(2)mpdupydt=Fdy+Fb-Fg-FsThe expressions of drag forceFd, buoyancyFb, gravity Fg, pressure gradient forceFp, and Saffman lift forceFs [19, 23] are substituted into (1) and (2):(3)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(4)mpdupydt=6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2wheremp is the mass of particle,upx is the velocity of particle in thex-axis direction,μ is the aerodynamic viscosity coefficient,rp is the radius of particle, ugx is the velocity of gas in thex-axis direction,Vp is the volume of particle,p is the pressure in the flow channel,upy is the velocity of particle in they-axis direction, ugy is the velocity of gas in they-axis direction, ρg is the density of gas, and g is gravity acceleration.In thex-axis direction, when the particles are accelerated to the maximum speed, the horizontal acceleration will be 0 and the particles maintain a constant velocity:(5)dupxdt=0Substituting (5) into (3)(6)6πμrpugx-upx-Vp∂p∂x=0In they-axis direction, when the particles are in equilibrium state, the vertical acceleration is 0:(7)dupydt=0Substituting (7) into (4)(8)6πμrpugy-upy+ρggVp-mpg-6.44μρg1/2rp2ugx-upxdugxdy1/2=0The particles move in the pipe for a long time and gradually reach a steady state.upx andupy in (6) and (8) are thex-direction andy-direction velocity when the contaminant particles reach the steady state and also are the initial velocity of particles entering the sensor chip.


## 2.2.2. Force and Motion Analysis of Particles Adsorbed on the Surface of the Chip

When the particles move inside the pipe, most of them get charged due to the collisions and frictions [24]. The charged particles additionally experience the electrical force from the sensor chip and the adhesion resistance from the gas. The electric field strength around the chip decreases along with the increase of distance, so most of the particles far away from the surface of the chip move normally in the pipe. Only the charged particles close to the chip are adsorbed by the electrical force generated on the sensor chip to overcome the gas adhesion resistance and accumulate on the surface of the chip. Particles far away from the surface of the chip are still forced byFd,Fb, Fg,Fp, andFs and flow horizontally along the pipe. The charged particles near the surface of the chip are affected by the electrical forceFe and the gas adhesion resistanceFr in addition to the effects ofFd,Fb, Fg,Fp, andFs, as shown in Figure 3. The electrical forceFe causes the particles to accumulate on the surface of the chip, and the adhesion resistanceFr prevents the particles from moving toward the surface of the chip.Figure 3
Schematic diagram of the forces when the particles are adsorbed to the surface of the chip.Fd: drag force;Fb: buoyancy; Fg: gravity;Fp: pressure gradient force;Fs: Saffman lift force;Fe: electrical force;Fr: adhesion resistance;d: distance between particle and chip; ugx: velocity of the gas inx-axis direction.The hot-film flow sensor consists of a heating resistor, an upstream temperature measuring resistor and a downstream temperature measuring resistor. When the sensor is energized, an electric field is generated around the heating resistor and the temperature measuring resistors in the middle of the chip. The heating resistor and the temperature measuring resistors are fabricated on the chip surface with the metal arrays. Although the total lateral extension of the metal arrays is significantly larger than those of the particles passing by, the width of a single metal wire (lateral extension) is small (only a few microns), which is similar to the particle size. So the electric field of a uniformly charged line source is utilized to estimate the electric force acting on the particles passing by. Assuming that the charge line density isλe and the particle charge isqp, the electrical forceFe of the charged particles [25] is expressed as(9)Fe=qpλe2πε0R-ywhereε0 is the vacuum dielectric constant andR is the radius of pipe.The particles additionally experience the adhesion resistance of the gas when they are adsorbed to the surface of the chip [26], which can be given by(10)Fr=πrp22CDρgupx2whereCD is the coefficient of resistance.According to Newton’s second law, in thex-axis direction, the particles still experience the horizontal component forceFdx of drag force and pressure gradient forceFp, which can be expressed as(11)mpdupxdt=Fdx+FpIn they-axis direction, the particles experience the electrical forceFe, adhesion resistanceFr, the vertical component forceFdy of drag force and Saffman lift forceFs, buoyancyFb, and gravity Fg are ignored [17], which can be given by(12)mpdupydt=Fe-Fr+Fdy-FsThe expressions of drag forceFd, pressure gradient forceFp, electrical forceFe, adhesion resistanceFr, and Saffman lift forceFs are substituted into (11) and (12):(13)mpdupxdt=6πμrpugx-upx-Vp∂p∂x(14)mpdupydt=qpλe2πε0R-y-πrp22CDρgupx2+6πμrpugy-upy-6.44μρg1/2rp2ugx-upxdugxdy1/2The charged particles near the chip can be adsorbed on the surface of the chip in the situation that the resultant force of the electrical force and the vertical component force of drag force must be greater than or equal to the resultant force of the adhesion resistance and the Saffman lift force. The equation can be given by(15)Fe+Fdy≥Fr+FsThe electrical force of the particles increases along with the decrease of the distance. When the distance between the particle and the surface of the chip is less than a certain value,Fe+Fdy>Fr+Fs, the particle accelerates toward the surface of the chip. When the distance between the particle and the surface of the chip is larger than a certain value, Fe+Fdy<Fr+Fs, the particle cannot be adsorbed on the surface of the chip. Therefore, a critical distancedc exists at which the particle will be absorbed to the surface of the chip when the distance between the particle and the chip is less than the critical distance; otherwise, the particle will not be adsorbed, as shown in Figure 4.Figure 4
Schematic diagram of particles adsorbed to the surface of the chip.The force equation of the particles at the critical distancedc can be considered as(16)Fec+Fdy=Fr+FswhereFec is the electrical force of the particles at the critical distancedc.The expressions of electrical forceFe, the vertical component forceFdy of drag force, adhesion resistanceFr, and Saffman lift forceFs are substituted into (16):(17)qpλe2πε0dc+6πμrpugy-upy=πrp22CDρgupx2+6.44μρg1/2rp2ugx-upxdugxdy1/2wheredc is the critical distance between the particle and the surface of the chip.


