- Email: [email protected]
A comparative study of the photon pressure force, the photophoretic force, and the adhesion van der Waals force
Optics Communications 245 (2005) 27–35 www.elsevier.com/locate/optcom
A comparative study of the photon pressure force, the photophoretic force, and the adhesion van der Waals force Tran X. Phuoc
*
National Energy Technology Lab, PO Box 10940, MS: 84-340, Pittsburgh, PA 15236, USA Received 18 June 2004; received in revised form 4 October 2004; accepted 7 October 2004
Abstract A comparative study of the photon pressure force, the photophoretic force, and the adhesion van der Waals force acting on particles attached to an optical window was presented. The goal is to explore the use of radiation forces for in situ cleaning of engine optical access windows. Using aluminum, glass, fly ash and soot particles on a glass substrate the calculations show that radiation forces could be several times greater than the van der Waals force and they are very effective for particle removal applications if radiation intensity is above a certain critical level. For soot and fly ash particles, which are typically present in many combustion environments, the photon pressure forces were about 3 times and the photophoretic forces were about 3 orders of magnitude greater than the van der Waals force. 2004 Elsevier B.V. All rights reserved.
1. Introduction When laser radiation is used as an ignition source or excitation source for optical measurements of the combustion process occurring inside an internal combustion engine the engine must be equipped with optical access windows. Over times, the optical windows might be contaminated by the gradual build up of combustion-generated particulates such as soot, fly ash and many other particles. The consequent loss in the window trans*
Corresponding author. Tel.: +1 412 386 6024. E-mail address: [email protected].
mission can degrade the quality of the measured information. Contaminants might absorb the laser beam presenting themselves as hot spots that might lead to uncontrolled ignition damaging the windows and disturbing the engine designed operation conditions. It is, therefore, required that the engine optical access windows must be routinely cleaned. In so doing, the engine has to be shut down and the windows have to be removed and manually cleaned using some sorts of solvents. Engine shut down is expensive and not desirable, especially for applications that continuous operation of the engine is required. Removing the optical windows might also break the window seals
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.10.047
28
T.X. Phuoc / Optics Communications 245 (2005) 27–35
resulting in engine pressure leaks. In order to avoid these problems, a new cleaning technique should be developed. Such a technique should be non-intrusive, and the cleaning is carried out while the engine is running so that engine shut down and window removing is no longer required. It has been known that when a particle is illuminated by a beam of photons it is subjected to a force called photon pressure force. This phenomenon has been observed [1–5] and has been used for particle trapping, manipulations, levitation [5–10]. If the particle or the surrounding gas absorbs the photon beam and is heated unevenly it is also subjected to an additional but different kind of radiation forces called photophoretic force [11–15]. We will show in the following sections that, depending on the laser fluence and the particle thermal and optical properties, the photon pressure force can be 3 times and the photophoretic force can be two to three orders of magnitude higher than the van der Waals force which is the principle force that holds small particles (less than 50 lm) to a substrate surface [16–18]. Such the powerful radiation forces are more than sufficient to remove any contaminant that is held to a substrate surface by any type of adhesion forces. The present study, therefore, conduct a comparative study of these forces. We then go on to conduct some experimental demonstrations to show that the radiation forces can be utilized for window particle removal applications.
2. Theoretical calculations The theoretical model assumes that a particle is attached to a glass surface by an adhesion force, Fa. The particle is an absorbing particle with the complex refractive index m2 = n2 ik2 and it is illuminated by a Gaussian laser beam which exerts radiation forces, Frad on the particle. The glass substrate is transparent to the laser beam. The removal mechanism is assumed to be due simply to the competition between the adhesion force and the radiation forces, that is, if Frad is greater than Fa the particle detaches, accelerates and moves away from the substrate surface. Thus, the calculation presented here is only a comparative study
showing the magnitudes of the various forces that we believe to be responsible for particle adhesion, and removal. These forces are briefly summarized as follows. 2.1. Adhesion forces Contaminants are held to a solid surface by forces such as van der Waals force, inertia force, electrostatic force, and capillary force. Among these, the van der Waals force is the principle one that holds small particles (less than 50 lm) [16–18]. For a spherical particle on a flat substrate, the van der Waals force is given as, [17] F VDW ¼
hLV a2c ; 8p2 Z 3
ð1Þ
where ac is the radius of the contact area (taken about 3–5% of the particle size), and Z is the atomic separation between the surface and the bottom surface of the particle, and hLV is the materialdependent Lifshitz–van der Waals constant which is from about 0.6 eV for polymers to about 9 eV for metals [16]. The Lifshitz–van der Waals constant hLV can be evaluated using the Hamaker coefficient as [16,17] hLV ¼
4pAP–S ; 3
ð2Þ
where AP–S is the Hamaker coefficient of particle of material p on a substrate of material s and it is calculated from the Hamaker constant as 1=2 Ap–s ¼ App Ass ; ð3Þ where App is the Hamaker constant of material p on substrate surface p and Ass is the Hamaker constant of material s on substrate surface s. The Hamaker constants for various materials [16] are tabulated in Table 1. The refractive index and the extinction coefficients of the materials were taken from Siegel and Howell [19]. Using the atomic separation of 8 · 1010 m and the contact surface area of 3% of the particle size, typical van der Waals forces of aluminum, copper, magnesium, fly ash and soot particles, all on glass surface were calculated and the results are shown in Fig. 1. For the particle size ranging from about 1 to 12 lm the van der Waals forces calculated for
