35 3 2014 3 15 Applied Mathematics and Mechanics Vol 35 No 3 Mar 15 2014 1000-0887 2014 03-0264-08 ISSN 1000-0887 LED Boltzmann * 430074 LED light emitting diode LED LED LED LED LED Boltzmann Boltzmann dl /D t /T Boltzmann O359 + 1 A doi 10 3879 /j issn 1000-0887 2014 03 004 LED LED 1-4 LED 1 1 LED Boltzmann LBM LBM Dupuis 5 LBM Yan 6 Inamuro 7 Bri- * 2013-10-23 2013-12-12 51376070 20100142110046 1989 E-mail lilan321@ hust edu cn 1974 E-mail Luoxb@ hust edu cn 264
265 ant 8 ab a Dispensing b Dispensing c d c Flowing d Flowing Fig 1 e f LED e Curing 1 f Phosphor gel morphology affects the LED performance LED Schematic diagrams of phosphor gel dispensing & shaping process in LED Boltzmann LED Boltzmann 1 LBM 1 1 Boltzmann LBM Shan-Chen 9-11 D3Q19 2 19 f ki x + e i dt t + dt - f ki x t = - 1 f τ ki x t - f eq ki x t k 1
266 LED Boltzmann k i τ k k f ki x t k f eq ki x t k 2 f eq ki Fig 2 [ - ] u2 c 2 s 2c 4 s 2c 2 s = ω i ρ 1 + e i u + e i u 2 D3Q19 Schematic of discrete velocity vectors in D3Q19 model ω i ω i = { 1 /3 i = 0 1 /18 i = 1 2 6 1 /36 i = 7 8 18 2 ρ x t = f eq i x t 3 ρ x t u x t = i i f eq i x t e i + τf 4 F F = F σ + F t + F g 5 F σ F t F g 3 σ G 4 θ G t Fig 3 Relationship between surface tension Fig 4 Relationship between contact angle coefficient σ and parameter G θ and parameter G t Shan-Chen V x x' = G σσ' ψ σ x ψ σ' x' F σ x = - ψ σ x G σσ' ψ σ' x + e i e i ψ x ψ x = 1 - e -ρ x G σσ' Green D3Q19 G x x' = { G e i = 1 G /2 e i = 槡 2 0 6 7
267 G G G σ 3 Shan-Chen F t x = - ρ x G t s x + e i e i s = 0 s = 1 G t θ θ G ti θ 4 F g F g x = gρ x g 1 2 5 1l u = 5 10-5 m 100l u 100l u 100l u D = 20l u 5 b 26l u 5l u 0 027 N /m 20 22 3 4 5 Pa s ρ G = 1 0 ρ L = 1 0 G = 0 521 G tg = - 0 018 G tl = - 0 499 7 τ G = τ L = 1 0 g G = - 0 000 3 g L = - 0 002 52 G L 8 9 a a Flat surface Fig 5 5 2 b b Square projection Physical model of phosphor gel coating technology 2 1 LED 6 3 t
268 LED Boltzmann a t = 1 b t = 50 c t = 100 d t = 200 e t = 400 f t = 600 g t = 800 h t = 1 200 i t = 1 600 6 Fig 6 Phosphor gel morphology changed during the coating process on flat surface 7 8 Fig 7 Phosphor gel morphology comparison Fig 8 Change of droplet contact line length to between simulation and experiment droplet diameter ratio with time 6 b c d
269 6 e f g 6 h i 6 i 7 8 dl /D dl D t /T t T dl /D t /T dl /D ~ t /T 0 6 2 2 LED a t = 1 b t = 50 c t = 100 d t = 200 e t = 400 f t = 600 g t = 800 h t = 1 200 i t = 1 600 Fig 9 9 Phosphor gel morphology changed during the coating process on square projection 9
270 LED Boltzmann 6 9 b c d 9 e 9 f 9 g h 9 i 10 Fig 10 Variation of droplet contact line length to droplet diameter ratio in axial and diagonal directions with the relative time 9 10 dl /D t /T dl /D ~ t /T 0 6 dl /D ~ t /T 0 48 3 Boltzmann Boltzmann dl /D t /T dl /D ~ t /T 0 6 dl /D ~ t /T 0 48 References 1 LIU Sheng LU O X iao-bing LED Packaging for Lighting Applications Design Manufacturing and Testing M U SA John W iley & Sons 2011 2 Zukauskas A Shur M S C aska R Introduction to Solid-State Lighting M New York U SA John W iley & Sons 2002 3 Pimputkar S Speck J S DenBaars S P Nakamura S Prospects for LED lighting J Nature Photonics 2009 3 4 180-182
271 4 HU Run YU Shan ZO U Yong ZHENG Hai W ANG Fei LIU Sheng LU O X iao-bing Near-/ mid-field effect of color mixing for single phosphor-converted light-emitting diode package J IEEE Photonics Technology Letters 2013 25 3 246-249 5 Dupuis A Yeomans J M Lattice Boltzmann modeling of droplets on chemically heterogeneous surfaces J Future Generation Computer Systems 2004 20 6 993-1001 6 Yan Y Y Zu Y Q A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio J Journal of Computational Physics 2007 227 1 763-775 7 Inamuro T O gata T T ajima S Konishi N A lattice Boltzmann method for incompressible twophase flows with large density differences J Journal of Computational Physics 2004 198 2 628-644 8 Briant A J Papatzacos P Yeomans J M Lattice Boltzmann simulations of contact line motion in a liquid-gas system J Philosophical Transactions of the Royal Society of London Series A 2002 360 1792 485-495 9 SHAN X iao-wen C HEN Hu-dong Lattice Boltzmann model for simulating flows with multiple phases and components J Physical Review E 1993 47 3 1815-1819 10 Shan X Doolen G M ulti-component lattice-boltzmann model with interparticle interaction J Journal of Statistical Physics 1995 81 1 379-393 11 SHEN Sheng-qiang BI Fei-fei GU O Ya-li Simulation of droplets impact on curved surfaces with lattice Boltzmann method J International Journal of Heat and Mass Transfer 2012 55 23 /24 6938-6943 3-Dimensional Lattice Boltzmann Simulation of Phosphor Jel Dispensing Process in Light Emitting Diodes LI Lan ZHENG Huai LU O Xiao-bing School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan 430074 P R China Abstract T o get white light emission it s common to use a blue LED light emitting diode chip to be coated w ith yellow emitting phosphor jel via a dispensing process T he phosphor jel dispensing process is of two-phase flow which decides the morphology and properties of the phosphor gel thus strongly influences both optical and thermal performances of the resulting LEDs It is important to describe the dispensing process accurately and improve the coating quality Based on the lattice Boltzmann method LBM a flow model of phosphor gel w as established to simulate the dispensing process T he dispensing and shaping processes of phosphor gel on flat surface and square projection w ere analyzed respectively Results show that LBM simulates the dispensing process of phosphor gel accurately and predicts the morphology w ell T he droplet contact line length changes as a pow er function of the droplet diameter on flat surface T he simulation results provide a theoretical basis for the optimization of the phosphor gel dispensing process Key words phosphor dispensing process flowing simulation lattice Boltzmann method Foundation item T he National Natural Science Foundation of C hina 51376070