## 2.3. Mathematical Model of Accumulation of Particles on Sensor Chip

The charged particles can be adsorbed and accumulated within the critical distancedc from the chip surface (o’ point) when they move in the pipe, as shown in Figure 5. They will be adsorbed by the electric field in the range of arc ‘MGN’. It means that the charged particles passing through arc ‘MGN’ will be adsorbed in thex-o-y plane. Seen from thez-o-y plane, the particles in the rectangular ‘ABCD’ will be adsorbed to accumulate on the surface of the chip.Figure 5
Schematic diagram of range of particles absorbed to the surface of the chip.The total mass of charged particles that can be adsorbed to the surface of the chip during timet is as follows [27]:(18)Mall=ηψVall=ηψlrdcupx-twhereηis the proportion of unipolar charged particles,Ψis the average mass concentration of particles,lr is the length of charged straight line, and upx- is the average velocity of the particles in the area ‘ABCD’.The velocity of the particles in thex-axis direction is solved by (6). Following from the Hagen–Poiseuille equation, ∂p/∂x and ugx can be given by(19)∂p∂x=ΔpL=8μqvπR4(20)ugx=Δp4μLR2-y2=2qvπR4R2-y2where Δp is the gas pressure difference,qv is the volumetric flow rate, andL is the length of pipe.Therefore, the expression of the particle velocity in thex-axis direction is as follows:(21)upx=ugx-Vp6πμrp∂p∂x=2qvπR4R2-y2-4qvVp3π2R4rpThe average particle velocity in the area ‘ABCD’ is given by(22)upx-=1dc∫R-dcRupxdy=qvπR4-23dc2+2Rdc-169rp2Substituting (22) into (18), the expression ofMall is(23)Mall=ηψlrdcupx¯t=ηψlrqvtπR4-23dc3+2Rdc2-169rp2dcA regularity is formed in the process of particle accumulation on the surface of the chip. The charged particles are mainly accumulated around the central region (the thin film resistance arrangement region) and keep a ‘U’-shaped distribution due to the electric field generated around the thin film resistor, as shown in Figure6. As the electric field in the edges of the electrodes is significantly increased, the cumulative thickness of the particles in the edge of the thin film resistor is larger than that in the middle of the thin film resistor in region A. The cumulative thickness of the particles in regions B, C, and D can be ignored because it is much smaller than that in region A. Assuming that the particles are equal-diameter spheres and the particles are accumulated regularly on the surface of the chip with positive italic rule. The cumulative state diagram is shown in Figure 7.Figure 6
Physical diagram of contaminant particles accumulated on the surface of the chip.Figure 7
Schematic diagram of the accumulation state of contaminant particles on the surface.The number of A-A cross-section particles is(24)N=i+i-1+⋯+i-j-1=ij-12j2+12jThe geometric relationship is(25)ht=2rpjsin⁡θ(26)b=a+2htcot⁡θ=2rpiThen the total number of particles accumulated on the surface of the chip is(27)Nall=lp2rpN=lp2rpaht+2ht2cot⁡θ4rp2sin⁡θ-ht28rp2sin2⁡θ+ht4rpsin⁡θwhereN is the number of A-A cross-section particles,lp is the particle ‘U’-shaped cumulative length,θis the bottom angle,a,b are the side lengths, andht is the cumulative thickness of the particles over time.According to the qualitative relationship of the particles themselves, the total number of particles (Nall) can also be expressed as(28)Nall=MallρpVpSubstituting (27) into (28)(29)ht2+2asin⁡θ+2rpsin⁡θ4cos⁡θ-1ht-16Mallrp3sin2⁡θ4cos⁡θ-1lpρpVp=0Solving (29)(30)ht=12Mallsin2⁡θ4cos⁡θ-1πlpρp+a+rp2sin2⁡θ4cos⁡θ-12-a+rpsin⁡θ4cos⁡θ-1Substituting (23) into (30)(31)ht=12ηψlrqvt-2/3dc3+2Rdc2-16/9rp2dcsin2⁡θ4cos⁡θ-1π2lpρpR4+a+rp2sin2⁡θ4cos⁡θ-12-a+rpsin⁡θ4cos⁡θ-1


## 3. Basic Test of Adsorption Accumulation and Reverse Calculation of Electric Parameter

### 3.1. Test Scheme and Platform

#### 3.1.1. Microsilicon Powder Test

In order to study the cause of the accumulation of tiny particles on the surface of the MEMS flow sensor chip, the contamination environment was simulated and the microsilicon powder test scheme was designed. The test was divided into Scheme I and Scheme II, as shown in Table1. In Scheme I, the No.1 sensor was energized while the No.2 sensor was not energized to compare the effect of energization on the accumulation of contaminant particles. In Scheme II, the chip of No.1 sensor was located at the top of the pipe, while the chip of No.3 sensor was located at the bottom of the pipe, to study the effect of chip position on the accumulation of contaminant particles.Table 1
MEMS hot-film flow sensor contaminant accumulation test scheme.
Scheme number Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium I Testing the effect of energization on contaminant accumulation 1 Energized 0.8 Air-micro-silica two-phase flow 2 No energized II Testing the effect of chip position on contaminant accumulation 1 Chip located at the top 3 Chip located at the bottomThe test circuit diagram and the physical diagram are shown in Figure8. The throttle valves 10, 11, and 12 are adjusted to control the flow through the sensor. The throttle valve 4 is adjusted to control the flow through the powder generator 7, thereby controlling the concentration of microsilica powder in the gas. The microsilica powder passes through the test sensors after being fully mixed with the gas in the mixing chamber 9. The concentration of the microsilicon powder is detected by an aerosol particle monitor 18 manufactured by TSI Company of the United States with model number DUSTTRAKTM II. During the test, the gas supply pressure is 0.1 MPa.Figure 8
Circuit and physical diagram of microsilicon powder test. 1: air source; 2: regulator; 3: ball valve; 4, 5, 10, 11, and 12: Throttle valves; 6: microsilica powder; 7: powder generator; 8: motor; 9: mixing chamber; 13, 14, and 15: No.1, No.2, and No.3 sensors; 16: powder recycling; 17: gas tank; 18: aerosol particle monitor.
(a)
Circuit diagram (b)
Physical diagramThe particles accumulated on the surface of the chip are generally considered to be measured by the laser due to their microsizes. Although the laser can measure the height of the contaminants, the overall morphology of the contaminants cannot be observed. After investigation, the digital microscope VHX-1000 of Keyence is finally used for the measurement. This microscope can achieve both 2D and 3D images. The distribution and cumulative thickness of microsilica particles on the surface of MEMS flow sensor chip can be shown clearly by the microscope.


