Simulations of dispersed multiphase flow at the particle level
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1 Simulations of dispersed multiphase flow at the particle level Jos Derksen Chemical Engineering Delft University of Technology Netherlands
2 Multiphase flow collective behavior particle-scale processes sediment transport bubbly flow blood (Pickering) emulsion predictive modeling & simulation flow dynamics mass transfer & mixing interface the particle scale ( meso-scale )
3 Macroscopic multiphase transport turbulent flow inertial particles wide spectrum of (length) scales particle size, tank size, turbulence scales 30 cm 2 ND Re = 10 ν 5 n p 6 10 Ayranci et al CES 2012
4 Unresolved vs resolved particles 2a p = d < particle size < fluid grid spacing particle dynamics based on empirical force correlations up to 10 8 particles 2a p = d > particle size > grid spacing no need for empiricism* up to 10 4 particles multi-scale *fine print
5 Quick overview of numerics* fluid flow d p scalar > particle motion Lattice-Boltzmann method for solving the flow of interstitial fluid 3D, time-dependent Explicitly resolve the solid-liquid interface: immersed boundary method particle size typically 12 grid-spacings Solve equations of linear and rotational motion for each sphere forces & torques: directly (and fully) coupled to hydrodynamics plus gravity hard-sphere collisions or soft interactions (mostly for non-spherical particles) *Derksen & Sundaresan, JFM 587 (2007)
6 A miniature mixing tank 2 Re= ND 2,000 ν φ 0.08 (3,600 spheres) ρ p ρ = 2.5 (glass beads in water) initial state zero velocity for solid & liquid all particles on the bottom θ 2 2 ρn D = = g 2a ( ρ ρ) p a modified Shields number 6 96 Derksen AIChEJ 2012
7 Start-up of suspension process φ 0.08 φ 0.24 φ 0.24 u v tip 0 1
8 Experimental Institut de Mécanique des Fluides de Toulouse refractive index matching for optical access a liquid fluidization Beijing University of Chemical Technology..& our simulation** Mo et al AIChEJ 2015 *Duru, Guazelli JFM 2002 **Derksen, Sundaresan JFM 2007
9 Re = u D ν starting from a vertical orientation More experimental validation very simple experiments a High School experiment Becker Can. J. Chem. Eng 1959
10 Mass transfer start with zero concentration in the liquid apply a c=1 boundary condition at the particle surface solve a convection-diffusion equation in c Liquid systems: resolution is a serious concern given high Schmidt numbers ν Sc = O 10 Γ vertical cross section 3 ( ) hydrodynamic resolution 2a=d p =16 horizontal cross section
11 Coupled overlapping domains* spherical grid attached to particle multiple particles will have overlapping shells** sphere & spherical grid move relative to Cartesian grid Cartesian outer grid Communication between the grids: linear interpolation velocity on the spherical grid is imposed from the outer grid concentration fields are two-way coupled between the grids...mixing rules * Derksen AIChEJ 2014 ** Derksen CEJ 2014
12 Two-sphere benchmark overall flow in x-direction
13 Fixed beds versus moving spheres u 2a Re= = 1 ν φ= 0.2 Sc 10 = 3 u v p 2a Re= = 1 ν φ= 0.2 Sc= 10 ρ ρ p l 3 = 4 sedimenting spheres g
14 Compare Sherwood numbers fixed bed level Re= 1 φ= 0.2 fixed bed level ρp ρ l = 4 the role of the density ratio
15 Some more mass transfer industrial applications hot melt extrusion* breakthrough in a micro reactor** most of the yellow agent adsorbs on the particles *Derksen et al ChERD 2015 **Derksen Micro Nano Fluidics 2014
16 Liquid-liquid dispersions (emulsions) Basic events break-up coalescence flow dynamics drop size distribution interfacial area inter-phase mass transfer apparent rheology stability product formulation
17 Turbulent emulsions two immiscible liquids in homogeneous, isotropic turbulence* same viscosity same density fully periodic boundary conditions 200η K Number of drops disperse phase volume fraction ϕ=0.20 V/Vinit t/τ K dissolution! t/τ K * Komrakova et al AIChEJ 2015
