Experiment and Simulation on Liquid Film Motor and its Application

Transcription

1 Experiment and Simulation on Liquid Film Motor and its Application Author:Gong zhenyan Adviser:Fang dexin, Tang Ping, Zhao Min Shanghai No.2 High School

2 Experiment and simulation on liquid film motor and its application Background On September 25th in 2008, the first paper [1] on the research of the rotational film under the high external electric field and with current passed through the film which was named as liquid film motor (LFM) was published online by A. Amjadi, R. Shirsavar and M. R. Ejtechadi, which has received great attention from the field of electro-hydrodynamics and other scientists all over the world. After that, researchers in Iran, China have done great simulations and experiment as well as proposed several different models to explain the phenomenon. As a research team mainly consisting of high school students who have great passion on physics, we are very much interested in this phenomenon and also have seen its potential in the manipulation of microfluid and nanofluid and its application on lab on chip which is one of the most popular technology having great potential contribution to biology and chemistry. So this paper will show our work on LFM and our specific illustration on its application. Innovation In this paper, the experimental method, the idea of the application is original. However, the leaky dielectric

3 model and the simulation is based on the work by Saville and R. Shirsavar [2]. Our result of simulation has smaller discrepancy in the order of magnitude with the experimental value than the previous work. Finally, as far as I m concerned, this is the first paper on LMF that illustrates its specific application on lab on chip which is one of the most popular technology having great potential contribution to biology and chemistry. The course of research Research on this problem mainly consists of 2 stages. In the IYPT, I adopted the dipole theory, but the experimental value didn t fit the simulation value well. To write this paper, I have done a lot of further work on it. In this stage, I use the leaky dielectric model to solve this problem and get better correspondence. This helps me to reveal the physical essence of the LFM. Abstract It has been found that the soap film formed in a flat frame can rotate in its plane when a strong external DC electric field and DC current perpendicular to the electric field is applied, the phenomenon of which is called liquid film motor in the field of electrohydrodynamics. I would like to divide my paper into 3 parts. The first part is the theory and the simulation. In

4 this part, we will use leaky dielectric model [3] which is a classical model in electrohydrodynamics to explain the phenomenon. Then, we describe the electrical and hydrodynamic equation and solve them numerically by using finite elements. The second part is the experiment. In the experimental part, we introduce the rotational threshold which we failed to use specific theory and simulation to explain. Then, we test different rotational speed under different external electric field and voltage of two electrodes and compare the result with the simulation. At the end of the experimental part, we give specific error analysis. The third part, we innovatively propose the application of the liquid film motor on lab on chip. Key words: electrohydrodynamics, liquid film motor, leaky dielectric model.

5 Contents: 1. Theory and simulation Leaky dielectric model Simulation Experiment Set-up Estimation of the thickness Rotational theshold Rotational speed Error analysis Applications Manufacturing process mixing chip centrifugal chip Reference... 15

6 1. Theory and simulation 1.1 Leaky dielectric model Since we regard the liquid film as a leaky dielectric, the strong external electric field carries the charge inside the film to the surface. Then, the induced free charge which accumulates on the surface modifies the external electric field applied, which is suggested by the Saville s work on leaky dielectric model shown in FIG.1 [4]. Then, the voltage of two electrodes contact to the film FIG.1 Illustration of induced charges on liquid film by the external electric field and electric forces on these charges from the inner electric field. directly will exert an electrical force on the induced charge, adding the shear stress on the two boundaries of the film with opposite direction, which causes the rotation. This is the clearest way of explaining the phenomenon. 1.2 Simulation Based on the leaky dielectric model, we use COMSOL5.0 to do the simulation which will be elaborated in this paper. First, we set a cuboid area of film surrounded by a cuboid area of air as shown in FIG.2 And some parameters is listed in FIG.3 film air dynamic viscosity(pa*s) 11.97*10^(-3) No use conductivity(s/m) 5.5*10^(-6) No use density(kg/m^3) 1100 No use relative permittivity 80 1 FIG.2 This figure shows the model of the simulation. Inner cuboid is the film with the size of 20mm*20mm*0.1mm. The outer cuboid is the air with the size of 30mm*30mm*1mm FIG.3 This figure illustrates the parameters used in the simulation. 1