#### 3.1.2. Air Test

To study the trend of the flow sensor accuracy over time under different filtration accuracy conditions, the sensors were tested with only air and monitored for a long time. The flow rates of the sensor and the morphology characteristics of the chip surface were compared by setting the filters with different filtration levels. The test scheme is shown in Table2. The test circuit diagram and the physical diagram are shown in Figure 9. A high-accuracy filter is attached in the front of the No.4 sensor, the model number is SFD100 and the filtration level is 0.01 μm. The filter used in the front of the No.5 sensor comes from the pneumatic modular FRL (air filter, regulator, and lubricator), the model number is AF60, and the filtration level is 5.0 μm.Table 2
Different filtration accuracy test scheme.
Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium Testing the effect of filtration accuracy on contaminant accumulation 4 High-accuracy filter 0.8 Clean air(0.01μm) 5 Low-accuracy filter Normal air(5.0μm)Figure 9
Circuit and physical diagram of air test. 1: air source; 2: regulator; 3: ball valve; 4 and 5: Throttle valves; 6: high-accuracy filter; 7 and 8: No.4 and No.5 sensors.


### 3.2. Test Results

#### 3.2.1. Microsilica Powder Test Results

The test was carried out for a total of 180 hours. The flow rate of the sensor and the cumulative thickness of the microsilica powder on the chip surface were measured at 60h, 120h, and 180h, respectively. The values are shown in Table3. The cumulative thickness of microsilica powder measured by the digital microscope is shown in Figure 10. As can be seen from Table 3, when the sensors are tested for 180 hours, the flow rate of No.1 sensor which is energized declines by 6.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 43.333%. The flow rate of No.2 sensor which is not energized declines by 1.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 10%. The flow rate of No.3 sensor which is placed opposite to No.1 sensor declines by 5.7 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 38%. The cumulative thickness of the particles on the chip surface of No.1 sensor is 42.864 μm, No.2 sensor is 12.343 μm, and No.3 sensor is 39.801 μm, respectively. The decrease amplitude of flow rate and the cumulative thickness of the particles on No.1 sensor are approximately four times that of No.2 sensor. The particles are accumulated around the central region (the thin film resistance arrangement region) of the chip surface when the sensor is energized, while the particles are irregularly accumulated and relatively few when the sensor is not energized. These results show that the accumulation of contaminant particles significantly increases under energization, which indicates that an electric field is generated on the sensor chip and exacerbates particle adsorption. The differences of the decrease amplitude of the flow rate and the cumulative thickness of the particles between No.1 sensor and No.3 sensor are negligible. It shows that the gravity of the particles has a little effect on the accumulation of the particles.Table 3
Flow rate measured by No.1~No.3 sensors and cumulative thickness of particles on chip surface.
Test time(h) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.1 No.2 No.3 No.1 No.2 No.3 60 15 11.8 14.6 12.3 25.893 3.086 19.526 120 15 10.2 14.0 11.4 33.997 7.026 27.742 180 15 8.5 13.5 9.3 42.864 12.343 39.801Figure 10
Cumulative thickness diagram of microsilicon powder on No.1~No.3 sensors.


#### 3.2.2. Air Test Results

The test was carried out for a total of 195 days. The flow rate of the sensor and the morphology on the chip surface were measured at 39 days and 195 days, respectively. The values are shown in Table4. The cumulative thickness of contaminants measured by the digital microscope is shown in Figure 11. As can be seen from Table 4, when the sensors are tested for 195 days, the flow rate of No.4 sensor with high-accuracy filter does not decrease compared to the reference flow rate of 15 L/min. The flow rate of No.5 sensor with low-accuracy filter declines by 0.3 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 2%. There is no obvious abnormality on the surface of No.4 sensor, while the oil mist is accumulated on the surface of No.5 sensor and the cumulative thickness is 2.325μm. The results show that the oil mist in the air is easily adsorbed on the surface of the sensor chip which do not pass through the high-accuracy filter. It illustrates that the sensors using high-accuracy filters can be uncontaminated and the accuracy will remain stable for a long time.Table 4
Flow rate measured by No.4 and No.5 sensors and cumulative thickness of contaminants on chip surface.
Test time(day) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.4 No.5 No.4 No.5 39 15 15 14.9 0 1.323 195 15 15 14.7 0 2.325Figure 11
Morphology and cumulative thickness diagram on No.4 and No.5 sensors.


