Model prediction and experimental validation Marco Zoeteweij Jacques van der Donck Richard Versluis
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 2
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 3
Scope of the project Contamination control Prevention of the unwanted detachment of particles from wall surface due to gas flows in the system, e.g. in lithographic processing Surface cleaning Cleaning (on purpose removal) of particles from a surface using a gas flow Relevant in High-End & Semiconductor industry High throughput of gasses gives large velocities and increased risk of particle contamination High requirements on cleanliness 4
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 5
Particle motion in flow What kind of motion to expect? 6
Particle motion 4 possible types At rest Lift Sliding Rotation 7
Forces on a particle in linear (wall-) shear flow P. Schmitz, J. Cardot (2002) 8
Forces acting on the particle Attraction Gravity F G = mg = ρvg Van der Waals 2 A d 2a = 1 2 + 12z0 z0d H FV G. Ahmadi 9
Forces acting on the particle Flow induced Drag G. Ahmadi F D 2 1 2 24η πd = 2ρU 1.7009 = d Ud 1.7009 3π η ρ 4 ( u u ) f p Lift G. Ahmadi 10 F L = 1.615 η d 2 ρ u η y 1/ 2 ( u u ) f p
Forces acting on the particle Flow induced Drag G. Ahmadi F D 2 1 2 24η πd = 2ρU 1.7009 = d Ud 1.7009 3π η ρ 4 ( u u ) f p Lift G. Ahmadi 11 F L = 1.615 η d 2 ρ u η y 1/ 2 ( u u ) f p
Forces acting on the particle - Overview Force [N] 1 0.1 0.01 1. 10 3 1. 10 4 1. 10 5 1. 10 6 1. 10 7 1. 10 8 1. 10 9 1. 10 10 1. 10 11 1. 10 12 1. 10 13 1. 10 14 1. 10 15 1. 10 16 1. 10 17 For micron-sized particlesf G << F V, so NOT depending on orientation of surface. Vd Waals Gravity Drag Lift 1. 10 7 1. 10 6 1. 10 5 1. 10 4 1. 10 3 0.01 0.1 1 Diameter [m] 12 Glass particles in air flow at atmospheric pressure
Reynolds number analysis 1.10 5 1. 10 4 1. 10 3 Re = U p dρ p η Re lift = 1.615d F attraction ρ η u y ρ 2 η Reynolds [-] 100 10 1 0.1 0.01 Particle Lift Sliding Rotation 1.10 3 1.10 7 1.10 6 1.10 5 1.10 4 1.10 3 0.01 0.1 1 Diameter [m] Re sliding = µ F attraction 1.7009 3π + µ 1.615d s s ρ η u y ρ 2 η 13 Re rotation = 0.94399 2πd F attraction + 1.7009 3πL L 1 2 + 1.615d ρ η u L y 2 ρ 2 η
Reynolds number analysis (1) 1. 10 5 1.10 4 1.10 3 Reynolds [-] 100 10 1 0.1 0.01 Rest Rotation Lift 100 micron 80 micron 1.6 micron Particle Lift Sliding Rotation 1.10 3 1. 10 7 1. 10 6 1. 10 5 1. 10 4 1. 10 3 0.01 0.1 1 Diameter [m] 14 Glass particles in air flow at atmospheric pressure
Reynolds number analysis (2) Reynolds [-] 1. 10 5 1. 10 4 1.10 3 100 10 1 Hard materials, Steel and Glass behave similar The soft PSL has a much larger critical diameter at the same shear rate 0.1 0.01 Particle Steel/ PSL/ Steel on Steel steel PSL PSL on PSL 1. 10 3 1. 10 7 1. 10 6 1. 10 5 1. 10 4 1. 10 3 0.01 0.1 1 Diameter [m] 15 Different materials, rotational motion only
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 16
Experimental validation Set-up Flow-cell with 10 mm slit-height Turbulent flow conditions (Re > 10 4 ) Shear rates at the lower surface ranging from 7 10 4 s -1 to 2 10 6 s -1 Linear velocity gradient in wall region (for z<0.1 mm) 17
Removal efficiency for different shear rates Residual [%] 100 90 80 70 60 50 40 7,89E+04 1,33E+05 2,20E+05 2,62E+05 3,21E+05 3,53E+05 1,93E+06 30 20 10 0 d 50 d 30 1 10 100 Diameter [micron] 18
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 19
Critical diameters for particle motion Gradient [1/s] dlift [µm] drot [µm] d50 [µm] 7.89 10 4 1740 25.6 27.0 1.33 10 5 1047 16.3 18.7 2.20 10 5 661 10.5 14.0 2.62 10 5 566 9.1 12.6 3.21 10 5 473 7.6 11.0 3.53 10 5 436 7.0 10.5 1.93 10 6 101 1.7 4.1 20
Several micron under prediction 40 Experiment Model 30 Diameter [micron] 20 10 0 1E+04 1E+05 1E+06 1E+07 Shear rate [1/s] 21
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 22
Discussion 40 Rotation diameter is a good estimator for the for the critical particle release diameter D ia m e te r [m ic r o n ] 30 20 `` Experiment Model 10 Not included in the model Electro static interaction Capillary effects Non-spherical particles Surface roughness 0 1E+04 1E+05 1E+06 1E+07 Shear rate [1/s] Implementation of these effects will improve accuracy 23
Structure of presentation Scope of the project Model on particle flow interaction Experiments Validation Discussion Conclusion 24
Conclusions Particle rotation responsible for initial motion and removal Model based on Van der Waals interaction and drag force predicts the experimentally obtained value within several micron The distribution in diameters of removed particles is wide, which is not implemented in the model. The model indicates the average diameter for which 50% of the particles is removed When including other effects in the model (e.g. electrostatic and capillary interaction, particle and surface shapes), the accuracy of the predictions will improve 25