T.X. Phuoc / Optics Communications 245 (2005) 27–35 Table 1 Material properties (The complex refractive indexes are at 0.589 lm wavelength for all metals and 1.064 nm for fly ash and soot) Material
A11 (1020 J)
n2
k2
kp(W/m K)
Silver Copper Gold Iron Magnesium Nickel Tungsten Aluminum Glass (dry air) Fly ash Soot
44 28 48 26 15 32 40 33 8.5 15.5 15.5
0.18 0.44 0.47 1.51 0.37 1.79 3.46 1.2 1.5 1.5 2
3.64 3.26 2.83 1.63 4.42 3.33 3.25 11.18 0.0 0.01 1
429 401 317 80.2 156 90.7 174 220 0.44 0.2 0.2
soot, fly ash and magnesium particles, were similar and they increased from about 3 mdyn when the particle size was 1.6 lm to 150 mdyn as the particle size was 12 lm. For the same range of the particle size the force for copper particles increased from 4 to 195 mdyn, and for aluminum particles, it increased from 5 to 220 mdyn. The values of the van der Waals force presented here are greater than the gravity force acting on the particle by a factor of about 107 and they could be tremendously greater if smaller atomic separation Z and larger particle contact surface area, ac, are used. For example, using Z = 4 · 1010 m and ac = 5% of the particle size, the van der Waals force of a copper particle on glass surface is about 4329 mdyn and the van der Waals force of an aluminum
29
particle on glass surface is 4877 mdyn. These values are about 20 times greater than the results shown in Fig. 1. As a result, a larger amount of external force should be needed in order to remove the particle effectively. 2.2. Radiation forces Radiation forces acting on the particle can be resulted mainly from the momentum of the radiation beam (photon pressure force, Fm), the uneven heating of the particle (photophoretic force, Fp) and the thermal expansion of the substrate. To simplify the calculation, the glass substrate is assumed to be transparent to the laser beam and we will discuss only the photon pressure force and the photophoretic force. Thus, the radiation force reduces to F rad ¼ F p þ F m :
ð4Þ
It has been known that, in the limit where Knudsen numbers Kn = l/a, (where l is the mean free path of the molecules of the surrounding gas and a is the particle size) are considerably less than 1 a surface temperature gradient DTs causes molecules of the surrounding gas to move due to the phenomenon known as Maxwellian Creep with a velocity given by V ¼
Klg DT s ; aqg T g
Fig. 1. van der Waals force as a function of particle size.
ð5Þ
30
T.X. Phuoc / Optics Communications 245 (2005) 27–35
where K is the thermal slip factor (from 3/4 to 1.7), lg is the viscosity of the gas, qg is the gas density, DTs is the surface temperature gradient, and Tg, is the gas temperature. Gas molecules slide over the particle surface from colder to hotter parts of the surface resulting in a tangential stress on the particle surface. If the surface temperature gradient is due to a non-uniform heating of the particle by an optical field, this force is called photophoretic force. Yalamov et al. [11] solved the boundaryvalue problem for the spherical geometry with the condition that at the particle surface the gas velocity is given by Eq. (5) and the force is given F ph ¼
4paKl2g IJ ; qg T g k p
ð6Þ
where kp is the thermal conductivity of the particle, I is the irradiating intensity, and J is the symmetry factor which is the most important factor that determines the direction of the force. The expression for J is [12–14] ! Z p Z 1 2 3 jEðr; hÞj 03 0 J ¼ n2 k 2 n x dx sin 2h dh ; 2 E20 0 0 ð7Þ 0
where x = r/a; n = 2pa/k is the size parameter, k is 2 the laser wavelength, jEðr; hÞj =E20 is the dimensionless energy distribution within the particle due to an external plane wave of amplitude E0. Numerical calculations for J can be performed using the complete Mie formula for the internal field. Detailed discussions of the calculation was reported by Mackowski [14]. For particles with an absorption length k/2pk2 a then one can assume that the laser beam is absorbed entirely on the illuminated surface. In this case, J can be approximated to be 0.5Qabs as discussed by Reed [15]. For particles with sizes such that k/2p a k/2pk2 and (n2 1) < 1, J can be obtained by the following explicit equation [11] 3ðn2 1Þ 4pn2 k 2 a J ¼ 2n2 k 2 : ð8Þ 5k 8n22 Photon pressure force have been determined by use of either wave theory or ray optics when the particle size is much larger than the laser wavelength [1,5,7]. Since the photon pressure is insignif-
icant compared to other radiation forces such as photophoretic force if the particle or the surrounding gas is an absorbing medium, these available models have been developed mainly for non-absorbing particles (k2 = 0). This study explores the use of radiation forces for particle removal and in situ cleaning of engine optical access windows. These applications involve with both absorbing and non-absorbing particles and particles with high thermal conductivity. For high thermal conductivity particles such as metal particles the photon pressure force can be significantly higher than the photophoretic force. Thus, the photon pressure force might have a significant role in these applications. In this case, the force equations that can account for the effect of the particle extinction coefficient, k2, developed by Phuoc [20] can be used. The x and y components for the force equations are Z n1 pa2 p=2 Fx ¼ I ðrÞ½1 þ R cos ð2h1 Þ þ H x sin h dh; c0 p=2 n X 2npk 2 n n1 2 Hx ¼ T d ð1Þ R exp k 1 cos ð2nh2 2h1 Þ ; ð9Þ Z n1 pa2 hmin I ðrÞÞ R sin ð2h1 Þ þ H y sin h dh; c0 hmax X 2npk 2 n 2 d ð1Þ Rn1 exp Hy ¼ T k I sin ð2nh2 2h1 Þ ; ð10Þ Fy ¼
where I(r) is the laser beam intensity profile (W/m2) and it is approximated by 2P 0 2r2 I ðr Þ ¼ exp ð11Þ px2 x2 and d ¼ 2a cos h2 ;
ð12Þ
where P0 is the total power of the beam (W), x is the beam width, R is the particle reflectivity. If the medium in which the laser beam is propagating is air (n1 = 1, k1 = 0 ! m1 = n1) R is given by
T.X. Phuoc / Optics Communications 245 (2005) 27–35
R¼
Rk þ R? ; 2 h R? ¼ h h Rk ¼ h
ð13Þ
n22 k 22 sin2 h1 n22 k 22 sin2 h1
n22 k 22 sin2 h1 n22 k 22 sin2 h1
2 2
2 2
þ 4n22 k 22 þ 4n22 k 22 þ 4n22 k 22 þ 4n22 k 22
i1=2 i1=2
i1=2 i1=2
31
by Reed [15], where Qabs is the absorption coefficient of the particle.