### 3.3. Reverse Calculation of Electric Parameter

It can be known from (31) that the cumulative thicknessht of the contaminant particles on the surface of the MEMS hot-film gas flow sensor chip is related to the critical distancedc. The critical distancedc can be solved by (17), where the electric parameterλe (the charge line density) is unknown. Due to the fact that the structure of the thin film resistance on the chip surface is quite complex and the size is small, the electric parameter is difficult to measure directly or calculate theoretically. Therefore, it is necessary to reversely calculate the line densityλe based on the data measured by the basic test. When the contaminant particles enter the surface of the chip, the velocity of the gas and the particle in thex-direction are shown in (20) and (21), respectively. And the velocity in they-direction is approximately zero. The expression of the charge line densityλe can be obtained by substituting (20) and (21) into the (17):(32)λe=-24πμrpqvε0dc3qpR4+48πμrpqvε0dc2qpR3+45.787qvrp4ε0dcR6qpμρgqvR-dcπ-64πμqvrp3ε0dc3qpR4After the charge line densityλe is calculated by the experimental data, it can be used as a constant and substituted into (17) to obtain the solution equation ofdc:(33)12μrpqvdc3R4-24μrpqvdc2R3-22.893qvrp4dcπR6μρgqvR-dcπ+32μqvrp3dc3R4+qpλe2πε0=0The values of the parameters in (31), (32), and (33) are shown in Table 5. The chargeqp and the proportionη of the microsilica particles are measured by the Millikan method [28]. The particle diameter is measured by a laser particle size analyzer with model number Mastersizer 2000. The concentration of the microsilicon powder is detected by an aerosol particle monitor with model number DUSTTRAKTM II. The side lengtha is approximately 0 as it is much smaller than the lengthb. The particle ‘U’-shaped cumulative length and the length of charged straight line are measured by the digital microscope VHX-1000 of Keyence. Other parameter values are constant.Table 5
Parameter values in the theoretical formula.
Parameter Value Unit q p 6.4×10−17 C η 0.22 d p 3.311 μm Ψ 5×10−6 kg/m3 a 0 m l p 1.2×10−3 m l r 8×10−4 m ε 0 8.85×10−12 F/m μ 17.9×10−6 Pas ρ g 1.21 kg/m3 ρ p 360 kg/m3 R 4×10−3 m θ 60 °Taking microsilica powder accumulation test of No.1 sensor as an example, the critical distancedc can be calculated by (31) based on the cumulative thickness of the particles measured at 60h, 120h, and 180h, respectively. The data is shown in Table 6. Then, the corresponding value of the charge line densityλe is solved by (32). As a result, the average value of the charge line densityλe is 5.172×10−10 C/m.Table 6
Value ofdc and λe calculated by the accumulation test of No.1 sensor.
Test time(h) Cumulative thickness on No.1 sensor(μm) Value ofdc based on Eq. (31)(μm) Value ofλe based on Eq. (32)(C/m) 60 25.893 66.893 5.706×10−10 120 33.997 61.351 4.803×10−10 180 42.864 62.651 5.008×10−10


## 3.1. Test Scheme and Platform

### 3.1.1. Microsilicon Powder Test

In order to study the cause of the accumulation of tiny particles on the surface of the MEMS flow sensor chip, the contamination environment was simulated and the microsilicon powder test scheme was designed. The test was divided into Scheme I and Scheme II, as shown in Table1. In Scheme I, the No.1 sensor was energized while the No.2 sensor was not energized to compare the effect of energization on the accumulation of contaminant particles. In Scheme II, the chip of No.1 sensor was located at the top of the pipe, while the chip of No.3 sensor was located at the bottom of the pipe, to study the effect of chip position on the accumulation of contaminant particles.Table 1
MEMS hot-film flow sensor contaminant accumulation test scheme.
Scheme number Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium I Testing the effect of energization on contaminant accumulation 1 Energized 0.8 Air-micro-silica two-phase flow 2 No energized II Testing the effect of chip position on contaminant accumulation 1 Chip located at the top 3 Chip located at the bottomThe test circuit diagram and the physical diagram are shown in Figure8. The throttle valves 10, 11, and 12 are adjusted to control the flow through the sensor. The throttle valve 4 is adjusted to control the flow through the powder generator 7, thereby controlling the concentration of microsilica powder in the gas. The microsilica powder passes through the test sensors after being fully mixed with the gas in the mixing chamber 9. The concentration of the microsilicon powder is detected by an aerosol particle monitor 18 manufactured by TSI Company of the United States with model number DUSTTRAKTM II. During the test, the gas supply pressure is 0.1 MPa.Figure 8
Circuit and physical diagram of microsilicon powder test. 1: air source; 2: regulator; 3: ball valve; 4, 5, 10, 11, and 12: Throttle valves; 6: microsilica powder; 7: powder generator; 8: motor; 9: mixing chamber; 13, 14, and 15: No.1, No.2, and No.3 sensors; 16: powder recycling; 17: gas tank; 18: aerosol particle monitor.
(a)
Circuit diagram (b)
Physical diagramThe particles accumulated on the surface of the chip are generally considered to be measured by the laser due to their microsizes. Although the laser can measure the height of the contaminants, the overall morphology of the contaminants cannot be observed. After investigation, the digital microscope VHX-1000 of Keyence is finally used for the measurement. This microscope can achieve both 2D and 3D images. The distribution and cumulative thickness of microsilica particles on the surface of MEMS flow sensor chip can be shown clearly by the microscope.


### 3.1.2. Air Test

To study the trend of the flow sensor accuracy over time under different filtration accuracy conditions, the sensors were tested with only air and monitored for a long time. The flow rates of the sensor and the morphology characteristics of the chip surface were compared by setting the filters with different filtration levels. The test scheme is shown in Table2. The test circuit diagram and the physical diagram are shown in Figure 9. A high-accuracy filter is attached in the front of the No.4 sensor, the model number is SFD100 and the filtration level is 0.01 μm. The filter used in the front of the No.5 sensor comes from the pneumatic modular FRL (air filter, regulator, and lubricator), the model number is AF60, and the filtration level is 5.0 μm.Table 2
Different filtration accuracy test scheme.
Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium Testing the effect of filtration accuracy on contaminant accumulation 4 High-accuracy filter 0.8 Clean air(0.01μm) 5 Low-accuracy filter Normal air(5.0μm)Figure 9
Circuit and physical diagram of air test. 1: air source; 2: regulator; 3: ball valve; 4 and 5: Throttle valves; 6: high-accuracy filter; 7 and 8: No.4 and No.5 sensors.


