Challenges of Fluid Flow in Absorbing Porous Media ... - FEFlow

Challenges of Fluid Flow in 

Absorbing Porous Media & Thin Layers 

Rodrigo Rosati* 

Principle Engineer, 

Procter & Gamble - Baby Care R&D 

FEFLOW 2009 Conference 

Berlin/Potsdam, Germany 

September 15, 2009 

Procter & Gamble © 2009 

Dr. Mattias Schmidt 

Research Fellow – Victor Mills Society, 

Procter & Gamble - Baby Care R&D

ABOUT THE PRESENTER 

Rodrigo Rosati is a Principal Engineer at P&G, 

working in the Baby Care R&D at Schwalbach 

Technical Center, Germany. 

He joined P&G in 1999, after graduating in Chemical 

Engineering at the University of Salerno, Italy. He 

has worked in the area of fluid flow modeling and 

absorbent core design since 2003. 

Procter & Gamble © 2009

• P&G at a glance 

Outline 

• Importance of Modeling & Simulation for R&D 

• Fluid Flow in Hygiene Products 

– Introduction 

– Introduction to Diaper Cores and AGM 

– Impact of AGM swelling on fluid flow 

• Typical challenges and opportunities for 

collaboration 


It began with Soap & Candles… 

Founded in 

1837 


•Fifth Oldest 

Company on the 

Fortune 50… 


William 

Procter 

Candle Maker 

James 

Gamble 

Soap Maker

P&G at a Glance 

First Consumer goods company in the world 

More than 300 brands 

More than 5 Billion consumers in more than 160 

countries 

Operations in more than 80 countries 

140 plants and 25 R&D centers worldwide 

ca. 138.000 employees 

Net sales: $83 Billion 

Net earnings: $12 Billion 

R&D Investment: >$2 Billion 


Billion-Dollar 

Brands 


Importance of 

Modeling & Simulation for R&D 


" 

! 

" 

# 

# 


!

Typical Challenges 

Products must perform when used 

… But face Fundamental 

Engineering Contradictions. 

•Materials … strong but soft—even wet, stretch not 

break, breath but contain, break…not tear/selectively 

tear. 

•Liquids … mixtures can’t separate, must stay where 

applied…but dispense easily. 

•Packages … design is key, be strong but light, never 

leak but open easily. 


Time 

days 

hrs 

sec 

ms 

ns 

fs 

Computational 

Chemistry 

Quantum 

Chemistry 

- subatomic 

Scales of Modeling 

Molecular 

Mechanics 

-atoms, 

molecules 

Coarse Grain 

or Mesoscale 

Modeling – 

Polymers 

angstroms nm microns mm m 

Distance 


Continuum or 

Finite Difference 

Finite Element 

MechEng/ChE 

(Closed Form 

Equations) 

Industrial Eng/ 

Operations Resrch 

(Statistical, Discrete 

Event, Agent Based) 

Computer Aided 

Engineering (CAE) 

km

Fluid Flow in 

Absorbent Hygiene Products 


Typical Liquid Handling Tasks in BabyCare 

DIAPERS WIPES 

Urine absorb & retain remove (from skin) 

BM contain & absorb remove (from skin) 

Lotion melt, release & deposit release & deposit (spread) 

(spread)(onto skin) (onto skin) 


Typical BabyCare Liquids 

Viscosity Surf. Tension Key ingredients 

Urine ~1 cP ~50 ... 65 mN/m water, salts, urea, 

surfactants 

BM ~10 6 ... 10 15 cP ~30 ... 60 mN/m water, bacteria, fibers, 

mucins, surfactants, salts 

Lotion solid at RT low (temp dep.) petrolatum, stearyl alcohol, 

(Diaper) aloe 

Lotion ~1 ... 500 cP ~30 ... 65 mN/m Water, silicone (2-3%), 

(Wipes Wipes) polymer (stabylen), 

preservatives, surfactant 


Porous Media Flow 

• Simulation of fluid flow in porous structures 

applied to product design of „paper products“ 

e.g. Diapers, Feminine Pads, Towels, Swiffer, Wipes, 

Make-up-Applications, Olay Facial Wipes ... 

• Being used to develop new designs and new 

materials 

• Richards equation is a typical formulation 


Absorbent Core Modeling 

( 

" + + % , 

) 


! " 

# ! " 

* 

$ % & '

Diaper Core Technology 

Diaper (from Side ) 

Front of 

Diaper 

Waist feature 

Acquisition Patch 

Backsheet Dusting Layer 

Storage Core (blend 

of AGM and cellulose) 


Lotion Stripes Topsheet 

Inside Surface 

Back of 

Diaper 

Outside Surface

Acquisition & 

Distribution 

•Nonwoven Layer 

•Modified Cellulose 

Fibers 

How does a diaper work? 