2c cos h1 þ cos2 h1
ð14Þ
; þ 2c cos h1 þ cos2 h1 2c sin h1 tan h1 þ sin2 h1 tan2 h1 R? :
ð15Þ
2c sin h1 tan h1 þ sin2 h1 tan2 h1
In these equations h1 = h and n1 sin1 = n2 sinh2. The directions of the force component, h, h1, and h2 are shown in Fig. 2. To explore if the radiation forces described by the above equations are sufficient for particle removal applications, some typical calculations were carried out. The photon pressure force was calculated by numerically integrating Eqs. (9) and (10) from hmin = p/2 to hmax = p/2. The photophoretic force was calculated using Eq. (6). For soot carbon and the fly ash particles we used the symmetry factor J as a function of the particle size from Mackowski [14]. For glass particles, since k2 = 0, the photophoretic force is zero. For metal particles, (Aluminum, copper, and magnesium), since k2 is large it was assumed that the absorption occurred at the illuminated face and the symmetry factor was set to be equal to 0.5Qabs as reported
Fig. 3 shows the photon pressure and the photophoretic forces as a function of the particle size. The laser fluence was 0.6 J/cm2. It is seen that, both the photon pressure and the photophoretic forces increased with the particle size. At this level of the laser fluence, the photon pressure forces were all greater than the van der Waals forces for all four particle types. Thus, at this level of the laser fluence, the photon pressure force is sufficient to remove all particles attached to the glass substrate by the van der Waals force. The removal is more effective for glass, fly ash and soot particles but less effective in the case of aluminum particle. The results on the photophoretic force indicate that, for fly ash and soot particles, the photophoretic forces were about 2–3 orders of magnitude greater than both the van der Waals and the
Fig. 2. A sketch of the laser-particle interaction for calculating the photon pressure.
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T.X. Phuoc / Optics Communications 245 (2005) 27–35
Fig. 3. Photon pressure and photophoretic force as a function of particle size.
photon pressure force. For the three metal particles it was not significant and it was about an order of magnitude less than both the photon pressure force and the van der Waals force. This is because the thermal conductivities of metals are significantly higher than those of both fly ash and soot. Thus, the photophoretic force is not effective for removing non absorbing particle and metal particles. It is, however, is more effective to remove soot and fly ash. A comparison of the radiation forces and the van der Waals forces as a function of the laser fluence is shown in Fig. 4. The particle size was10 lm. The van der Waals force for aluminum particle on glass surface was constant at about 0.1 dyn which is about an order of magnitude higher than those for glass, fly ash and soot particles which were about from 0.05 to 0.07 dyn. For all particle types, the photon pressure forces were lower than the van der Waals forces when the laser fluence was low but it increased and surpassed the van der Waals forces as the laser fluence increased. The critical laser fluence, which is defined as the laser fluence at which the photon force overcomes the van der Waals forces, can be determined and it depends on both the particle size and particle optical properties. For the present study, it is about
0.6 J/cm2 for aluminum particles, 0.2 J/cm2 for soot particle and 0.4 J/cm2 for fly ash and glass particles. It must be noted that, the calculations reported here were obtained in the case at which the particle was at the center of the laser beam. Therefore, the gradient force, acting in the direction perpendicular to the laser beam is perfectly zero and the particle removal is due solely to the action of the axial force. If it is greater than the adhesion force, which is the van der Waals force in this case, the particle is lifted out and removed from the substrate surface. If the particle is off center of the laser beam then the gradient force is not equal to zero providing an additional force in the direction parallel to the substrate surface. As a result, the particle is rolled before it is lifted by the axial component. As reported by Phuoc [20] a particle can be pushed away from, (the gradient component is negative), or pulled into the center of a laser beam, (the gradient force component is positive), depending on the particle size, refractive index and the extinction coefficient. Thus, the ability of the photon pressure force to remove a particle effectively also depends on these parameters. Since the axial force component decreases from its maximum value at the beam center to zero at the edge of the beam width, if the particle is rolled into the beam center the
T.X. Phuoc / Optics Communications 245 (2005) 27–35
33
Fig. 4. The van der Waals force, photon pressure and the photophoretic force as a function of the laser fluence.