7 Then, we first set up the electric current. In COMSOL5.0, we have the governing equation as follow. J Q j J E J e E V Here, we disregard any convective current due to the low Reynolds number Re v / l ( v is the characteristic velocity, is the permittivity of the film, l is the length of the film, is the conductivity.), which means the electric current field is an irrotational field. So we can have the continuity of the electric current to characterize the electric current. We solve it in the steady status with the boundary condition of the U el. The picture below shows the potential variation in the film. ( ) 0 U el FIG.4 This figure shows the potential distribution inside the film. The potential varies linearly from one side to the other. In this picture, the potential difference given is 10V. After that, we can consider the external electric field. Since the conductivity of the air is negligible because it is a perfect insulator which means that there is no free charge. So the electric potential follows the Laplace equation which is the Poisson equation under special circumstances. After we have solved the electric current field and got the potential on six surfaces, we use it and the U ext as the boundary conditions to solve the distribution of the external electric field in the steady status. The picture below shows the distribution of the external electric field. 2

8 0 2 U ext FIG.5 This figure shows the distribution of the external electric field. With the induced charge, the external electric field is modified and curves near the boundary. After obtaining the electric field, we can compute the electrical force. In our problem, there is a shear stress originated from the electrical force. In the simulation, we use the shear stress in the COMSOL. This stress can be derived from the Maxwell stress tensor [5]. t [ T ] n E [ E ] q E t n s t Considering q which is the surface charge density q E air ext Therefore, the electrical force actuating on each surface can be written as T E E i air ext x Since we ve already had the stress on the film, we can use the Navier-Stokes equation to govern the motion of the film. The low Reynolds number allows us to neglect the inertial term and simplify it to Stokes equation. ( ) 2 v v p v We solve the laminar flow also in a steady state. The result of the simulation will be compared with the experimental result in the experimental part. 3

9 2. Experiment 2.1 Set-up The experimental set-up is quite simple, which is shown in the FIG.6 It includes two graphite electrodes (yellow) connected with DC current supply, a capacitor (dark grey) made of aluminum connected with high voltage supply and two plastic bars to form the rectangular frame. 2.2 Estimation of the thickness + - High voltage supply 2cm 2cm 3cm + DC supply (1-1000v) - 5 degree 10.5cm 10.5cm (a) (b) FIG.6 These are the top view (a) and the side view (b) of the schematics of the set-up. 2.3 Rotational threshold In the experiment, the material we use to form the soap film is 30%, 60% and 90% glycerol-water solution. To control the thickness of the soap film which affects the rotation, we use the interference pattern to predict the overall thickness. In specific, we tilted the film for 5 degree to let the thickness of increase proportionally. So we controlled the thickness of the thinner side of the film by comparing the interference color with the color in FIG.7. We don t start our experiment until we see the dark yellow pattern (FIG.8) which can be easily spotted in the experiment as shown in the 4

10 FIG.8 This is a classical work in colorimetry. The principle is quite simple, although it includes great complicated work. In the film interference, since a certain thickness corresponds to a particular reflectivity (equivalent) of a certain beam of light with a specific wave length, then we can use the spectrum calculated to derive the visual color. That s the rationality of our way to control the thickness. Then we set the Eext (external electric field), and we elevate the Uel (voltage of two electrodes). We put down Eext and Uel when the film starts rotating. We found that for a certain type of film with the same thickness, EextU el const. After the product reaches a constant or a threshold, the film starts rotating. In my experiment, we found that the constant depends on the proportion of glycerol. The higher the proportion, the higher the threshold as shown in FIG.9 FIG.7 The thickness of the film corresponds to the color of the interference pattern FIG.8 The thickness of the film increases proportionally from the right side to the left side. We predict that the thickness of the thinner side is around 250nm. 5

11 Rotation No rotation FIG.9 Double algorithm of Eext and Uel. 2.4 Rotational speed We tested the rotational speed under different Eext and Uel. We controlled the thickness in the same way I ve mentioned. We record the rotation using Canon EOS600D (FIG.10) with 40fps and we put the video into Tracker which is a particle analysis software. We trace the film interference color in various distance from the rotational center manually since the rotational pattern is rather like the concentric rings in different colors as shown in FIG.11. We trace pattern in each distance for 2 periods of rotation after it rotates for 1 minute which means that it achieves the steady state and get the mean rotational period. After that, we can have velocity and angular velocity. 6

