Presentation onPresentation on

Modelling of liquid flow in Modelling of liquid flow in NonwovensNonwovens

Presented byPresented by

VIJAY.S. BELEVIJAY.S. BELE

INDIAN INSTITUTE OF TECHNOLOGY DELHIINDIAN INSTITUTE OF TECHNOLOGY DELHI

Definitions & basics …….Definitions & basics …….

Wetting :-Wetting :-

Process by which a fiber-air interface is replaced with aProcess by which a fiber-air interface is replaced with afiber-liquid interface – often measured by the contact angle.fiber-liquid interface – often measured by the contact angle.

Absorption :-Absorption :-

Liquid uptake into the fibers/materials themselves.Liquid uptake into the fibers/materials themselves.

Wicking:-Wicking:-

Liquid uptake into the material via capillary action – this isLiquid uptake into the material via capillary action – this isresponsible for the bulk of the liquid movement into a fabric.responsible for the bulk of the liquid movement into a fabric.

Adsorption:-Adsorption:-

Thin layer of liquid on face of material.Thin layer of liquid on face of material.

Contact angleContact angle

Contact angle is a measure of the wetting of a liquid on a solid surface. It is Contact angle is a measure of the wetting of a liquid on a solid surface. It is expressed in degrees, with 0 degrees being complete wetting and 180 expressed in degrees, with 0 degrees being complete wetting and 180

degrees being absolute non-wettingdegrees being absolute non-wetting. .

Surface tensionSurface tension

When one fluid is a gas the tension is termed surface tension, when both When one fluid is a gas the tension is termed surface tension, when both fluids are liquids it is termed interfacial tension. fluids are liquids it is termed interfacial tension.

Polar liquids, such as water, have strong intermolecular interactions and Polar liquids, such as water, have strong intermolecular interactions and

thus high surface tensions.thus high surface tensions.

complete wetting when γSG > γSL + γLG zero wetting when γSL > γSG + γLG &

POROSITYPOROSITY

The porosity of a material is defined as the fraction of void space within The porosity of a material is defined as the fraction of void space within the material. the material.

ρb = fabric weight ( g / cm 2 ) / thickness (cm)

WickingWicking wicking is liquid uptake by the capillaries (interstices) formed by the yarns wicking is liquid uptake by the capillaries (interstices) formed by the yarns

and fibersand fibers

For a positive capillary pressure, the values of θ have to be between 0° and For a positive capillary pressure, the values of θ have to be between 0° and 90°. 90°.

where:where: is the liquid-air surface tension (J/m² or N/m) is the liquid-air surface tension (J/m² or N/m) θθ is the contact angle is the contact angle ρρ is the density of liquid (kg/m3) is the density of liquid (kg/m3) gg is acceleration due to gravity (m/s²) is acceleration due to gravity (m/s²) rr is radius of tube (m) is radius of tube (m)

Wicking height is

Darcy`s lawDarcy`s law

Unit- m/s

Mainly used for slow , viscous & laminar fluid flow

Washburn's equationWashburn's equation :- :-

It describes It describes capillary flowcapillary flow in porous materials. in porous materials.

It is the relationship between distance wet & time It is the relationship between distance wet & time

where t is the time for a liquid of viscosity η and surface tension γ to penetrate a distance L into a fully wettable, porous material whose average pore diameter is D.

Important ConsiderationsImportant Considerations

Wicking and absorption are influenced by:Wicking and absorption are influenced by:

Fiber Properties,Fiber Properties, Fiber Orientation Distribution – NonwovenFiber Orientation Distribution – Nonwoven

Structure,Structure, Fabric Density, Thickness andFabric Density, Thickness and Fiber and Fabric FinishFiber and Fabric Finish

Different permeability Different permeability modelsmodels

Specific permeability of a nonwoven fabric is a characteristic feature of fabric Specific permeability of a nonwoven fabric is a characteristic feature of fabric structure & represents the void capacity through which a liquid can flow.structure & represents the void capacity through which a liquid can flow.

Unit is mUnit is m22

Three theories-Three theories-

Capillary channel theory.Capillary channel theory.

Drag force theory.Drag force theory.