removal is more effective. The removal becomes less effective if the particle is rolled away from the beam center. Although the photophoretic force on low thermal conductivity, absorbing particles can be three orders of magnitude higher than the adhesion force the effectiveness of the photophoretic force to remove such particles depends strongly on the particle size. Since the direction of the photophoretic force depends on the sign of the symmetry factor J which depends on the location of the absorption center within a particle. The absorption center, on the other hand, depends on the particle size and the extinction coefficient. If the particle size a k/2pk2 then the absorption center locates in the illuminated side and the force is in the direction of the laser beam. In this case, the force is in the opposite direction to the adhesion force and the removal is possible if it is greater
than the van der Waals force. If a < k/2pk2 the absorption center locates in the shaded side and the force is in the opposite direction of the laser beam. In this case, the particle suffers an additional force that pushes it into the substrate surface and the removal is impossible. This behavior can be seen clearly by looking at the forces acting on the fly ash and the soot particles which are the typical particles found in combustion environments. The difference in the complex refractive index between soot and fly ash does not result in differences in the photon pressure force but significant differences in the photophoretic behavior. For example, for highly absorbing soot particles, the photophoretic force had a positive value through out the range of the size parameter reported here while the photophoretic force for fly ash had a negative value and it was zero at n 40, (a 6.77 lm), and became
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T.X. Phuoc / Optics Communications 245 (2005) 27–35
Fig. 5. Images of the glass substrate contaminated with aluminum particles and clear stripes whose particles were removed after using laser beam.
positive for n > 40. Thus, the photophoretic force has the ability to remove all soot particles of sizes greater than about 1 lm. However, for fly ash particles it is effective only for particles of sizes greater than about 6.77 lm. For smaller fly ash particles it becomes negative and it acts again the direction of the removing force. Thus, the removing force applied must not only overcome the van der Waals force but also the photophoretic force in this case. 3. Experimental demonstrations To demonstrate the ability of the radiation forces to remove particles from a glass window a simple experiment was set up. The experiment used a pulse Nd-Yag laser producing a beam at 0.532 lm and 5 ns pulse width. The pulsing rate was 10 Hz. The beam was allowed to propagate through a glass substrate. The front surface of the glass was coated with methanol suspended aluminum particles of size in the 40 lm range. The glass then was dried and all loose particles were removed using a nitrogen jet. The substrate was placed on a micrometer translator so that it can be scanned across the laser beam. Fig. 5 shows three images of three aluminum-coated glass surfaces with clear stripes whose particles were removed by a laser beam. The stripe of the first image was cleaned by a beam of 5 mJ and the last two were cleaned using 10 and 20 mJ beams, respectively. It is clear that, all the clear stripes were as wide as the beam width with two well defined edges indicating that the laser beam was able to remove the particles in its path. The removal efficiency, however, depends on the laser energy.
For example, when a beam of about 5 mJ was used the removing was poor and the remaining particles were seen scattering everywhere across the laser beam. The removing efficiency became more effective as the laser energy increased as indicated by the second and the third images. Many studies on laser removing particles from electronic and optical surfaces have been reported and the cleaning mechanism has been attributed to the thermal expansion of both the particles and the substrate or the explosive expansion in the capillary spaces under and around the particles [21]. By carefully inspecting the stripes we observed no sign of either surface damages or stains. Thus, the particle removing process did not involve significantly with chemical or thermal processes resulted from particle absorption and heating as discussed by Lee et al. [21]. Since we used aluminum particles for this experimental demonstration, the photophoretic force is about an order of magnitude lower than both the photon pressure and the van der Waals forces as discussed in the previous section, the removal, therefore, is attributed mainly to the pressure induced by the laser beam.
4. Conclusions A comparative study of the van der Waals, photophoretic, and photon pressure forces for incylinder laser cleaning of contaminated optical windows has been presented. A simple experimental demonstration was reported indicating that the photon pressure induced by a laser beam is able to clean a contaminated window effectively if the laser beam fluence is above a critical value.
T.X. Phuoc / Optics Communications 245 (2005) 27–35
References [1] A. Ashkin, Biophys. J. 61 (1992) 569. [2] A. Askin, Phys. Rev. Lett. 24 (1970) 156. [3] C.G. Segundo, G.R. Ortiz, M.V. Munitz, Opt. Commun. 225 (2003) 115. [4] M.I. Mishchenko, J. Quant. Spectrosc. Radiative Tran. 70 (2001) 811. [5] S. Nemoto, H. Togo, Appl. Opt. 37 (1998) 6386. [6] M.J. Renn, R. Pastel, J. Vac. Sci. Technol. 16 (1998) 3859. [7] R.C. Gauthier, S. Wallace, J. Opt. Soc. Am. 12 (1995) 1680. [8] K. Taguchi, M. Tanaka, M. Ikeda, Opt. Commun. 194 (2001) 67. [9] F. Benabid, J.C. Knight, P.St.J. Russell, Opt. Express 10 (2002) 1195. [10] M.J. Renn, R. Pastel, H.J. Lewandowski, Phys. Rev. Lett. 82 (1999) 1574.
35
[11] Y.I. Yalamov, V.B. Kutukov, E.R. Shchukin, J. Colloid Interf. Sci. 57 (1976) 564. [12] S. Armold, M. Lwittes, J. Appl. Phys. 53 (1982) 5314. [13] A.B. Pluchino, Appl. Opt. 22 (1983) 103. [14] D.W. Mackowski, Int. J. Heat Mass Tran. 32 (1989) 843. [15] D.L. Reed, J. Aerosol Sci. 8 (1977) 123. [16] R.A. Bowling, in: K.L. Mittal (Ed.), Particles on Surface, Plenum Press, New York, 1988, p. 129. [17] Y.F. Lu, W.D. Song, B.W. Ang, N.H. Hong, D.S.H. Chan, T.S. Low, Appl. Phys. A: Mater Sci. Process 65 (1977) 9. [18] J.M. Lee, K.G. Watkins, J. Appl. Phys. 89 (2001) 6496. [19] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, New York, 1972. [20] T.X. Phuoc, Opt. Commun., 241 (2004) 271. [21] S.J. Lee, K. Imen, S.D. Allen, J. Appl. Phys. 74 (1993) 7044.