Liquid Handling Tasks of diaper Cores 

 


Storage Core: 

AGM + Cellulose

Final 

Absorption 

How does a diaper work? 

Liquid Handling Tasks of diaper Cores 

• AGM can absorb about 30 times of its own weight, whereas cellulose can 

absorb only around 4 times of its own weight. 

AGM 

70% 

Pampers Core 


Airfelt 30%

- . 

What is AGM? 

+ / + 0 0 

+ + 

0 + + / + 1 2 

CO2H 

Na + 

3 // 4 / + + 0 


O 

O 

R - C - Et 

C = O 

COO 

Na + 

CO2H 

CO2H 

Na + 

COO 

Na + 

CO2H 

Na +

• Take up urine and lock it away – as much as possible! 


(Storage Capacity) 

• Transport urine within itself, e.g. within a swollen gel bed. 

• Work reasonably fast. 

Function of AGM 

(Permeability) 

(Speed)

5 ( 

! 

6 ) - 

What is „Gel Blocking“? 

5 

5 


(

∂S 

∇ • J + φ 

∂t 

Modeling Fluid Flow in Diaper Cores: 

Non swelling Porous Media 

= 

0 

kkr 

ρ 

µ 

J = − 

cap 

p( S) = p 

saturation 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

des 

( ∇P 

− g) 

p p 0 − abs ( Smax 

) S − 

p ( ) 

0 S max 

0 2 4 6 8 10 

pressure (kPa) 

absorption measurement 

desorption measurement 

absorption fit 

desorption fit 

incomplete cycle 

incomplete fit 

Continuity Equation 

Darcy‘s Law 

1 

1 

n 

( 

m 

) 

des 

−1 

des 

+ p ( S ) 

abs 


max 

Implementation of 

capillary pressure 

hysteresis

Modeling Fluid Flow in Diaper Cores: 

AGM-containing cores 

• AGM absorbs liquid „away from the pores between AGM 

particles and fibers“ 

– Acts like a „sink term“ in the fluid flow equation of the pore structure 

– Liquid absorbed into each AGM particle by diffusion / osmotic process 

– Swelling of AGM changes the pore structure 

• Described as „two types of liquid“ 

– m 1 : „mobile fluid“ in the pore structure 

– m 2 : „immobile“ fluid in the gel 

• Requires modified equation system 

– Richards equation extended by „sink term“ 

– Key properties of pore structure now depend on m 2 

– Additional equation for absorption of liquid into the gel phase 


Swelling Model Equations 


Example: Multilayer Core Structure incl. AGM 

• Pictures show snapshots of fluid in pores (~saturation) and fluid in AGM at two different 

times after a gush onto a pre-loaded core 

• Illustrates how upper acquistition layers and interstitials are being dewatered and fluid is 

absorbed into the AGM 

Short time after gush „In equilibrium“ after gush 


Challenges & Opportunities for 

Collaboration 


Typical Challenges 

• Designs are long / large area but very thin 

– Difficult to mesh properly (balance of speed / accuracy) 

• Product developers want the answers fast 

– Computation time, stability of simulations new algorithms 

– Need to be able to run lots of simulations 

• Extreme material properties 

– Typical porosities ~90% or higher 

– Large parameter contrast in K(S) and Pc(S) and hysteresis 

– Properties change during use (swelling, external pressure changes) 

– Thin materials (see below) 

• Multiple physical effects 

– Porous Media Flow 

– Free Surface Flow 

– Mechanical Deformation 

• Liquids can be difficult 

– Surfactants – Surface tension as function of time, Surfactant Transport 

– Non-newtonian effects – most equations do not apply to high porosities 


Opportunities for Collaboration 

• Fluid flow models in presence of 

– Thin layers 

– Hydrophobic layers / bridging 

• Micromodels to predict K(S, p ext ), Pc(S, p ext ), n(p ext ) 

– Design materials with target K(S), ... 

• (More direct) Measurement of K(S) 

• Initial wetting behavior of very dry materials (analogy to 

soil) 

• Experimental characterization of surfactant release and 

transport in porous media 


Thin Layers – Key Definitions & Relevance 

• A „thin layer“ is characterized by typical pore dimensions that are 

similar (order-of-magnitude) to the thickness (or: the smallest 

dimension) of the layer. 

