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…….
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