12 FIG.10 These two pictures illustrate the position of the camera and the light source to get the best film interference pattern. FIG.11 This picture show the analysis of the rotational speed using Tracker. The concentric rings are also visible in the picture. The velocity becomes higher away from the center and reaches the peak in around 0.6~0.7 in experiment, while the simulation one is which matches the experimental one considering the error. And also they match each other in the order of magnitude. Also, we have discovered both in simulation and in experiment that the higher the Eext and Uel, the higher the velocity. The rotational speed is independent of the conductivity. And the higher the dynamic viscosity, the slower it rotates. 7

13 FIG.12 These two pictures demonstrate the velocity under different Uel. FIG.13 This picture demonstrates the velocity under different Eext. FIG.14 These two pictures demonstrate the velocity under different conductivity. 8

14 FIG.15 This two pictures demonstrate the velocity under different dynamic viscosity 2.5 Error analysis Regarding the rotational threshold experiment, the error mainly comes from the elevation of the Uel. Because when you are elevating the voltage, slow motion of the LMF can be seen which makes it hard to judge the rotation which has 5V error. Also, the error comes from the measurement of the distance between two polar plates about 0.5cm because it is hard to achieve absolute parallel state. Regarding the rotational speed, there are mainly errors in distance and velocity. Unlike the rotation of rigid body, the rotational center of LMF always have slightly displacement. This causes the rotation near the center fluctuate more severely than that far from the center which is from r/r=0 to r/r=0.4, 0.02 from r/r=0.4 to r/r=0.8 and 0.01 from r/r=0.8 to r/r=1. Since the frame number per second is rather low, there can have 0.02s in each period of rotation. 3. Application On April 23 rd in 2014, A. Amjadi s research team [6] first used the LMF to generate electricity which was quite successful. Recently, M. Nasiri s research team [7] recently suggested its potential in lab-on-chip but didn t study further, no need to mention the specific illustration of the application. As a team consisting of high school 9

15 students, it s impossible for us to put the application into practice with the limitation of finance and capability. But based on our knowledge on the LFM, we came up with the ideas of mixing chip and centrifugal chip using the dynamic characteristic shown in the LFM. 3.1 Manufacturing process: First we need to fabricate a photo mask with the structure of the chip, while the process of the mask has been illustrated in reference [8]. Two areas for electrodes Mixing area Exit Fig.16 the picture of the photo mask for mixing chip Entrance of solution Two areas for electrodes Centrifugal area Channel for pressure Fig.17 the picture of the photo mask for centrifugal chip Entrance of solution 10

16 Then, we will move on to the manufacturing process which mainly have 6 steps. [9] Layer of photoresist Layer of chrome Substrate Fig.18 Form a layer of chrome on a smooth and clean substrate. Use the machine to spread the photoresist evenly on the layer of chrome. UV Mask Layer of photoresist Substrate Layer of chrome Fig.18 Cover the mask made on the layer of photoresist and expose it under the ultraviolet rays. Layer of photoresist Layer of chrome Fig.19 Use the film development to get rid of the photoresist which has been exposed under the UV. Substrate Layer of photoresist Layer of chrome Substrate Fig.20 Use certain fluid to erode the layer of chrome. Layer of photoresist Layer of chrome Substrate Fig.21 Wet etch the substrate and equip the substrate with the structure of channels. And the thickness of the structure is 800±200nm. Substrate Fig.22 Get rid of the photoresist and chrome 11

17 Cover glass Substrate Fig.23 Use high temperature bonding method to combine the cover glass with the substrate. Then the chip is finished. 3.2 Mixing chip Set-up The mixing chip mainly has 3 parts the entrance channels, the mixing area and the exit channels. The overall set up is placed on an insulated base, with two polar plates served as a capacitor connected with high voltage supply (0-50kv) and inserted perpendicularly in the base and two electrodes connected with a DC supply (0-1000v). The base is placed horizontally and the thickness of the channels and mixing area is 800±200nm. Operating principle You can add several types of solution through the entrance channels to the mixing area and you can manufacture more entering channels if necessary during the manufacturing process. When you finish adding, you can turn on the two suppliers and then the rotational mixing process is automatically on. Finally, you can get the solution out of the mixing area through the controlling the pressure. Advantage and disadvantage Since the rotation speed depends on the strength of external electric field and the voltage of two electrodes, the time of mixing is controllable. Mixing time will become shorter with the elevation of two types of voltages. Also this chip can be easily connected with other chips if needed. But the problem is that it can t mix the solution with all electric dipole moment under 1 Debye according to the work by R. Shirsavar [10] and also rotating for too long can cause the centrifugal separation. 12

