Selected literatures introduction about gas-liquid flow in microchannels

Reporter: Zhang WeihuaSupervisor: Professor Xin Feng

I • Fundamentals

II • Maldistribution

III• Producing droplets

IV• Simulation methods

V• Research orientation and aim

Contents

Fundamentals

Flow patterns

Mixer geometry

Pressure drop

Jean-François Manceau et al. New regime of droplet generation in a T-shape microfluidic junction (2013)

Flow patterns

minθ

Fundamentals

Fundamentals

Mixer geometry

K.D.P. Nigam et al. Slug flowin curved microreactors: Hydrodynamic study (2007)

Fundamentals

Pressure drop

J.C.Schouten et al. Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers (2009)

BrethertonBretherton’s analysis is valid for very small liquid film thickness df and in absence of significant inertial and gravitational forces, i.e. Cab → 0 and

1<</= 21 σuDρWe bhb

And results in:32

67.0= bc

f CaDd

cbb D

σCaP 3

2

)3(16.7=Δ

Aussillous and Quéré:

32

32

34.3+1

67.0=

b

b

c

f

Ca

CaDd

KreutzerKreutzer et al. consider the liquid flow in the slugs to be a fully developed Hagen–Poiseuille flow

cDUρf

zP 4

)21(=

dd 2

Fanning-

))(+1(16

= b

gl

gl

s

c

gls Ca

ReLD

aRe

f

)+

()dd(=)

dd(

sb

ssc LL

LzP

zP --

)32

)3(16.7+1(

16=

32

bs

bc

gls CaL

CaDRe

f

212

1

)+(Re2=

4))+(

21(=)

dd(

c

lggls

clgss D

UUμfD

UUρfzP-

Fig. 1 Schematic of Taylor flow showing the definitions of the unit cell, gas bubble length Lb and the liquid slug length Ls. The lengths of the nose Lnose and tail Ltail sections of the gas bubble are also indicated

lgfb

bb UUu

AA

uAA

+=)1(+ -

Mass balance-based Model

fb

bbb

l uAA

δLFAA

U )1(+)+(= -sb

bb LL

uF

+=)(= δLF

AA

U bbb

g -

)+()+(32

=)+)()+(21

)(4

)(Re16

(=Δ 22

1gl

δLD

UUμδLUUρ

DP b

c

lglblg

cs

)34.3+1()3(16.7

=Δ32

32

bc

bb CaD

CaσP

)34.3+1()3(16.7

+)+()+(32

=Δ+Δ=Δ32

32

2bc

bb

c

lglbsuc CaD

CaσδL

DUUμ

PPP

Accounting for a non-negligible liquid film thickness:

The frictional pressure loss in one liquid slug:

The pressure drop over a unit cell:

))34.3+1)(+)(+(32

)3(16.7+1(

)+()+)(+(32

=

))34.3+1(

)3(16.7+)+(

)+(32(

+1

=+

Δ=)

dd(

32

32

32

32

21

2

bblgl

bc

sbc

bgl

bc

bb

c

lgl

sbsb

uc

CaδLUUμCaDσ

LLDδLUUμ

CaDCaσ

δLD

UUμLLLL

PzP-

The pressure drop over a unit length of channel:

Pressure drop Model

22

32=

)+()+)(+(32

c

ll

sbc

blgl

DUμ

LLDδLUUμ

bblgl CaAA

UUμσ 1

=)+(

)34.3+

1+32

3×16.7+1(

32=)

dd(

31

32

2bbbb

c

c

ll

CaCaAA

δLD

DUμ

zP-

)34.3+

1+32

3×16.7+1)(

Re16

(=31

32

gl bbbb

cs CaCaA

AδL

Df

l

b

bb UF

AA

δL=

+1

)34.3+

132

3×16.7+1)(

Re16

(=31

32

gl bbl

bcs CaCaU

FDf

)34.3+

132

3×16.7+1(

32=)

dd(

31

32

2bbl

bc

c

l

CaCaUFD

Dμ

zP-

Substituting, then get:

Rewritten by:

And:

For a stagnant liquid film:

Then:

Experimental:

Maldistribution

Elevated pressure

Microchannel Network

MaldistributionElevated pressure

Chen Guangwe et al. Gas-liquid two-phase flow in microchannel at elevated pressure(2013)

M. Saber,J.M.Commenge. Microreactor numbering-up in multi-scale networks for industrial-scale applications: Impact of flow maldistribution on the reactor performances. (2007)

MaldistributionMicrochannel Network

1

1

1

=

2=1212 ++2=Δ n

ni

iqRQRQRP ∑

4

128=

m

mm Dπ

LμR

( ))max(

min)max(100=

qqq

Md-

q

qqN

Sd

N

ii

ˆ

)ˆ(1

1

100= 1=

2∑ --

optB

BoptB

CCC

dvˆ

100=-

∑ Nii i

Ni

iA

Bii

A

B

qCC

q

CC

=1=

=

1=0

0

∑ )(=

ˆ

The frictional pressure drop through the two-scale device:

The flow Maldistribution and Standard/Yield deviation defined as:

With:

Robustness

11

Δ=*Δ

QRPN

PNormalized pressure drop:

Microdroplets

T-controlled bubble condensation method

Luo GS et al. Generation of monodispersed microdroplets by temperature controlled bubble condensation processes (2013)

Figure 2. Main components of the temperature controlled microfluidic system. (a) The mini-evaporator fabricated from a stainless steel pipe (b) The air bath (bottom-up) fabricated with anodized aluminum. A glass window is placed on the metal shell to observe the inside. (c) The capillary embedded coflowing generators (d) The cooling unit with 2 m long cooling pipe.

Simulation

Fan LS et al. Experiment and lattice Boltzmann simulation of two-phase gas–liquid flows in microchannels (2007)

))v,(),x((1

=),x()1+,c+x( )( σσeqσi

σiσ

σii

σi nftf

τtftf ---

The simulation was performed on the D2Q9 lattice

),(=),( txftxni

σi

σ ∑

σσ

σσ

ρτ

F+u=v

∑ σσσ

σσσσ

τρ

τρ∑ u=u

The number density and momentum of each component:

),(c=),(u txftxni

σii

σσ ∑The equilibrium value of the velocity:

Where:

σs

σf

σ F+F=F

),(=),( txfmtxρi

σi

σ

σ ∑∑),(F

21

+),(=),(U),( txtxfcmtxtxρi

σ

i

σii

σ

σ ∑∑∑),(),(

21

+),(=),( 22 txψtxψGctxnctxp σ

σσ

σσσs

σ

σs

∑∑

iiσ

σ iiσσ

σσf ψTGψ c)c+x()x(=F ∑ ∑-

iii i

isσσσ

s sTGψ c)c+x()x(=F ∑ ∑-

The interaction force on component σ:

The macroscopic variables:

Research OrientationI

Influence of mixing zone geometry on gas-liquid flow pattern and slug formation

II

Novel method to reduce maldistribution or non-uniformity in microreactor numbering-up

III

Experimental and numerical simulation of suitable microdroplet producing method

IV

Explore applicable LBM method to simulate gas-liquid flow in microchannel

V

More …