CHEG Special Topics in Mixing. Lecture 7 Liquid-Liquid Mixing. Copyright 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche All rights reserved.

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1 CHEG Speial Topis in Mixing Leture 7 Liqui-Liqui Mixing Copyright 000, A.W. Ethells, R.K.Grenville & R.. LaRohe All rights reserve.

2 Uses for Liqui-Liqui Mixing Uses Contating for Mass Transfer Single Mixer-Settler Stage Columns Prouts Stable Emulsions Foo an Cosmeti Prouts Mixing Leture 7 Slie

3 Multiphase Systems Soli-Liqui Fixe Surfae Area Gravity plays moerate role Gas-Liqui Variable Surfae Area Gravity plays strong role Liqui-Liqui Variable Surfae Area Gravity plays weak role Mass Transfer Similarity in mass transfer orrelations Mixing Leture 7 Slie

4 Multiphase Flow Regimes Bak-mixe Continuous (Liqui) Phase Soli-Liqui, Liqui-Liqui, Gas-Liqui Bak-mixe isperse Phase Soli-Liqui, Liqui-Liqui Plug Flow isperse Phase Gas-Liqui Challenges What is the interfaial surfae area? What are the film oeffiients? J = kla( C C) Equilibrium Stages often use with Liqui-Liqui Systems Presumes mass transfer is fast an omplete within resiene time * Mixing Leture 7 Slie 4

5 Liqui-Liqui rop Breakup Key Priniple - rops have a harateristi strength that epens on rop size haraterize by 1 σ N m N = = m m where σ = interfaial = tension fore = area an [ stress] = rop iameter In a given flui stress fiel, rops will break until the harateristi strength an no longer be overome rops break own to a imum size beyon whih they will no longer break not all rops will be that imum size there will be a rop size istribution Mixing Leture 7 Slie 5

6 Mass Transfer in Liqui-Liqui Systems Mass Transfer Rate, J * J = kla( C C) Average rop Sizes Various averages possible whih iffer bases on rop size istribution Sauter mean iameter, - average of surfae area per unit volume of all rops = i i i Nee to estimate interfaial area, a 6φ a = where φ = total volume of isperse phase Mixing Leture 7 Slie 6

7 rop Break-up in Low Visosity Turbulent Flow rop Weber Number (We) Break-up ours above a ritial (We) ( We) Break-up Stress in Turbulent Flow - Reynols Stress τ = σ τ = ( ) ( u v ) ρ ( u ) ρ [ breakup stress] [ stabilizing stress] Assume rops muh larger than Kolmogoroff length sale so affete by eies in the inertial sub-range ( u ) l E ε Assume u = l E ( ε ) l E 1 Mixing Leture 7 Slie 7

8 rop Break-up in Low Visosity Turbulent Flow At rop break-up, break-up stresses balane stabilizing stresses τ ρ ( ) ( ε ) We = = = onst ( σ ) ( σ ) ρ ( ε ) ( σ ) σ ρ 0.6 ε 0.4 ε - loal power per volume not average In stirre tanks, use power per impeller swept volume Assume ε P ρv imp Combine to give = Po ρn π ρ 4 5 w = σ ρ Po N π ρn σ 5 α ( N ) 0.6 = 0.4 Po N πα ( We) ε N Stuies show = 1.7 ( avies orrelation) Mixing Leture 7 Slie 8

9 vs. Power per Mass σ ρ 0.6 ε 0.4 Stirre Tanks may not be best for liqui rop ispersion wie istribution of ey sizes an energy issipation rates bypassing Mixing Leture 7 Slie 9

10 Equilibrium rop Size istribution Low to Moerate isperse Phase Visosity Sauter Mean iameter inluing visosity effets (Calabrese, Wang & Bryner, 1986) 49 ata sets (Rushton turbine) 5 = We µ = N ρ where Vi σ ρ 1 Vi 1 5 Cumulative Volume Frequeny (Wang & Calabrese, 1986) 146 ata sets F v = erf Mixing Leture 7 Slie 10

11 Minimum ispersion Spee N J - minimum impeller spee to isperse liqui roplets N J Correlation for 6-blae isk impeller (Penney, et al., 1999) N J ρg S = g σ where H C S = f,, Z T T H = height of light Z = total liqui height, m ρ = ensity h ρ = ensity l of of light N J = Froue g heavy ρg = Gouher σ 1 phase in stati onition, m phase, phase, number 1 number ρ h ρh ρl kg kg m m 1 4 ( ) [ inertial fores] Fr = [ gravitational fores] ( ) [ gravitational fores] Go = [ interfaial fores] Mixing Leture 7 Slie 11

12 Time to Reah Equilibrium rop Size Time to ahieve equilibrium rop size long times 5-0 minutes at lab-sale hours at plant-sale Two parallel proess onept (Balyga & Bourne) Breakup - fast proess Coalesene - slow proess Rate of rop Break-up probability of rop going through impeller zone irulation time V t Q = Q tank volume important Mixing Leture 7 Slie 1

13 Coalesene - Important Fators Flow fiel an ollision rate Volume fration of the isperse phase Visosity of both phases Conition, age, visosity an mobility of rop interfaes Presene of partiulates, surfatants or suspening agents Coalesene an our at many loations whih ompliates interpretation impeller blaes baffles liqui surfae Mixing Leture 7 Slie 1

14 Population Balane Equation Mixing Leture 7 Slie 14

15 Separator (eanter) esign Liqui-liqui Flow into a Cylinrial Vessel Quiet Zone where interfae forms Coalesene Layer or Ban Assume rops in both phases Settle to oalese an form interfae Avoi interfering with settling proess Gravity separation Settling rate given by Stoke s Law V s = ρ 18g ρ µ esign for a ertain ut size for instane, get all rops above 15 mirons Keep (through flow)/(veloity) equal to ut size settling rate Mixing Leture 7 Slie 15

Determination the Invert Level of a Stilling Basin to Control Hydraulic Jump

Determination the Invert Level of a Stilling Basin to Control Hydraulic Jump Global Avane Researh Journal of Agriultural Siene Vol. (4) pp. 074-079, June, 0 Available online http://garj.org/garjas/inex.htm Copyright 0 Global Avane Researh Journals Full Length Researh Paper Determination