A comparative study of the photon pressure force, the photophoretic force, and the adhesion van der Waals force Tran X. Phuoc
*
National Energy Technology Lab, PO Box 10940, MS: 84-340, Pittsburgh, PA 15236, USA Received 18 June 2004; received in revised form 4 October 2004; accepted 7 October 2004
Abstract A comparative study of the photon pressure force, the photophoretic force, and the adhesion van der Waals force acting on particles attached to an optical window was presented. The goal is to explore the use of radiation forces for in situ cleaning of engine optical access windows. Using aluminum, glass, fly ash and soot particles on a glass substrate the calculations show that radiation forces could be several times greater than the van der Waals force and they are very effective for particle removal applications if radiation intensity is above a certain critical level. For soot and fly ash particles, which are typically present in many combustion environments, the photon pressure forces were about 3 times and the photophoretic forces were about 3 orders of magnitude greater than the van der Waals force. 2004 Elsevier B.V. All rights reserved.
1. Introduction When laser radiation is used as an ignition source or excitation source for optical measurements of the combustion process occurring inside an internal combustion engine the engine must be equipped with optical access windows. Over times, the optical windows might be contaminated by the gradual build up of combustion-generated particulates such as soot, fly ash and many other particles. The consequent loss in the window trans*
Corresponding author. Tel.: +1 412 386 6024. E-mail address: [email protected].
mission can degrade the quality of the measured information. Contaminants might absorb the laser beam presenting themselves as hot spots that might lead to uncontrolled ignition damaging the windows and disturbing the engine designed operation conditions. It is, therefore, required that the engine optical access windows must be routinely cleaned. In so doing, the engine has to be shut down and the windows have to be removed and manually cleaned using some sorts of solvents. Engine shut down is expensive and not desirable, especially for applications that continuous operation of the engine is required. Removing the optical windows might also break the window seals
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.10.047
28
T.X. Phuoc / Optics Communications 245 (2005) 27–35
resulting in engine pressure leaks. In order to avoid these problems, a new cleaning technique should be developed. Such a technique should be non-intrusive, and the cleaning is carried out while the engine is running so that engine shut down and window removing is no longer required. It has been known that when a particle is illuminated by a beam of photons it is subjected to a force called photon pressure force. This phenomenon has been observed [1–5] and has been used for particle trapping, manipulations, levitation [5–10]. If the particle or the surrounding gas absorbs the photon beam and is heated unevenly it is also subjected to an additional but different kind of radiation forces called photophoretic force [11–15]. We will show in the following sections that, depending on the laser fluence and the particle thermal and optical properties, the photon pressure force can be 3 times and the photophoretic force can be two to three orders of magnitude higher than the van der Waals force which is the principle force that holds small particles (less than 50 lm) to a substrate surface [16–18]. Such the powerful radiation forces are more than sufficient to remove any contaminant that is held to a substrate surface by any type of adhesion forces. The present study, therefore, conduct a comparative study of these forces. We then go on to conduct some experimental demonstrations to show that the radiation forces can be utilized for window particle removal applications.
2. Theoretical calculations The theoretical model assumes that a particle is attached to a glass surface by an adhesion force, Fa. The particle is an absorbing particle with the complex refractive index m2 = n2 ik2 and it is illuminated by a Gaussian laser beam which exerts radiation forces, Frad on the particle. The glass substrate is transparent to the laser beam. The removal mechanism is assumed to be due simply to the competition between the adhesion force and the radiation forces, that is, if Frad is greater than Fa the particle detaches, accelerates and moves away from the substrate surface. Thus, the calculation presented here is only a comparative study
showing the magnitudes of the various forces that we believe to be responsible for particle adhesion, and removal. These forces are briefly summarized as follows. 2.1. Adhesion forces Contaminants are held to a solid surface by forces such as van der Waals force, inertia force, electrostatic force, and capillary force. Among these, the van der Waals force is the principle one that holds small particles (less than 50 lm) [16–18]. For a spherical particle on a flat substrate, the van der Waals force is given as, [17] F VDW ¼
hLV a2c ; 8p2 Z 3
ð1Þ
where ac is the radius of the contact area (taken about 3–5% of the particle size), and Z is the atomic separation between the surface and the bottom surface of the particle, and hLV is the materialdependent Lifshitz–van der Waals constant which is from about 0.6 eV for polymers to about 9 eV for metals [16]. The Lifshitz–van der Waals constant hLV can be evaluated using the Hamaker coefficient as [16,17] hLV ¼
4pAP–S ; 3
ð2Þ
where AP–S is the Hamaker coefficient of particle of material p on a substrate of material s and it is calculated from the Hamaker constant as 1=2 Ap–s ¼ App Ass ; ð3Þ where App is the Hamaker constant of material p on substrate surface p and Ass is the Hamaker constant of material s on substrate surface s. The Hamaker constants for various materials [16] are tabulated in Table 1. The refractive index and the extinction coefficients of the materials were taken from Siegel and Howell [19]. Using the atomic separation of 8 · 1010 m and the contact surface area of 3% of the particle size, typical van der Waals forces of aluminum, copper, magnesium, fly ash and soot particles, all on glass surface were calculated and the results are shown in Fig. 1. For the particle size ranging from about 1 to 12 lm the van der Waals forces calculated for