## 3.1.1. Microsilicon Powder Test

In order to study the cause of the accumulation of tiny particles on the surface of the MEMS flow sensor chip, the contamination environment was simulated and the microsilicon powder test scheme was designed. The test was divided into Scheme I and Scheme II, as shown in Table1. In Scheme I, the No.1 sensor was energized while the No.2 sensor was not energized to compare the effect of energization on the accumulation of contaminant particles. In Scheme II, the chip of No.1 sensor was located at the top of the pipe, while the chip of No.3 sensor was located at the bottom of the pipe, to study the effect of chip position on the accumulation of contaminant particles.Table 1
MEMS hot-film flow sensor contaminant accumulation test scheme.
Scheme number Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium I Testing the effect of energization on contaminant accumulation 1 Energized 0.8 Air-micro-silica two-phase flow 2 No energized II Testing the effect of chip position on contaminant accumulation 1 Chip located at the top 3 Chip located at the bottomThe test circuit diagram and the physical diagram are shown in Figure8. The throttle valves 10, 11, and 12 are adjusted to control the flow through the sensor. The throttle valve 4 is adjusted to control the flow through the powder generator 7, thereby controlling the concentration of microsilica powder in the gas. The microsilica powder passes through the test sensors after being fully mixed with the gas in the mixing chamber 9. The concentration of the microsilicon powder is detected by an aerosol particle monitor 18 manufactured by TSI Company of the United States with model number DUSTTRAKTM II. During the test, the gas supply pressure is 0.1 MPa.Figure 8
Circuit and physical diagram of microsilicon powder test. 1: air source; 2: regulator; 3: ball valve; 4, 5, 10, 11, and 12: Throttle valves; 6: microsilica powder; 7: powder generator; 8: motor; 9: mixing chamber; 13, 14, and 15: No.1, No.2, and No.3 sensors; 16: powder recycling; 17: gas tank; 18: aerosol particle monitor.
(a)
Circuit diagram (b)
Physical diagramThe particles accumulated on the surface of the chip are generally considered to be measured by the laser due to their microsizes. Although the laser can measure the height of the contaminants, the overall morphology of the contaminants cannot be observed. After investigation, the digital microscope VHX-1000 of Keyence is finally used for the measurement. This microscope can achieve both 2D and 3D images. The distribution and cumulative thickness of microsilica particles on the surface of MEMS flow sensor chip can be shown clearly by the microscope.


## 3.1.2. Air Test

To study the trend of the flow sensor accuracy over time under different filtration accuracy conditions, the sensors were tested with only air and monitored for a long time. The flow rates of the sensor and the morphology characteristics of the chip surface were compared by setting the filters with different filtration levels. The test scheme is shown in Table2. The test circuit diagram and the physical diagram are shown in Figure 9. A high-accuracy filter is attached in the front of the No.4 sensor, the model number is SFD100 and the filtration level is 0.01 μm. The filter used in the front of the No.5 sensor comes from the pneumatic modular FRL (air filter, regulator, and lubricator), the model number is AF60, and the filtration level is 5.0 μm.Table 2
Different filtration accuracy test scheme.
Test purpose Sensor number Scheme description Test parameter Flow(L/min) Test medium Testing the effect of filtration accuracy on contaminant accumulation 4 High-accuracy filter 0.8 Clean air(0.01μm) 5 Low-accuracy filter Normal air(5.0μm)Figure 9
Circuit and physical diagram of air test. 1: air source; 2: regulator; 3: ball valve; 4 and 5: Throttle valves; 6: high-accuracy filter; 7 and 8: No.4 and No.5 sensors.


## 3.2. Test Results

### 3.2.1. Microsilica Powder Test Results

The test was carried out for a total of 180 hours. The flow rate of the sensor and the cumulative thickness of the microsilica powder on the chip surface were measured at 60h, 120h, and 180h, respectively. The values are shown in Table3. The cumulative thickness of microsilica powder measured by the digital microscope is shown in Figure 10. As can be seen from Table 3, when the sensors are tested for 180 hours, the flow rate of No.1 sensor which is energized declines by 6.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 43.333%. The flow rate of No.2 sensor which is not energized declines by 1.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 10%. The flow rate of No.3 sensor which is placed opposite to No.1 sensor declines by 5.7 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 38%. The cumulative thickness of the particles on the chip surface of No.1 sensor is 42.864 μm, No.2 sensor is 12.343 μm, and No.3 sensor is 39.801 μm, respectively. The decrease amplitude of flow rate and the cumulative thickness of the particles on No.1 sensor are approximately four times that of No.2 sensor. The particles are accumulated around the central region (the thin film resistance arrangement region) of the chip surface when the sensor is energized, while the particles are irregularly accumulated and relatively few when the sensor is not energized. These results show that the accumulation of contaminant particles significantly increases under energization, which indicates that an electric field is generated on the sensor chip and exacerbates particle adsorption. The differences of the decrease amplitude of the flow rate and the cumulative thickness of the particles between No.1 sensor and No.3 sensor are negligible. It shows that the gravity of the particles has a little effect on the accumulation of the particles.Table 3
Flow rate measured by No.1~No.3 sensors and cumulative thickness of particles on chip surface.
Test time(h) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.1 No.2 No.3 No.1 No.2 No.3 60 15 11.8 14.6 12.3 25.893 3.086 19.526 120 15 10.2 14.0 11.4 33.997 7.026 27.742 180 15 8.5 13.5 9.3 42.864 12.343 39.801Figure 10
Cumulative thickness diagram of microsilicon powder on No.1~No.3 sensors.


### 3.2.2. Air Test Results

The test was carried out for a total of 195 days. The flow rate of the sensor and the morphology on the chip surface were measured at 39 days and 195 days, respectively. The values are shown in Table4. The cumulative thickness of contaminants measured by the digital microscope is shown in Figure 11. As can be seen from Table 4, when the sensors are tested for 195 days, the flow rate of No.4 sensor with high-accuracy filter does not decrease compared to the reference flow rate of 15 L/min. The flow rate of No.5 sensor with low-accuracy filter declines by 0.3 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 2%. There is no obvious abnormality on the surface of No.4 sensor, while the oil mist is accumulated on the surface of No.5 sensor and the cumulative thickness is 2.325μm. The results show that the oil mist in the air is easily adsorbed on the surface of the sensor chip which do not pass through the high-accuracy filter. It illustrates that the sensors using high-accuracy filters can be uncontaminated and the accuracy will remain stable for a long time.Table 4
Flow rate measured by No.4 and No.5 sensors and cumulative thickness of contaminants on chip surface.
Test time(day) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.4 No.5 No.4 No.5 39 15 15 14.9 0 1.323 195 15 15 14.7 0 2.325Figure 11
Morphology and cumulative thickness diagram on No.4 and No.5 sensors.


