FILTRATION | TYPES OF FILTRATION | RATE OF FILTRATION

       OVERVIEW         

 Basic Filtration - Hey guys, in this space we'll be talking about everything related to filtration, ranging from simple definition to complex derivations of rate of filtration.

 Filtration  basically refers to the separation of a slurry containing solids into two fractions using a permeable medium. This permeable medium is called the filter medium . 

One of the fractions is the clear liquid called filtrate and the other fraction is the solids .Filtrate gets passed through the filter medium and the solids are collected over the filter medium. These collected solids are known as 'cake'. And this filtration type is called Cake Filtration.

Filtration is very much similar to Sedimentation but it is preferred over sedimentation when we have a shortage of time because sedimentation works over the principle of gravity settling which is comparatively a weaker force than pressure difference.

The valuable product may be :

1. The clear filtrate.

2. The solid cake.

Classification of Filtration :

Filters are classified depending upon :

(A)  the product desired :

  1. Cake filters : Cake is the desired product. This is used when the concentration of solids is high.

  2. Clarifying filters : Clarified liquid or filtrate is the desired product. Used when the concentration of solids is negligible.

(B)  the basis of Operating Cycle:

  1. Batch filter : The cake is removed after one complete run. Eg. Plate and Frame filter.

  2. Continuous filter : cake is continuously being removed. Eg. Continuous Rotary drum filter. 

(C)  Driving force involved :

  1. Gravity filter

  2. Pressure filter 

  3. Vacuum filter 

  4. Centrifugal filter

(D)  Mechanical arrangement of filter media :

  1. Filter press : filters are in series arrangement.

  2. Leaf filter : as individual leaves dipped in slurry.

  3. Rotary drum filter : on rotary type rolls in the slurry.

RATE OF FILTRATION :

The Driving force of Filtration is Pressure difference. The slurry is allowed to be incident onto the filter medium as shown. 

The cake gradually builds up on the medium and resistance to flow progressively increases.

The entire filtration system provides two types of resistances to the passage of slurry :

1. Filter medium resistance. (due to the material from which filter medium is made)

2. Cake resistance. (due to the deposition of cake) 

             
Initially ,at the start of filtration there is no cake present so the cake resistance is zero. But , filter medium resistance won't be zero.

 As the time proceeds ,Cake develops on the surface of filter medium so that the Cake resistance goes on increasing and the pores of filter medium start getting choked by the solid particles so the filter medium resistance also increases.

 So,  at time t=0 , Cake Resistance=0 , Filter Medium resistance= c           

  at t=x , x>0 , Cake resistance>0 , Filter Medium resistance >c.   

Pressure drop across constant pressure cake filtration :

Cake filtration

Flux  =   Driving force    =  P₁ - P₂   .

                Resistance               R

For constant pressure filtration, (P₁  - P₂) = constant.

So, as time passes, resistance to filtration increases and so the Rate of filtration decreases.  

Here, overall pressure drop, ΔP = (P₁ - P')+(P' - P₂)

                                                  

                                                        = ΔPₘ  +  ΔPₑ

where, ΔPₘ = pressure drop across filter medium

             ΔPₑ = pressure drop across cake.

For a laminar flow of slurry through cake height, we use Ergon's equation :

             ΔPₑ   =    150 u μ (1-ε)²  

                L              (ΦDₚ)² ε³

where, μ = viscosity of slurry

            u = superficial velocity of slurry

            ε = porosity of cake

           Φ = sphericity of particle

But we know, Φ =   6Vₚ 

                                Sₚ Dₚ

        ∴   ΔPₑ  =    150 u μ (1-ε)²  

                L            (6Vₚ /Sₚ)² ε³

                     =   k' u μ (1-ε)²  (Sₚ/Vₚ)²

                                       ε³  

         ∴  ΔPₑ  =    k' u μ (1-ε)² L (Sₚ/Vₚ)²

                                        ε³  

Now, mass of retained solids = ⍴ₚ A L(1-ε)

      C  =          mass of solids retained      

                    volume of filtrate collected (V)

      ∴  mass of solids retained = CV

      ∴  CV =  ⍴ₚ A L(1-ε)

      ∴  L =    CV   

                    ⍴ₚ A (1-ε)

Substituting, u =              ΔPₑ           

                                  k' μ (1-ε)² (Sₚ/Vₚ)² CV  

                                         ⍴ₚ A (1-ε) ε³

                         =              ΔPₑ           

                                  k' μ (1-ε) (Sₚ/Vₚ)² CV  

                                         ⍴ₚ A ε³

                        =               ΔPₑ           

                                  k' (1-ε) (Sₚ/Vₚ)²   ( μCV )

                                               ⍴ₚ ε³             A

Let,   k' (1-ε) (Sₚ/Vₚ)²  =α=specific cake

                     ⍴ₚ ε³                 resistance.

    ∴  u  =   ΔPₑ A  

                 α ( μCV )

    ∴  α  =    ΔPₑ A     =  (m/kg)

                   u ( μCV )

If  α = f (ΔP, L ) then it is a compressible cake.

If  α ≠ f (ΔP, L ) then it is an incompressible cake.

     Also,  α  =  k (ΔP)ⁱ 

where i = compressibility coefficient

     i = 0 for completely incompressible cake

     i = 1 for completely compressible cake.

In industries,  0.2 ≤ i ≤ 0.8

Now, we know from above that , u =   ΔPₑ A  

                                                               α ( μCV )

∴ Pressure drop  = ΔPₑ =  α ( μCV ) u 

    across cake                               A   

                                            

Similarly, it is known that  Rₘ  =   ΔPₘ  

                                                          μ u 

∴ Pressure drop across filter medium = ΔPₘ = Rₘ u μ

∴ Overall Pressure drop = ΔP = ΔPₘ+ΔPₑ = Rₘuμ + {[α(μCV)u]/A }

Rate of filtration :

 Superficial  =  dV/dt   =             ΔP             

 velocity u            A            α ( μCV )  + Rₘ μ

                                                   A

   So,    dV  =           ΔP                             

             dt            α ( μCV )  + Rₘ μ

                                  A²               A

    

       ∴   dt    =   α ( μCV )   +   Rₘ μ 

             dV            ΔP A²          ΔP A

Now,   Let  α ( μC )  = kₖ   and   Rₘ μ  = B

                      ΔP A²                      ΔP A

     ∴   dt   =  kₖ V  +  B  → The filtration equation.
          dV

Integrating from t=0 to t, we get,  t =  kₖ V²  + BV

                                                                    2

                     

     ∴       t    =    kₖ V   +  B

              V            2                 

Plot of V vs  t/V

        

Comparing with y = mx + c , we get to know that if we plot a graph of t/V vs V , slope of it gives the value of  kₖ/2 and the intercept gives the value of B.

kₖ and B are independent of area .

Also,  Washing =  Volume of wash water used  

           time t                 Final rate of washing

Uses Of Filtration : Filtration is used to remove particles from or to :

1.  Clarify juices

2.  Extracts

3.  Vegetable and Fish oils

4.  Fermented beverages

5.  Recirculated cooking oil

6.  Flume water, milk, and soy milk.

7.  Separate potato starch from potato fruit water

8.  Fats from vegetable oils in fractionation processes. 

9.  Crystals from mother liquors

10.Chemically precipitated impurities.

Thanks for reading. If you found it useful, do let me know in the comments section.