T.X. Phuoc / Optics Communications 245 (2005) 27–35 Table 1 Material properties (The complex refractive indexes are at 0.589 lm wavelength for all metals and 1.064 nm for fly ash and soot) Material
A11 (1020 J)
n2
k2
kp(W/m K)
Silver Copper Gold Iron Magnesium Nickel Tungsten Aluminum Glass (dry air) Fly ash Soot
44 28 48 26 15 32 40 33 8.5 15.5 15.5
0.18 0.44 0.47 1.51 0.37 1.79 3.46 1.2 1.5 1.5 2
3.64 3.26 2.83 1.63 4.42 3.33 3.25 11.18 0.0 0.01 1
429 401 317 80.2 156 90.7 174 220 0.44 0.2 0.2
soot, fly ash and magnesium particles, were similar and they increased from about 3 mdyn when the particle size was 1.6 lm to 150 mdyn as the particle size was 12 lm. For the same range of the particle size the force for copper particles increased from 4 to 195 mdyn, and for aluminum particles, it increased from 5 to 220 mdyn. The values of the van der Waals force presented here are greater than the gravity force acting on the particle by a factor of about 107 and they could be tremendously greater if smaller atomic separation Z and larger particle contact surface area, ac, are used. For example, using Z = 4 · 1010 m and ac = 5% of the particle size, the van der Waals force of a copper particle on glass surface is about 4329 mdyn and the van der Waals force of an aluminum
29
particle on glass surface is 4877 mdyn. These values are about 20 times greater than the results shown in Fig. 1. As a result, a larger amount of external force should be needed in order to remove the particle effectively. 2.2. Radiation forces Radiation forces acting on the particle can be resulted mainly from the momentum of the radiation beam (photon pressure force, Fm), the uneven heating of the particle (photophoretic force, Fp) and the thermal expansion of the substrate. To simplify the calculation, the glass substrate is assumed to be transparent to the laser beam and we will discuss only the photon pressure force and the photophoretic force. Thus, the radiation force reduces to F rad ¼ F p þ F m :
ð4Þ
It has been known that, in the limit where Knudsen numbers Kn = l/a, (where l is the mean free path of the molecules of the surrounding gas and a is the particle size) are considerably less than 1 a surface temperature gradient DTs causes molecules of the surrounding gas to move due to the phenomenon known as Maxwellian Creep with a velocity given by V ¼
Klg DT s ; aqg T g
Fig. 1. van der Waals force as a function of particle size.
ð5Þ
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T.X. Phuoc / Optics Communications 245 (2005) 27–35
where K is the thermal slip factor (from 3/4 to 1.7), lg is the viscosity of the gas, qg is the gas density, DTs is the surface temperature gradient, and Tg, is the gas temperature. Gas molecules slide over the particle surface from colder to hotter parts of the surface resulting in a tangential stress on the particle surface. If the surface temperature gradient is due to a non-uniform heating of the particle by an optical field, this force is called photophoretic force. Yalamov et al. [11] solved the boundaryvalue problem for the spherical geometry with the condition that at the particle surface the gas velocity is given by Eq. (5) and the force is given F ph ¼
4paKl2g IJ ; qg T g k p
ð6Þ
where kp is the thermal conductivity of the particle, I is the irradiating intensity, and J is the symmetry factor which is the most important factor that determines the direction of the force. The expression for J is [12–14] ! Z p Z 1 2 3 jEðr; hÞj 03 0 J ¼ n2 k 2 n x dx sin 2h dh ; 2 E20 0 0 ð7Þ 0
where x = r/a; n = 2pa/k is the size parameter, k is 2 the laser wavelength, jEðr; hÞj =E20 is the dimensionless energy distribution within the particle due to an external plane wave of amplitude E0. Numerical calculations for J can be performed using the complete Mie formula for the internal field. Detailed discussions of the calculation was reported by Mackowski [14]. For particles with an absorption length k/2pk2 a then one can assume that the laser beam is absorbed entirely on the illuminated surface. In this case, J can be approximated to be 0.5Qabs as discussed by Reed [15]. For particles with sizes such that k/2p a k/2pk2 and (n2 1) < 1, J can be obtained by the following explicit equation [11] 3ðn2 1Þ 4pn2 k 2 a J ¼ 2n2 k 2 : ð8Þ 5k 8n22 Photon pressure force have been determined by use of either wave theory or ray optics when the particle size is much larger than the laser wavelength [1,5,7]. Since the photon pressure is insignif-
icant compared to other radiation forces such as photophoretic force if the particle or the surrounding gas is an absorbing medium, these available models have been developed mainly for non-absorbing particles (k2 = 0). This study explores the use of radiation forces for particle removal and in situ cleaning of engine optical access windows. These applications involve with both absorbing and non-absorbing particles and particles with high thermal conductivity. For high thermal conductivity particles such as metal particles the photon pressure force can be significantly higher than the photophoretic force. Thus, the photon pressure force might have a significant role in these applications. In this case, the force equations that can account for the effect of the particle extinction coefficient, k2, developed by Phuoc [20] can be used. The x and y components for the force equations are Z n1 pa2 p=2 Fx ¼ I ðrÞ½1 þ R cos ð2h1 Þ þ H x sin h dh; c0 p=2 n X 2npk 2 n n1 2 Hx ¼ T d ð1Þ R exp k 1 cos ð2nh2 2h1 Þ ; ð9Þ Z n1 pa2 hmin I ðrÞÞ R sin ð2h1 Þ þ H y sin h dh; c0 hmax X 2npk 2 n 2 d ð1Þ Rn1 exp Hy ¼ T k I sin ð2nh2 2h1 Þ ; ð10Þ Fy ¼
where I(r) is the laser beam intensity profile (W/m2) and it is approximated by 2P 0 2r2 I ðr Þ ¼ exp ð11Þ px2 x2 and d ¼ 2a cos h2 ;
ð12Þ
where P0 is the total power of the beam (W), x is the beam width, R is the particle reflectivity. If the medium in which the laser beam is propagating is air (n1 = 1, k1 = 0 ! m1 = n1) R is given by
T.X. Phuoc / Optics Communications 245 (2005) 27–35
R¼
Rk þ R? ; 2 h R? ¼ h h Rk ¼ h
ð13Þ
n22 k 22 sin2 h1 n22 k 22 sin2 h1
n22 k 22 sin2 h1 n22 k 22 sin2 h1
2 2
2 2
þ 4n22 k 22 þ 4n22 k 22 þ 4n22 k 22 þ 4n22 k 22
i1=2 i1=2
i1=2 i1=2
31
by Reed [15], where Qabs is the absorption coefficient of the particle.