## 3.2.1. Microsilica Powder Test Results

The test was carried out for a total of 180 hours. The flow rate of the sensor and the cumulative thickness of the microsilica powder on the chip surface were measured at 60h, 120h, and 180h, respectively. The values are shown in Table3. The cumulative thickness of microsilica powder measured by the digital microscope is shown in Figure 10. As can be seen from Table 3, when the sensors are tested for 180 hours, the flow rate of No.1 sensor which is energized declines by 6.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 43.333%. The flow rate of No.2 sensor which is not energized declines by 1.5 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 10%. The flow rate of No.3 sensor which is placed opposite to No.1 sensor declines by 5.7 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 38%. The cumulative thickness of the particles on the chip surface of No.1 sensor is 42.864 μm, No.2 sensor is 12.343 μm, and No.3 sensor is 39.801 μm, respectively. The decrease amplitude of flow rate and the cumulative thickness of the particles on No.1 sensor are approximately four times that of No.2 sensor. The particles are accumulated around the central region (the thin film resistance arrangement region) of the chip surface when the sensor is energized, while the particles are irregularly accumulated and relatively few when the sensor is not energized. These results show that the accumulation of contaminant particles significantly increases under energization, which indicates that an electric field is generated on the sensor chip and exacerbates particle adsorption. The differences of the decrease amplitude of the flow rate and the cumulative thickness of the particles between No.1 sensor and No.3 sensor are negligible. It shows that the gravity of the particles has a little effect on the accumulation of the particles.Table 3
Flow rate measured by No.1~No.3 sensors and cumulative thickness of particles on chip surface.
Test time(h) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.1 No.2 No.3 No.1 No.2 No.3 60 15 11.8 14.6 12.3 25.893 3.086 19.526 120 15 10.2 14.0 11.4 33.997 7.026 27.742 180 15 8.5 13.5 9.3 42.864 12.343 39.801Figure 10
Cumulative thickness diagram of microsilicon powder on No.1~No.3 sensors.


## 3.2.2. Air Test Results

The test was carried out for a total of 195 days. The flow rate of the sensor and the morphology on the chip surface were measured at 39 days and 195 days, respectively. The values are shown in Table4. The cumulative thickness of contaminants measured by the digital microscope is shown in Figure 11. As can be seen from Table 4, when the sensors are tested for 195 days, the flow rate of No.4 sensor with high-accuracy filter does not decrease compared to the reference flow rate of 15 L/min. The flow rate of No.5 sensor with low-accuracy filter declines by 0.3 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 2%. There is no obvious abnormality on the surface of No.4 sensor, while the oil mist is accumulated on the surface of No.5 sensor and the cumulative thickness is 2.325μm. The results show that the oil mist in the air is easily adsorbed on the surface of the sensor chip which do not pass through the high-accuracy filter. It illustrates that the sensors using high-accuracy filters can be uncontaminated and the accuracy will remain stable for a long time.Table 4
Flow rate measured by No.4 and No.5 sensors and cumulative thickness of contaminants on chip surface.
Test time(day) Sensor flow rate(L/min) Particle cumulative thickness(μm) Ref. No.4 No.5 No.4 No.5 39 15 15 14.9 0 1.323 195 15 15 14.7 0 2.325Figure 11
Morphology and cumulative thickness diagram on No.4 and No.5 sensors.


## 3.3. Reverse Calculation of Electric Parameter

It can be known from (31) that the cumulative thicknessht of the contaminant particles on the surface of the MEMS hot-film gas flow sensor chip is related to the critical distancedc. The critical distancedc can be solved by (17), where the electric parameterλe (the charge line density) is unknown. Due to the fact that the structure of the thin film resistance on the chip surface is quite complex and the size is small, the electric parameter is difficult to measure directly or calculate theoretically. Therefore, it is necessary to reversely calculate the line densityλe based on the data measured by the basic test. When the contaminant particles enter the surface of the chip, the velocity of the gas and the particle in thex-direction are shown in (20) and (21), respectively. And the velocity in they-direction is approximately zero. The expression of the charge line densityλe can be obtained by substituting (20) and (21) into the (17):(32)λe=-24πμrpqvε0dc3qpR4+48πμrpqvε0dc2qpR3+45.787qvrp4ε0dcR6qpμρgqvR-dcπ-64πμqvrp3ε0dc3qpR4After the charge line densityλe is calculated by the experimental data, it can be used as a constant and substituted into (17) to obtain the solution equation ofdc:(33)12μrpqvdc3R4-24μrpqvdc2R3-22.893qvrp4dcπR6μρgqvR-dcπ+32μqvrp3dc3R4+qpλe2πε0=0The values of the parameters in (31), (32), and (33) are shown in Table 5. The chargeqp and the proportionη of the microsilica particles are measured by the Millikan method [28]. The particle diameter is measured by a laser particle size analyzer with model number Mastersizer 2000. The concentration of the microsilicon powder is detected by an aerosol particle monitor with model number DUSTTRAKTM II. The side lengtha is approximately 0 as it is much smaller than the lengthb. The particle ‘U’-shaped cumulative length and the length of charged straight line are measured by the digital microscope VHX-1000 of Keyence. Other parameter values are constant.Table 5
Parameter values in the theoretical formula.
Parameter Value Unit q p 6.4×10−17 C η 0.22 d p 3.311 μm Ψ 5×10−6 kg/m3 a 0 m l p 1.2×10−3 m l r 8×10−4 m ε 0 8.85×10−12 F/m μ 17.9×10−6 Pas ρ g 1.21 kg/m3 ρ p 360 kg/m3 R 4×10−3 m θ 60 °Taking microsilica powder accumulation test of No.1 sensor as an example, the critical distancedc can be calculated by (31) based on the cumulative thickness of the particles measured at 60h, 120h, and 180h, respectively. The data is shown in Table 6. Then, the corresponding value of the charge line densityλe is solved by (32). As a result, the average value of the charge line densityλe is 5.172×10−10 C/m.Table 6
Value ofdc and λe calculated by the accumulation test of No.1 sensor.
Test time(h) Cumulative thickness on No.1 sensor(μm) Value ofdc based on Eq. (31)(μm) Value ofλe based on Eq. (32)(C/m) 60 25.893 66.893 5.706×10−10 120 33.997 61.351 4.803×10−10 180 42.864 62.651 5.008×10−10