Unit cell theory- fibres are assumed to be aligned in periodic pattern Unit cell theory- fibres are assumed to be aligned in periodic pattern such as squares, trianglesuch as squares, triangle

Basic assumptions Basic assumptions

Nonwoven fabric is -Nonwoven fabric is - HomogeneousHomogeneous Isotropic orIsotropic or Unidirectional orUnidirectional or anisotropicanisotropic

Modelling capillary wickingModelling capillary wicking

Wicking process can be divided into Wicking process can be divided into four categoriesfour categories

Pure wickingPure wicking Wicking + diffusionWicking + diffusion Wicking + adsorptionWicking + adsorption Wicking + diffusion + adsorptionWicking + diffusion + adsorption

Capillary pressure (Laplace`s Capillary pressure (Laplace`s equation) equation)

Hagen-poiseuille equation

Lucas –washburn equation

Dh r2∆P---- = ------Dt 8ŋh

Where h is the distance through which fluid flow in time t

Mao- Russell equationsMao- Russell equations

Another problem in applying capillary channel theory to describe the Another problem in applying capillary channel theory to describe the liquid absorption in nonwovens is the difficulty in quantifying the average liquid absorption in nonwovens is the difficulty in quantifying the average equivalent capillary radii because:equivalent capillary radii because:

-The capillary channels differ in size and shape. -The capillary channels differ in size and shape.

- They are also interconnected as well as interdependent to form a three- - They are also interconnected as well as interdependent to form a three- dimensional network system.dimensional network system.

- The capillary channels in real nonwoven fabrics do not have circular - The capillary channels in real nonwoven fabrics do not have circular cross sections and are not necessarily uniform along their lengths.cross sections and are not necessarily uniform along their lengths.

Directional permeability in anisotropic nonwovensDirectional permeability in anisotropic nonwovens

AssumptionsAssumptions -fibres alligned in z direction are perpendicular to fabric plane-fibres alligned in z direction are perpendicular to fabric plane - fibre distribution in z direction is homogeneous & uniform- fibre distribution in z direction is homogeneous & uniform - flow along the z direction is ignored- flow along the z direction is ignored

df is the fibre dia

z is the fraction of fibres aligned in Z direction

Fibre orientation distribution functionliquid flow direction

Fibre orientation in each direction of fabric plane

Ω(α)

θα

φ Volume fraction of solid materials

Mao- Russell 2D model for Capillary pressureMao- Russell 2D model for Capillary pressure

AssumptionsAssumptions same dia fibre & no alignment in z directionsame dia fibre & no alignment in z direction High porosity , homogenousHigh porosity , homogenous Fibres obeys fibre orientation distribution functionFibres obeys fibre orientation distribution function

Is the directional capillary pressure

Since we know capillary pressure & specific permeability , so putting these values in darcy law we get the rate of liquid absorption or wicking rate in the direction of flow.

P(θ)

Relationship between distance wicked by liquid & time can be obtained In the form of Lucas-Washburn eq

where

Determination of spreading Determination of spreading lengthlength

Rate of absorption

Capillary pressureDirectional permeability

1. Apply a median filter to remove salt and pepper noise.2. Apply a Gaussian filter to smooth the edges.3. Threshold the image by selecting the gray levels occupying. the wetted area and suppressing the others.4. Extract the boundary.5. Track the boundary, find the center of gravity and track.

Permeability's in 3D NONWOVEN structuresPermeability's in 3D NONWOVEN structures

For isotropic structuresFor isotropic structures

For fibre alignment in fabric plane

z is the fraction of fibres aligned in Z direction

Emperical equation for pore sizeEmperical equation for pore size

Liquid expulsion porometryLiquid expulsion porometry

Where d = pore dia (mm)= surface tension (N/m)P = capillary pressure equivalent to applied pressure (pa)

Contact angle is assumed to be zero

Smaller the pore dia, greater will be the applied pressure required to overcome the Capillary pressure and to push the liquid out of the pore.

Wrotnowski`s model for pore Wrotnowski`s model for pore sizesize

Where tex = fibre linear densitydf is the fibre dia in (m)

Fibres arranged in square pattern in model

Goeminne`s equationGoeminne`s equation

Hagen-poisullie`s equationε is the porosity

Some other models for Some other models for permeabilitypermeability

Based on drag force theoryBased on drag force theory Emersleben`s equation-Emersleben`s equation-

Happel`s model-

(unidirectional)

Empirical modelsEmpirical models

To be studied……..To be studied……..

3D models……..3D models……..

Fibre orientation……Fibre orientation……

Pore size distribution…….Pore size distribution…….

THANK YOU FOR YOUR THANK YOU FOR YOUR ATTENTIONATTENTION