2c cos h1 þ cos2 h1
ð14Þ
; þ 2c cos h1 þ cos2 h1 2c sin h1 tan h1 þ sin2 h1 tan2 h1 R? :
ð15Þ
2c sin h1 tan h1 þ sin2 h1 tan2 h1
In these equations h1 = h and n1 sin1 = n2 sinh2. The directions of the force component, h, h1, and h2 are shown in Fig. 2. To explore if the radiation forces described by the above equations are sufficient for particle removal applications, some typical calculations were carried out. The photon pressure force was calculated by numerically integrating Eqs. (9) and (10) from hmin = p/2 to hmax = p/2. The photophoretic force was calculated using Eq. (6). For soot carbon and the fly ash particles we used the symmetry factor J as a function of the particle size from Mackowski [14]. For glass particles, since k2 = 0, the photophoretic force is zero. For metal particles, (Aluminum, copper, and magnesium), since k2 is large it was assumed that the absorption occurred at the illuminated face and the symmetry factor was set to be equal to 0.5Qabs as reported
Fig. 3 shows the photon pressure and the photophoretic forces as a function of the particle size. The laser fluence was 0.6 J/cm2. It is seen that, both the photon pressure and the photophoretic forces increased with the particle size. At this level of the laser fluence, the photon pressure forces were all greater than the van der Waals forces for all four particle types. Thus, at this level of the laser fluence, the photon pressure force is sufficient to remove all particles attached to the glass substrate by the van der Waals force. The removal is more effective for glass, fly ash and soot particles but less effective in the case of aluminum particle. The results on the photophoretic force indicate that, for fly ash and soot particles, the photophoretic forces were about 2–3 orders of magnitude greater than both the van der Waals and the
Fig. 2. A sketch of the laser-particle interaction for calculating the photon pressure.
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T.X. Phuoc / Optics Communications 245 (2005) 27–35
Fig. 3. Photon pressure and photophoretic force as a function of particle size.
photon pressure force. For the three metal particles it was not significant and it was about an order of magnitude less than both the photon pressure force and the van der Waals force. This is because the thermal conductivities of metals are significantly higher than those of both fly ash and soot. Thus, the photophoretic force is not effective for removing non absorbing particle and metal particles. It is, however, is more effective to remove soot and fly ash. A comparison of the radiation forces and the van der Waals forces as a function of the laser fluence is shown in Fig. 4. The particle size was10 lm. The van der Waals force for aluminum particle on glass surface was constant at about 0.1 dyn which is about an order of magnitude higher than those for glass, fly ash and soot particles which were about from 0.05 to 0.07 dyn. For all particle types, the photon pressure forces were lower than the van der Waals forces when the laser fluence was low but it increased and surpassed the van der Waals forces as the laser fluence increased. The critical laser fluence, which is defined as the laser fluence at which the photon force overcomes the van der Waals forces, can be determined and it depends on both the particle size and particle optical properties. For the present study, it is about
0.6 J/cm2 for aluminum particles, 0.2 J/cm2 for soot particle and 0.4 J/cm2 for fly ash and glass particles. It must be noted that, the calculations reported here were obtained in the case at which the particle was at the center of the laser beam. Therefore, the gradient force, acting in the direction perpendicular to the laser beam is perfectly zero and the particle removal is due solely to the action of the axial force. If it is greater than the adhesion force, which is the van der Waals force in this case, the particle is lifted out and removed from the substrate surface. If the particle is off center of the laser beam then the gradient force is not equal to zero providing an additional force in the direction parallel to the substrate surface. As a result, the particle is rolled before it is lifted by the axial component. As reported by Phuoc [20] a particle can be pushed away from, (the gradient component is negative), or pulled into the center of a laser beam, (the gradient force component is positive), depending on the particle size, refractive index and the extinction coefficient. Thus, the ability of the photon pressure force to remove a particle effectively also depends on these parameters. Since the axial force component decreases from its maximum value at the beam center to zero at the edge of the beam width, if the particle is rolled into the beam center the
T.X. Phuoc / Optics Communications 245 (2005) 27–35
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Fig. 4. The van der Waals force, photon pressure and the photophoretic force as a function of the laser fluence.