## 4. Verification Test and Analysis of Contaminant Accumulation Model

### 4.1. Verification Test and Result

In order to verify the correctness of the theoretical model, the atmospheric mild contamination test was simulated. The concentration of the microsilica powder was adjusted to 100μg/m3 and 200 μg/m3, respectively. The test scheme is shown in Table 7. In this test, the cumulative thickness of the particles on the surface of the chip was tested every 300 hours, and a total of four cycles were tested. The flow rates measured by the sensors at different time are shown in Table 8. As can be seen from Table 8, when the sensors are tested for 1200 hours, the flow rate of No.6 sensor declines by 1.8 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 12%. The flow rate of No.7 sensor declines by 3.1 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 20.667%. When the gas flow rates are 1 L/min and 5 L/min, respectively, the values of the critical distancedc can be calculated based on (33) to be 56.922 μm and 25.406 μm. The theoretical values of the cumulative thickness of the microsilica powder on the surface of the sensor chip at different time can be calculated by substituting thedc value into (31). The theoretical calculation values and test measurement values of the cumulative thickness of the microsilica powder on No.6 and No.7 sensors at different time are shown in Table 9. The comparison diagram is shown in Figure 12. The cumulative thickness of microsilica powder measured by the digital microscope is shown in Figure 13. After 1200-hour test, the cumulative thickness of particles on the surface of No.6 sensor chip is 15.028μm, while that of No.7 sensor is 20.921μm. It can be seen from Figure 12 that the theoretical values of the cumulative thickness on the surface of No.6 sensor and No.7 sensor chip are in good agreement with the test values.Table 7
Theoretical model verification test scheme for contaminant accumulation.
Test purpose Sensor number Scheme description Test parameter Flow(L/min) Concentration of micro-silica (μg/m3) Test medium Verifying the correctness of theoretical model 6 Energized, chip located at the top 1 100 Air-micro-silica two-phase flow 7 5 200Table 8
Flow rate measured by No.6 and No.7 sensors.
Test time(h) Reference value No.6 sensor No.7 sensor (L/min) Flow rate(L/min) Decrease amplitude of accuracy(%) Flow rate(L/min) Decrease amplitude of accuracy(%) 300 15 14.4 4% 14.0 6.667% 600 15 13.9 7.333% 13.3 11.333% 900 15 13.6 9.333% 12.6 16% 1200 15 13.2 12% 11.9 20.667%Table 9
Theoretical and test values of cumulative thickness on No.6 and No.7 sensors.
Test time Cumulative thickness on No.6 sensor(μm) Cumulative thickness on No.7 sensor(μm) (h) Theoretical value Test value Theoretical value Test value 300 6.905 6.344 10.263 10.012 600 10.272 10.706 15.046 14.801 900 12.867 13.156 18.724 18.331 1200 15.058 15.028 21.828 20.921Figure 12
Comparison diagram of theoretical and test values of cumulative thickness on No.6 and No.7 sensors.Figure 13
Cumulative thickness diagram of microsilicon powder on No.6 and No.7 sensors.


### 4.2. Analysis of Factors Affecting Accumulation

According to (31), the cumulative thickness of particles on the surface of the sensor chip is mainly related to the particle concentrationΨ, the particle radiusrp, and the critical distancedc. The critical distancedc can be calculated by (33). It can be seen from (33) that the critical distancedc is related to the particle radiusrp, the particle chargeqp, and the chip surface charge line densityλe. Therefore, the particle concentrationΨ, the particle radiusrp, the particle chargeqp, and the chip surface charge line densityλe are the major factors affecting particle accumulation. When the gas flow rate is 1 L/min, the effects of various factors on the cumulative thickness of the particles are shown in Figure 14. As can be seen from Figures 14(a), 14(c), and 14(d), the cumulative thickness of the particles increases along with the increase of the particle concentration, the particle charge, and the chip surface charge line density. After 100 hours of accumulation, the cumulative thickness increases from 8.655μm to 12.571μm when the particle concentration increases from 0.5mg/m3 to 1mg/m3, and the increase amplitude is 45.246%. The cumulative thickness increases from 12.571μm to 18.127μm when the particle charge increases from 1.6×10−17C to 3.2×10−17C, and the increase amplitude is 44.197%. The cumulative thickness increases from 29.176μm to 41.652μm when the chip surface charge line density increases from 5×10−9C/m to 1×10−8C/m, and the increase amplitude is 42.761%. Figure 14(b) shows that the cumulative thickness of the particles decreases along with the increase of the particle radius. After 100 hours of accumulation, the cumulative thickness decreases from 7.902μm to 4.079μm when the particle radius increases from 2μm to 4μm, and the decrease amplitude is 48.380%. The reason for the decline is that the larger the particle radius, the greater the air adhesion resistance. It is more difficult for the particles to be adsorbed to the surface of the chip because a greater electrical force is required to overcome the adhesion resistance.Figure 14
Diagram of the effects of various factors on cumulative thickness.
(a)
Particle concentration (b)
Particle radius (c)
Particle charge (d)
Charge line density


