A general approach for predicting the filtration of soft and permeable colloids: the Milk example

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A general approach for predicting the filtration of soft and permeable colloids: the Milk example

Antoine Bouchoux, Peng Qu, Patrice Bacchin, Geneviève Gésan-Guiziou

To cite this version:

Antoine Bouchoux, Peng Qu, Patrice Bacchin, Geneviève Gésan-Guiziou. A general approach for predicting the filtration of soft and permeable colloids: the Milk example. Euromembrane 2015, Sep 2015, Aachen, Germany. 2015. �hal-01209883�

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A general approach for predicting

the filtration of soft and permeable colloids : the Milk example

A. Bouchoux, P. Qu, P. Bacchin, G. Gésan-Guiziou

Euromembrane Aachen– 6-10 sept. 2015 1 FRANCE

Rennes

Toulouse

Science and Technology of milk and eggs

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- Filtration in the dairy sector

•Operations largely used: ≈ 40% of the membrane area installed in food sector Concentration of milk components Cheese manufacture, stadardization, … Fractionation of milk components Ingredients with high added value

Operations not well mastered & Performance impossible to predict

•Variability of production duration and quality of produced fractions

•Difficulties of cleaning

High consumption of water(2-6 m³of water / 100 m²of membranes / cleaning operations)

detergents and energy...

2

Context

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- Micro- and Ultra- filtration (crossflow) of skimmed milk

Context

•casein micelles = main contributor to accumulation at the membrane surface

Casein micelle (colloid)

• Casein micelle = soft and porous « natural » colloid

High concentration of colloids

[Gésan-Guiziou et al., JMS, 1999;

Jimenez-Lopez et al, SPT, 2008]

~80% of milk proteins, C ≈ 25 g/L

caseins : a_s1, a_s2, b, k (3:1:3:1) minerals : phosphate and calcium Composition :

Colloidal object (≈ sphere) ^:

large size distribution ~50-250nm, average diameter ≈ 100nm highly hydrated (3.7g of water / g protein)

Structure :

core web of caseins + calcium phosphate nanoclusters surfacek-casein, highly charged

The internal structure is not totally elucitated…

?

k-casein

[Walstra, Int. Dairy. J., 1999 ] [de Kruif et al., Adv. Colloid Interface Sci., 2012 ]

[Bouchoux et al., Biophys.J., 2010]

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• To propose a methodology for building a model that is able to predict the performance of the filtration (J, concentration gradient) of soft and permeable colloids

… by taking into account the approaches previously developped for non deformable and non permeable colloids (like hard spheres)

Objective

Note :

- dead-end filtration case only

- native « casein micelles » as model experimental system

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Filtration modeling for colloids

5

- Theory

dx d dx

dP   

J permeation flux P pressure k(f)permeability

R_PLresistance of the polarized layer

 osmotic pressure f volume fraction

dynamic viscosity of the solvent

Compression and permeation in a deposit/gel

dx dP R

dx d k dx

d J R

PL PL

PL

1 1



 ^

 

 





dx k d

dx k dP

J  ^gel   ^gel 



[Bacchin, Gordon Research Conference Membranes,2006]

[Bowen et Jenner, Chem. Engng.Sci., 1995]

[Bacchin et al., J.Membrane Sci., 2006]

[Elimelech et Bhattacharjee, J.Membrane Sci., 1998]

Case of dead-end filtration

Diffusion and convection

in polarized layer

_crit

P

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 Two parameters for the filtration modelling for colloids

 (C/f): Colloidal osmotic pressure (colloidal interactions) k (C/f): Hydraulic permeability (size, form, concentration)

6

- Theory

dx d

J k( ) (f)



f 





 A single equation to describe concentration polarisation and deposit layers

J permeation flux P pressure kpermeability

 osmotic pressure Cconcentration

_crit

P

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Happel

3 / 5

2 3

/ 5 3

/ 2 1

2 3

3 5

. 4 5

. 4 3 9 2

f

f f

f

f 





 

 ^p

happel

k r

Carnahan-Starling

 ³

3 2

1 1

f f f f





 

 nkT

Permeability Osmotic Pressure

7

- Theory: non-interacting hard spheres

DP

dx d

J k( ) (f)



f 





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[Bacchin et al., Desalination, 2006]

_crit

8

Deposit

- Theory: charged hard spheres

Happel

3 / 5

2 3

/ 5 3

/ 2 1

2 3

3 5

. 4 5

. 4 3 9 2

f

f f

f

f 





 

 ^p

happel

k r

dx d

J k( ) (f)



f 





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- Theory: deformable and porous colloid (casein micelles)

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[Bouchoux et al., Biophys. J., 2009]

d_p=100nm Happel

3 / 5

2 3

/ 5 3

/ 2 1

2 3

3 5

. 4 5

. 4 3 9 2

f

f f

f

f 





 

 ^p

happel

k r

Prediction

Experiment

How to determine k for concentrated layers of casein micelles ?

dx d

J k( ) (f)



f 





: osmostic stress/ membrane osmometer

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Permeability

Filtration modeling -

10

[Bouchoux et al., Biophys. J., 2009]

Determination of k

Dead-end filtration of native casein micelles, C 1g/L

dx d

J k( ) (f)



f 





Strategy 1: Reverse-calculation approach [Bowen et Williams, J. Membrane Sci., 2001]

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11

e C

J  k ^slice  D



) (

0 bag

cas cas

bag bag

A M A

e V 



 

Determination of k

Strategy 2: osmotic compression approach

ethickness of the slice

Mcas

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12

The different approaches for the determination of k are coherent Experimental values of k are distributed over one single curve Results: permeability

Filtration modeling - Determination of k

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13

Before close-packing: k micelles < k_happel (hard spheres)

 Polydispersity in size : unlikely [Li et Park, Ind. Eng. Chem. Res., 1998]

 Impureties, degradation ?

3 / 5

2 3 / 5 3

/ 2 1

2 3

3 5

. 4 5

. 4 3 9 2

f

f f

f

f 





 

 ^p

happel

k r

d_p=100nm

Results: permeability

d_p=100 nm

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14

After close-packing: k  internal organisation of casein micelle

Casein micelle interior = collection of non

connected hard spheres d_p=8.8nm

3 / 5

2 3 / 5 3

/ 2 1

2 3

3 5

. 4 5

. 4 3 9 2

f

f f

f

f 





 

 ^p

happel

k r

Results: permeability

d_p=100 nm

d_p=8.8 nm

[Bouchoux et al., Biophys.J., 2010]

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15

[Bouchoux et al., Biophys. J., 2009][Bouchoux et al., Biophys. J., 2009]

Results: modelling

Prediction is possible dx

C d

C

J   k( ) ( )



Filtration modeling - Development of the model

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16

[David et al.,Langmuir, 2008]

SAXS

X Rays

Pression X rays

Model validation

Pressure

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17

[David et al.,Langmuir, 2008]

SAXS

The results are satisfying

Model validation

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Conclusion

• Proposal of a generic methodology for building a model able to predict the performance (J, C) of the filtration of soft and permeable colloids (casein micelles)

• Methodology based on

- models developped for the filtration of hard spheres

- experimental determinations of the colloidal osmotic pressure  (C) and permeability k(C)

Model ((C), k(C))

Dead-end  crossflow?

Perspectives

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Thank you for your attention ! Acknowledgments

PhD Thesis P. Qu Région Bretagne & INRA