Mathematics of Hydroextraction

Basket Type Hydro

 Water removal from Textile Packages has always been a challanging task. In the 70s, it was only the basket type hydroextactor, where textile packages where horizontally kept and basket rotated on its axis to centrifuge the water. The improvement over the years was to have a spindle on which the yarn packages were loaded and then the basket spins.

Water removal from textile packages is again dependent upon the moistre regain and the abosorption properties of the yarn. In case of polyester, it can be 90% moistre removal and in case of cotton, it can be only 50% and viscose only 30%.

The interesting part of this technology was the mathematics, which shows the moistre removal rate and percentage of residual moistre.

Centrifugal Acceleration Governs The Rate Of Water Removal From Porous Package,

 This Also Defines When The Equilibrium Stage

Is Reached Between Surface Tension And Centrifugal Forces

The Governing Equation

C= 4o(2)f (2) r

Where f is the frequency of rotation of centrifuge

Within Bracket shows, to the power of the preceeding symbol

Variation of Centrifugal Acceleration is Cause For Terminal Retention of Water in a Package

Retention is Time Dependent : Water before escaping from Package should Move Through It To Outside Surface

Rate of Movement Depends Upon 

Balance Between Viscous Flow Forces

And

Accelerating Centrifugal Force And Restraining Capillary Forces

Large Capillaries Empty First and Small Capillaries Empty With Difficulty

The Mass of Retention In Capillary is Given By the Equation

Ahs = ltCosq / C

Where A  is the Area of capillary, l the peripheral length of capillary, h the height to which the capillary is filled with water, s is viscosity of the liquid, t , the surface tension and q the contact angle, C , the centrifuge acceleration.

Hence Mass Retention is Inversely Proportional To Centrifuge Acceleration

As C is increased, more capillaries opened and a stage is reached, when capillary retention is proportional to 1/ C

At any point in the Package, the rate of Movement of Moisture (u) in a centrifugal gravitation force (C) 

Is Given By    u = CK

Where K is the Permeability of the package

This is the maximum amount of water, that can be removed by Centrifugal Field Against Capillary Forces

In case of Cotton, it is 45%

Polyester Textured , it is 90 to 94%

 Acrylic : 90%

Nylon : 90%

Viscose : 30%

Polyester Sewing Thread : 90%

Based on the Above Numbers, it is now possible to Calculate the Spinning Time To Achieve the Equilibrium Stage For Hydro with speed variable.

Conclusion For Basket Hydroextractors

During Hydroextraction, water migrates from the Porous Package In Direction of Centrifugal Field. Rate of movement depending mainly on the Porous Structure of the Package, the water retention and the field strength.

As larger pores empty, retention reduces and rate of flow declines until balance is reached when capillary forces retain moisture within the material against the influence of the centrifugal forces.

As per Theory, the Porosity of Package and Pore Size Distribution is an important element of Hydro-extractors. Current Hydro-extraction system does not provide the element of squeezing the water initially out of the package and creating enough porosity within the package for easy removal of water.

Axis Type Hydroextractor

Unlike Basket Hydro , where at the Radial End of Basket, the Packages move with Basket.

The Axis Spinning spins the Packages on its own Axis.

In Basket Hydro, the Effect of variation of Centrifugal Field was insignificant for Moisture Retention.

In Axial Spinning, the centrifugal acceleration depends upon the spinning speed and also depends upon the size of the package.

Larger the Package, Greater The Acceleration

Maximum Acceleration At Outside 

Cmax = 4p(2)f(2)R0

Where f is freq. of rev, R0 is OD of Package

Within Bracket shows to the Power of Pie or f 

Where as the Average Acceleration within the package is given by

 Cav = Cmax 2/3 ( R1/R0  + R0/ R1+R0)

Where R1 is the ID of package

As OD of Package Increases, Avg and Max acceleration Increase for a Given Speed 

Acceleration Increases as Rate of Rotation Increases

But interestingly from the equation, as OD increases, the Cav reduces and hence the Water Retention in Packages Become Higher

Technically, one would expect that Retention Of Moisture In Axis spinning packages should be lower then Basket Hydro

But In Real Life Experiments it was seen that the Small Packages Dried 

More Then Large Packages exactly following the equation

This is explained as below

Moisture Is Distributed Evenly Through The Package

High Retention Zone Occurs At Outside Surface, 

Most Remote From Centrifugal Axis

Spot The Large Molecules At The End Of Package after Hydroextaction

Caused By Migrating Molecules To End Of Package Under Centrifugal Field

But Unable To Escape On Account of Surface Tension Forces

Result is Crooked Packages

For Same Value Of Cmax , effect of each zone retention on overall retention of moisture  will be Proportional to

Package Circumference / Cross Sectional Area

That is

R0/ C ( R0 (2) - R1(2))

Retained Water can be Divided Into Two Parts

That Dispersed Throughout the Porus Material

That Held At Or Near The Outside Surface

Rate Of Equilibrium In This Case Depends Upon

Porous Structure

Field Strength Within Package

Conclusion

Axis Type Hydroextractor Has A Major Shortcoming In Fluid Separation From Textile Material

Correction To System

It was First Done By Dr Frauchiger in Switzerland

Who Designed Package Holding And Pressing To Break The Boundary Layer And Break the Surface Tension to allow the large molecules removal.

Hydro with Fingers

Optimal Hydro,Compliant with Technology.

 In short, the Axis type Hydro has a major shortcoming and gives oval shaped packages. Yet is the most popular hydro sold in the world , because of its productivity.
The Dr Frauchiger hydro also has a high productivity, but extremely expensive machine, but worth the investment.