## 4.1. Verification Test and Result

In order to verify the correctness of the theoretical model, the atmospheric mild contamination test was simulated. The concentration of the microsilica powder was adjusted to 100μg/m3 and 200 μg/m3, respectively. The test scheme is shown in Table 7. In this test, the cumulative thickness of the particles on the surface of the chip was tested every 300 hours, and a total of four cycles were tested. The flow rates measured by the sensors at different time are shown in Table 8. As can be seen from Table 8, when the sensors are tested for 1200 hours, the flow rate of No.6 sensor declines by 1.8 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 12%. The flow rate of No.7 sensor declines by 3.1 L/min compared to the reference flow rate of 15 L/min, and the decrease amplitude is 20.667%. When the gas flow rates are 1 L/min and 5 L/min, respectively, the values of the critical distancedc can be calculated based on (33) to be 56.922 μm and 25.406 μm. The theoretical values of the cumulative thickness of the microsilica powder on the surface of the sensor chip at different time can be calculated by substituting thedc value into (31). The theoretical calculation values and test measurement values of the cumulative thickness of the microsilica powder on No.6 and No.7 sensors at different time are shown in Table 9. The comparison diagram is shown in Figure 12. The cumulative thickness of microsilica powder measured by the digital microscope is shown in Figure 13. After 1200-hour test, the cumulative thickness of particles on the surface of No.6 sensor chip is 15.028μm, while that of No.7 sensor is 20.921μm. It can be seen from Figure 12 that the theoretical values of the cumulative thickness on the surface of No.6 sensor and No.7 sensor chip are in good agreement with the test values.Table 7
Theoretical model verification test scheme for contaminant accumulation.
Test purpose Sensor number Scheme description Test parameter Flow(L/min) Concentration of micro-silica (μg/m3) Test medium Verifying the correctness of theoretical model 6 Energized, chip located at the top 1 100 Air-micro-silica two-phase flow 7 5 200Table 8
Flow rate measured by No.6 and No.7 sensors.
Test time(h) Reference value No.6 sensor No.7 sensor (L/min) Flow rate(L/min) Decrease amplitude of accuracy(%) Flow rate(L/min) Decrease amplitude of accuracy(%) 300 15 14.4 4% 14.0 6.667% 600 15 13.9 7.333% 13.3 11.333% 900 15 13.6 9.333% 12.6 16% 1200 15 13.2 12% 11.9 20.667%Table 9
Theoretical and test values of cumulative thickness on No.6 and No.7 sensors.
Test time Cumulative thickness on No.6 sensor(μm) Cumulative thickness on No.7 sensor(μm) (h) Theoretical value Test value Theoretical value Test value 300 6.905 6.344 10.263 10.012 600 10.272 10.706 15.046 14.801 900 12.867 13.156 18.724 18.331 1200 15.058 15.028 21.828 20.921Figure 12
Comparison diagram of theoretical and test values of cumulative thickness on No.6 and No.7 sensors.Figure 13
Cumulative thickness diagram of microsilicon powder on No.6 and No.7 sensors.


## 4.2. Analysis of Factors Affecting Accumulation

According to (31), the cumulative thickness of particles on the surface of the sensor chip is mainly related to the particle concentrationΨ, the particle radiusrp, and the critical distancedc. The critical distancedc can be calculated by (33). It can be seen from (33) that the critical distancedc is related to the particle radiusrp, the particle chargeqp, and the chip surface charge line densityλe. Therefore, the particle concentrationΨ, the particle radiusrp, the particle chargeqp, and the chip surface charge line densityλe are the major factors affecting particle accumulation. When the gas flow rate is 1 L/min, the effects of various factors on the cumulative thickness of the particles are shown in Figure 14. As can be seen from Figures 14(a), 14(c), and 14(d), the cumulative thickness of the particles increases along with the increase of the particle concentration, the particle charge, and the chip surface charge line density. After 100 hours of accumulation, the cumulative thickness increases from 8.655μm to 12.571μm when the particle concentration increases from 0.5mg/m3 to 1mg/m3, and the increase amplitude is 45.246%. The cumulative thickness increases from 12.571μm to 18.127μm when the particle charge increases from 1.6×10−17C to 3.2×10−17C, and the increase amplitude is 44.197%. The cumulative thickness increases from 29.176μm to 41.652μm when the chip surface charge line density increases from 5×10−9C/m to 1×10−8C/m, and the increase amplitude is 42.761%. Figure 14(b) shows that the cumulative thickness of the particles decreases along with the increase of the particle radius. After 100 hours of accumulation, the cumulative thickness decreases from 7.902μm to 4.079μm when the particle radius increases from 2μm to 4μm, and the decrease amplitude is 48.380%. The reason for the decline is that the larger the particle radius, the greater the air adhesion resistance. It is more difficult for the particles to be adsorbed to the surface of the chip because a greater electrical force is required to overcome the adhesion resistance.Figure 14
Diagram of the effects of various factors on cumulative thickness.
(a)
Particle concentration (b)
Particle radius (c)
Particle charge (d)
Charge line density


## 5. Conclusions

( 1 ) A theoretical model of contaminant adsorption accumulation with various affecting parameters on MEMS hot-film gas flow sensor is established. From the model, it can be analyzed that the cumulative thickness of the particles increases while the growth rate declines over time. There are significant effects on the rate and thickness of contaminant accumulation with the particle concentration, the particle radius, the particle charge, and the electric field strength on the chip surface. The cumulative thickness of the particles increases along with the increase of the particle concentration, the particle charge, and the electric field strength on the chip surface but decreases along with the increase of the particle radius. Therefore, the rate and thickness of contaminant accumulation can be significantly reduced by decreasing the particle concentration, the particle charge, and the electric field strength on the chip surface, which can prolong the life of the sensor. These disciplines provide a theoretical basis for design and use of this type of sensor to control contamination at a minimum value.( 2 ) The cumulative thickness of the particles on the surface of the sensor chip and the variation of the sensor accuracy are obtained by the test. The cumulative thickness of the particles increases while the accuracy decreases over time. The measured data shows that when the gas flow rate is 5L/min, the cumulative thickness of the particles is 10.012μm after the sensor works for 300 hours, and the related accuracy is reduced by 6.667%. The cumulative thickness is 14.801μm after 600 hours working, and the related accuracy is reduced by 11.333%. The cumulative thickness is 18.331μm after 900 hours working, and the related accuracy is reduced by 16%. The cumulative thickness is 20.921μm after 1200 hours working, and the related accuracy is reduced by 20.667%. These results of the test fit those of the theoretical model.( 3 ) The test results indicate that the electrical force is the dominant cause of contaminant adsorption accumulation. By decreasing the electric field around the MEMS sensor surface such as decreasing the voltage across the thin film resistor, the cumulative thickness of the particles can be effectively reduced. The test results also show that the contamination can be significantly reduced by increasing the filtration accuracy of the gas. This suggests that the accuracy of the sensor can be maintained for a long time under the condition that the filtration accuracy reaches 0.01μm.



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*Source: 6246259-2019-02-19.xml*