Only few number of pore layers through the caliper 

Caliper (thickness) often non-uniform 

3D pore structure is influenced by interface / adjacent layers 

• Why are thin layers so important in absorbent products? 

TS, AQL and NWCC have a big impact on speed of acquisition and dryness 

performance 

Acquisition System 

Top-sheet (TS): hydrophilic (spunbond) or hydrophobic (apertured TS) 

Storage Core 

Note: we are using 2 different systems 

1. NW AQL (Acquisition Layer) / curly fibers combination (in most designs) 

2. NW AQL only (in low-tier designs) 


NWCC (non-woven core cover) 

NWDL (not fluid flow relevant) 

Backsheet (not fluid flow relevant)

Thin Layers – Challenges: 

Is Darcy Model still valid? 

Only few number of pore layers through the caliper 

For short pores, e.g. through the thickness of such porous materials, can 

we still assume that the permeability tensor is independent from the 

pressure gradient, given the inertial effects at the inlet/exit of the pores? 

How to define a consistent REV for these layers? 

Example of thin SMS (spunbond-meltblownspunbond) 

nonwoven: side view 




Meshing 

Even regardless from the REV limitations, the thinness of these materials 

results in significantly higher number of mesh elements, with increased 

computational time and tough numerical challenges. Do we need a novel 

theory/approach addressing meshing/numerical challenges? 

Disconnected liquid / Instability effects may be present 

How can we describe these effects, particularly at the 

interfaces? 




„Bridging“ across the thin hydrophobic layer may be a 

dominating effect* 

How to incorporate this effect into Darcy Model? 

r 

R r 

r r 

R r 

r 

θ 

∆ 

P B 

= 

R 


4γh 

2 

+ h 

2 

2γ 

cosϑ 

= 

R 

if 

else 

h ≤ R ⋅ 

1− 

sinϑ 

cosϑ 

∆P B : bridging pressure 

γ: surface tension of the liquid 

h: caliper of the sample 

R: radius of the largest pore 

ϑ.: liquid solid contact angle (> 90°) 

and ϑ > 90° 

* This means that the flow may not be just driven by 

capillary pressure differential but also by absolute 

pressures / curvature of meniscus.



Apertured Topsheet: example of hydrophobic 

porous material 


Apertured Topsheet Nonwoven before 

activation


Geometry & Surface Heterogeneity 

Inhomogeneous pore structure (patterned embossing, laydown, different fiber 

density, interpenetration between layers at interface) 

Inhomogeneous hydrophilicity (surface properties, surfactant coating & 

distribution, interpenetration between layers at interface) 

Additional challenge is the change of the fluid in contact upon surfactant wash-off: 

liquid surface tension can be reduced from 72 mN/m to 30-40mN/m 

Example of bonding pattern on a nonwoven 

material 


Curly fibers penetrating into AQL


Lab Characterization 

• Difficult to characterize in the lab for their fluid flow model input data 

Example: Capsorption 

Measure saturation dependent on hydraulic head 

Challenges : 

Thin layer uptake is only 200-300mg 

-> measure 10 layers 

-> use smaller frit 

Evaporation: 100mg/h 

-> tighter equipment (28mg/h) 


• Thin NW layer 

Pc(S): Comparison 1 layer and 10 layers 

• 1 layer has more g/g 

uptake than 10 layers 

• Interfaces between 

sample and weight / frit 

form new pores 

• Difference in uptake 

especially at low 

pressures, 

i.e. large pore size 

(>0.3mm) 


sample uptake per layer in g 

0.300 

0.250 

0.200 

0.150 

0.100 

0.050 

0.000 

1 vs. 10 layers – additional examples 

Scimat 1st cycle 

Topsheet 1st cycle 

Material A Material B 

0 20 40 60 80 100 

pressure in cm 

uptake per layer in g 

0.500 

0.400 

0.300 

0.200 

0.100 

0.000 

10 layers 

1 layer 

uptake per layer in g 

Neptune6 1st cycle Material C 

0 20 40 60 80 100 



0.450 

0.400 

0.350 

0.300 

0.250 

0.200 

0.150 

0.100 

0.050 

0.000 

0 20 40 60 80 100 


10 layers 

1 layer 

10 layers 

1 layer

Thin Layers – Opportunities 

• Implementation into macroscopic fluid flow models 

– Partially saturated flow (2-phase) 

– Preference is to „include effectively“ into Darcy / Richards 

Approach (e.g. Interfacial condition?) 

– Include mixed wettability 

– Surfactant release 

• Reliable lab characterization (model input) 

– Thin layer characterization 

– Interface characterization 

• Model validation 


Thank you! 

Questions?

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