18 - High voltage supply (0-50kv) + Two polar plates Mix Base + DC supply (1-1000v) Electrodes - Fig.24 This picture shows the top view of the mixing chip. 3.3 Centrifugal chip Set-up The set-up is quite similar to that of the mixing chip. The centrifugal chip mainly has 3 parts the entrance channels, the mixing area and the exit channels. The overall set up is placed on an insulated base, with two polar plates serving as a capacitor connected with high voltage supply (0-50kv) and inserted perpendicularly in the base and two electrodes connected with a DC supply (0-1000v). The base is placed horizontally and the thickness of the channels and mixing area is 800±200nm. Operating principle You can add the solution through the entrance channels to the centrifugal area by pulling the micro needle cylinder. When you finish adding, you can turn on the two suppliers and then the centrifugal separation process is 13

19 automatically on. Advantage and disadvantage Since the rotational speed is controllable, the time of the centrifugal process can be prolonged or shortened by changing the two types of voltage. We know this by the simple formula given below. Consider the centrifugal force of each molecule, here m is the mass of each molecule, w is the angular velocity and r is the distance from the position of the particle to the center of the rotation. F 2 mw r.(1) Then, when the molecule starts moving, it achieves the force balance of the centrifugal force and viscous force, ignoring the gravity since we can consider is as a 2D chip with its thickness about 800nm. F F viscous. (2) 2 dr m r.(3) dt So we have 2 dr m r dt... (4) Actually, this is how sedimentation coefficient S is deduces. From equation (4) we can see that the higher the angular velocity, the faster the separation process. But the problem is that since I have done neither simulation, nor experiment, I reckon that it can separate the solution with 2 types of solute successfully, but I m not sure if it can deal with the solution with more types of solute because the velocity varies from the center to the boundary. And also, I haven t come up with a way of separation after centrifuge. That why I call it a centrifugal chip instead of a centrifugal separation chip. Still, it can t separate mix the solution with all electric dipole moment under 1 Debye and those insulating liquid. 14

20 - High voltage supply (0-50kv) + Two polar plates Centrifugal area Electrodes Base + DC supply (1-1000v) - Micro needle cylinder Fig.25 This picture is the top view of the centrifugal chip. 4. Reference [1] Amjadi A, Shirsavar R, Radja NH, Ejtehadi MR (2009) A liquid film motor. Microfluid Nanofluid 6(5): [2] M. Nasiri, R. Shirsavar, T. Saghaei, A. Ramos (2015) Simulation of liquid film motor: a charge induction mechanism. Microfluid Nanofluid 19: [3] Saville DA (1997) Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Ann Rev Fluid Mech 29(1):27-64 [4] M. Nasiri, R. Shirsavar, T. Saghaei, A. Ramos (2015) Simulation of liquid film motor: a charge induction mechanism. Microfluid Nanofluid 19: [5] Melcher JR, Taylor GI (1969) Electrohydrodynamics: a review of the role of interfacial shear 15

21 stresses. Ann Rev Fluid Mech 1(1): [6] A. Amjadi, M. S. Feiz, R. M. Namim (2014) Liquid soap film generates electricity: A suspended liquid film rotating in an external electric field as an electric generator. Microfluid Nanofluid [7] M. Nasiri, R. Shirsavar, T. Saghaei, A. Ramos (2015) Simulation of liquid film motor: a charge induction mechanism. Microfluid Nanofluid 19: [8] Manz A, Graber N, Widmer H M. Sens Actuators B,1990. BI: 244 [9] Harrison DJ, Manz A, Fan Z H, et al. Anal Chem, 1992, 64:1926 [10] R. Shirsavar, A. Amjadi, A. Tonddast- Navaei (2011) Electrically rotating suspend films of polar liquids. Exp Fluids 50: