Numerical Analysis of Bubble-Powered Micropump in Chemical Engineering
This study focuses on developing a numerical model to simulate a micropump driven by bubble formation and growth. The research covers various sub-models such as initial liquid heating, bubble growth, and collapse, with the objective of understanding the operation of the micropump. Basic assumptions, conservation equations, and liquid-vapor boundary representation are discussed to provide a comprehensive overview of the study.
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Dept. of Chemical Engineering and Biotechnology Numerical Analysis of Bubble Powered Micropump Gad A. Pinhasi Matan Pe er and Amos Ullmann COMSOL CONFERENCE 2019 Cambridge, September 24 26 1
Micro Pump A lab-on-a-chip (LOC) Micro Fluidic Pumps Insulin Pump (drug delivery) Electronics cooling, Ink Printers, 1mm Active Mixer (Evans et al., 1997) Micro-channels and Pump (Lin and Tsai, 2002) 2
Bubble Micro-Pump Driving force Bubble formation, growth and collapse Vapor volume change Flow control Diffuser/Nozzle Unsteady Pumping flow Pulsing flow No moving parts Jung and Kwak (2007) Tsai and Lin (2002) 3
Bubble Lifetime Cycle Heating Waiting Time Bubble formation: Stable bubble criterion Nucleation Bubble growth Inertia Controlled Diffusion Controlled Collapse Problem: Discontinuity in the flow field in time Deniray and Kim (2004) 4
The Objective Developing a numerical model to simulate the operation of a micro-pump driven by bubble formation and growth. Sub-models: Initial liquid heating, Formation of a critical bubble, Bubble growth and collapse The liquid flow through the nozzles system. 5
Basic Assumptions Laminar flow Heating with constant heat flux. Duty cycle (= 80%) Initial liquid temperature: Ambient Initial Hemispherical critical bubble on the wall Case Study: Displacement Pump: 2D, 3D analysis Bubble growth simulation: 2D spherical Bubble Pump: 2D analysis th DC=th/Tc q Tc t 6
Conservation Equations Continuity Heat and Mass Transfer at the Boundary Phase Change Moving boundary = t ( ) + = u 0 Momentum: NS Eq. u + u = u q k T t , i net L , interface n 2 , = ( ) ( ) q h m T = + + g + u u n p u I i net LG e 3 Heat Eq.: Convection Liquid Heat q Vapor T ( ) e + = u C T k T m h p fg t Evaporation me 7
Liquid-Vapor Boundary Representation Level Set Method Fluid interface representation Level-set Parameter [0,1], =0.5 Fixed Grid Interface n Vapor Liquid RB 1 + = u r m interface t = = + n u u n interface 5 . 0 = ( ) = 1 ( ) = + G L G 8
Bubble Formation Criterion Wall heating Semi-infinite body Constant heat flux k 4 A Liquid Heating 0 2 2 q t x x x = exp T T erfc t 0 t 2 2 t t Critical Radius Critical Radius B 2 = R , B c P P G L Nucleation Heating Plate Hsu (1962) RB 9 Bubble
Liquid Liquid Heating Model Bubble Nucleation Criterion No Heating surface t+dt Yes Interface formation Bubble formation Bubble Growth Model Bubble growth No Bubble Collapse Criterion t+dt Yes Bubble Removal Liquid 10
The CFD Tools MATLAB Based Main program Script (MATLAB) COMSOL Multiphysics Physics: Laminar flow Heat Transfer Fixed Grid Boundary problem: Level set Grid generator Solver Post Proceeding COMSOL Multiphysics and the LiveLink for MATLAB Combine user code and software functions and solvers: 11
Results 1. Diffuser/Nozzle Characteristics 2. Displacement Pump 3. Bubble growth 4. Bubble pump 12
Diffuser/Nozzle Characteristics Steady state flow Minor losses Coef.: K Effectiveness High directed flow Diffuser Nozzle 1000.0 1 2 = x 2 throat p u diffuser nozzle 100.0 = x x x x Nozzel Diff 10.0 1.0 13 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 Re
3D Displacement Pump P P = h 2 1 p g v cycle T 1 ( ) = Q Q Q dt ( ) ( ) = t T + 1 2 net b b 0sin v 2 v t cycle T 0 cycle A Q h Q h Q h 1.2 0.012% 16 Hz 24 Hz 32 Hz 40 Hz 16 Hz - Eff 24 Hz - Eff 32 Hz - Eff 40 Hz - Eff net p net p net p = = = 1.0 0.010% W PdV Pvdt input Efficiency [Wnet/Win] 0.8 0.008% hp [mm] 0.6 0.006% 0.4 0.004% 0.2 0.002% 0.0 0.000% 0 1 2 3 4 5 14 Net Flow [ l/min]
Spherical Bubble Growth Bubble radius time history 3DAnalysis Axial symmetry Comparison against analytical models Diffusion Controlled Inertia Controlled 15
Bubble Pump th DC=th/T q Boundary conditions Pressure drop Heater segment Initial Conditions: Initial temperature: 298K Contact angle 90 Hemispherical liquid domain T t 1 mm 2 mm 0.03 mm 1 mm 0.3 mm 0.18 mm Heating Plate 16
Bubble Growth Stage Velocity-Pressure map 17
Bubble Pump Velocity and flow rate Net flow rate 3.81E-7[m2/s] 9.14 [ l/min] Bubble radius cycle T 1 ( ) = Q Q Q dt Bubble Collapse 1 2 net b b cycle T Bubble Growth R = 0.14mm 0 Net Flow Rate [m2/s] Bubble Radius [m] Duty cycle = 80% Heat Flux in = 1M [W/m2] Heat Flux out = 10k [W/m2] 18 Time [s] Time [s]
Bubble Pump Head and Efficiency 0.350 9.00E-09 8.00E-09 0.300 7.00E-09 0.250 6.00E-09 Efficiency Wflownet/WHeatin 5.00E-09 0.200 hp [mm] 4.00E-09 0.150 3.00E-09 2.00E-09 0.100 1.00E-09 1 Q h Q h net p net p = = 0.050 W 0.00E+00 qdt input T 0.000 -1.00E-09 -1.0 1.0 3.0 5.0 7.0 9.0 Net Flow [ l/min] 19 q=900k, 18.5Hz q=950k, 19.2Hz q=1M, 20Hz q=900k, 18.5Hz q=950k, 19.2Hz q=1M, 20Hz
Summery A numerical model was developed to simulate the operation of a micro-pump driven by bubble formation and growth. The model solves the time dependent conservation equation for viscid fluid: mass, momentum and convection heat transfer. The Level-Set method is being used to represent the gas-liquid interface. The analysis is made by using finite element software- COMSOL Multiphysics. The model was tested against analytical model for diffusive bubble growth. 20
Pinhasi, G.A., Pe'er, M. and Ullmann, A. (2019) Numerical Analysis of Bubble Powered Micropump , Proceedings of COMSOL Conference 2019, Cambridge, September 24 26. 21