removal is more effective. The removal becomes less effective if the particle is rolled away from the beam center. Although the photophoretic force on low thermal conductivity, absorbing particles can be three orders of magnitude higher than the adhesion force the effectiveness of the photophoretic force to remove such particles depends strongly on the particle size. Since the direction of the photophoretic force depends on the sign of the symmetry factor J which depends on the location of the absorption center within a particle. The absorption center, on the other hand, depends on the particle size and the extinction coefficient. If the particle size a k/2pk2 then the absorption center locates in the illuminated side and the force is in the direction of the laser beam. In this case, the force is in the opposite direction to the adhesion force and the removal is possible if it is greater
than the van der Waals force. If a < k/2pk2 the absorption center locates in the shaded side and the force is in the opposite direction of the laser beam. In this case, the particle suffers an additional force that pushes it into the substrate surface and the removal is impossible. This behavior can be seen clearly by looking at the forces acting on the fly ash and the soot particles which are the typical particles found in combustion environments. The difference in the complex refractive index between soot and fly ash does not result in differences in the photon pressure force but significant differences in the photophoretic behavior. For example, for highly absorbing soot particles, the photophoretic force had a positive value through out the range of the size parameter reported here while the photophoretic force for fly ash had a negative value and it was zero at n 40, (a 6.77 lm), and became
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T.X. Phuoc / Optics Communications 245 (2005) 27–35
Fig. 5. Images of the glass substrate contaminated with aluminum particles and clear stripes whose particles were removed after using laser beam.
positive for n > 40. Thus, the photophoretic force has the ability to remove all soot particles of sizes greater than about 1 lm. However, for fly ash particles it is effective only for particles of sizes greater than about 6.77 lm. For smaller fly ash particles it becomes negative and it acts again the direction of the removing force. Thus, the removing force applied must not only overcome the van der Waals force but also the photophoretic force in this case. 3. Experimental demonstrations To demonstrate the ability of the radiation forces to remove particles from a glass window a simple experiment was set up. The experiment used a pulse Nd-Yag laser producing a beam at 0.532 lm and 5 ns pulse width. The pulsing rate was 10 Hz. The beam was allowed to propagate through a glass substrate. The front surface of the glass was coated with methanol suspended aluminum particles of size in the 40 lm range. The glass then was dried and all loose particles were removed using a nitrogen jet. The substrate was placed on a micrometer translator so that it can be scanned across the laser beam. Fig. 5 shows three images of three aluminum-coated glass surfaces with clear stripes whose particles were removed by a laser beam. The stripe of the first image was cleaned by a beam of 5 mJ and the last two were cleaned using 10 and 20 mJ beams, respectively. It is clear that, all the clear stripes were as wide as the beam width with two well defined edges indicating that the laser beam was able to remove the particles in its path. The removal efficiency, however, depends on the laser energy.
For example, when a beam of about 5 mJ was used the removing was poor and the remaining particles were seen scattering everywhere across the laser beam. The removing efficiency became more effective as the laser energy increased as indicated by the second and the third images. Many studies on laser removing particles from electronic and optical surfaces have been reported and the cleaning mechanism has been attributed to the thermal expansion of both the particles and the substrate or the explosive expansion in the capillary spaces under and around the particles [21]. By carefully inspecting the stripes we observed no sign of either surface damages or stains. Thus, the particle removing process did not involve significantly with chemical or thermal processes resulted from particle absorption and heating as discussed by Lee et al. [21]. Since we used aluminum particles for this experimental demonstration, the photophoretic force is about an order of magnitude lower than both the photon pressure and the van der Waals forces as discussed in the previous section, the removal, therefore, is attributed mainly to the pressure induced by the laser beam.
4. Conclusions A comparative study of the van der Waals, photophoretic, and photon pressure forces for incylinder laser cleaning of contaminated optical windows has been presented. A simple experimental demonstration was reported indicating that the photon pressure induced by a laser beam is able to clean a contaminated window effectively if the laser beam fluence is above a critical value.
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References [1] A. Ashkin, Biophys. J. 61 (1992) 569. [2] A. Askin, Phys. Rev. Lett. 24 (1970) 156. [3] C.G. Segundo, G.R. Ortiz, M.V. Munitz, Opt. Commun. 225 (2003) 115. [4] M.I. Mishchenko, J. Quant. Spectrosc. Radiative Tran. 70 (2001) 811. [5] S. Nemoto, H. Togo, Appl. Opt. 37 (1998) 6386. [6] M.J. Renn, R. Pastel, J. Vac. Sci. Technol. 16 (1998) 3859. [7] R.C. Gauthier, S. Wallace, J. Opt. Soc. Am. 12 (1995) 1680. [8] K. Taguchi, M. Tanaka, M. Ikeda, Opt. Commun. 194 (2001) 67. [9] F. Benabid, J.C. Knight, P.St.J. Russell, Opt. Express 10 (2002) 1195. [10] M.J. Renn, R. Pastel, H.J. Lewandowski, Phys. Rev. Lett. 82 (1999) 1574.
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[11] Y.I. Yalamov, V.B. Kutukov, E.R. Shchukin, J. Colloid Interf. Sci. 57 (1976) 564. [12] S. Armold, M. Lwittes, J. Appl. Phys. 53 (1982) 5314. [13] A.B. Pluchino, Appl. Opt. 22 (1983) 103. [14] D.W. Mackowski, Int. J. Heat Mass Tran. 32 (1989) 843. [15] D.L. Reed, J. Aerosol Sci. 8 (1977) 123. [16] R.A. Bowling, in: K.L. Mittal (Ed.), Particles on Surface, Plenum Press, New York, 1988, p. 129. [17] Y.F. Lu, W.D. Song, B.W. Ang, N.H. Hong, D.S.H. Chan, T.S. Low, Appl. Phys. A: Mater Sci. Process 65 (1977) 9. [18] J.M. Lee, K.G. Watkins, J. Appl. Phys. 89 (2001) 6496. [19] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, New York, 1972. [20] T.X. Phuoc, Opt. Commun., 241 (2004) 271. [21] S.J. Lee, K. Imen, S.D. Allen, J. Appl. Phys. 74 (1993) 7044.