18 A methods slide: binary liquids : order parameter controls composition advection-diffusion + = chemical potential = = coupled with hydrodynamics through body force = 1 a diffuse interface 0 interface thickness surface tension / = 2 = proper interface is resolution: 1 2 Briant, Yeomans Phys Rev E 2004
19 Ca= Make the flow simpler: breakup in shear µ γ ɺ m a σ Capillary number resolution: a=20 starting point: spherical drop with radius a Ca= 0.42 Re= 0.06 λ= 1 just above Ca c (Ca-critical) a=25 quick dissolution The good news: breakage / non-breakage is largely independent of resolution a=30 Komrakova et al IJMF 2014
20 Coalescence in shear Theory, Experiments, and Motivation complex interfaces: charge, steric effects, variable tension coalescence approach film drainage simulations at critical conditions are challenging topological change; 30 nm film vs. 100 µm drops clean polymer systems hydrodynamics, surface tension, van der Waals forces sliding charged surfaces and electrolytes additional electrostatic interactions Chen et al. Langmuir 2009
21 Uncharged drops Δ! capillary number determines outcome of collision Ca= ρνrγɺ σ Δ /2" =&.() Δ " #$ = 2 % % % = Ca = sliding =2 uniform density & viscosity Guido, Simeone J Fluid Mech(1998) Ca = temporary bridge Ca = coalescence Shardt, Derksen, Mitra Langmuir 2013
22 We are (fairly) grid independent Solid black: " =75, =4 Dashed red: " =37.5, =2 Ca = 0.08 Ca = 0.09 Ca = 0.1 Doubling interface resolution does not change outcome. adequately resolved with =2
23 Critical capillary numbers Ca= ρνrγɺ σ ΔY R.towards lower Δ /2" to compare with experiments
24 need higher resolution Δ /2" =0.2 " =200 / Ca = 0.1 Ca = 0.2 Ca = 0.25 Ca = ρνrγɺ σ De Bruynet al. JCIS2013 Shardt, Mitra, Derksen Langmuir 2014
25 Evolution of film thickness Film thickness (l.u.) critical capillary number 0.1 to 0.25 at 67 8 = Ca = 0.01 Ca = 0.1 Ca = 0.05 Ca = 0.2 Ca = 0.25, 0.3 Ca = 0.05 Ca = 0.10 Ca = 0.01 Ca = 0.20 Ca = 0.25 Ca = Time, #$ a good question would be: how big are these drops actually? an estimate can be based on minimum film thickness minimum film thickness 5 10 l.u. ~ 30 nm " =200: ; Critical film thickness imagine simulating coalescence of 1 mm drops
26 ρν Ca a γɺ = = 0.06 σ Charged drops uncharged charged with Debye length 1 κ = 0.2a increasing electric field strength factor 10 each time
27 coker Sedimentation/fluidization with an emphasis on non-spherical particles steel cubes in fluidization apparatus* sedimenting red blood cells *Richardson and Zaki Trans. Inst. Chem. Eng. 32 (1954)
28 RBC s as sample non-spherical particles Specific challenges* collision handling repulsive spring force between surface points also used for immersed boundary ρp ρ= 1.07 use modified finite difference method for stability low density ratio high solids volume fraction (~0.45) compaction procedure for initialization frequent collisions x ( δ ) F = k x * Shardt & Derksen, IJ Multiphase Flow 47 (2012)
29 Settling of a dense suspension all boundaries are periodic 291 particles =0.35 body force on fluid removing particles reveals flow crosssection balances gravity resolution D = 20 nodes
30 Hindered settling Re= D The RZ fit suggestsre = 18.2 an - on average - inclined RBC 1 void fraction u slip Richardson-Zaki (RZ) u ( 1 φ) = n
31 Human erythrocyte sedimentation rate U. Woermann edu.cpln.ch/hemosurf/data/lab-images/all_esrs.jpg Typical human ESR is 3 9 =0.35 Simulations: 0.18 mm/h surface forces between RBCs and proteins in blood cause agglomeration ESR blood tests
32 Acknowledgements Collaborators & students Sponsors Gaopan Kong & Eric Climent in Toulouse Junyan Mo, Zhipeng Li & Bruce Gao in Beijing Alexandra Komrakova, Inci Ayranci, Suzanne Kresta, Orest Shardt & Jue Wang in Edmonton Sankaran Sundaresan in Princeton
33 Beyond continuum modeling example: aggregation of nanoparticles & liquid bridges Molecular Dynamics TiO 2 nanoparticles 8 nm spheres in a classical Lennard- Jones fluid (red=vapor; yellow=liquid; green=solid) f R R 1 = σπr (+ is attractive) 1 3 V molar NB: 3nm N Av
34 Liquid bridge (molecular) dynamics
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