Patent ID: 11921025
Assignee: NIKON CORPORATION
Field: Measurement (Instruments)
Classification: CPC G | IPC G

Claim 10:
11. A method for estimating one or more characteristics of a slurry that includes a plurality of particles suspended in a dispersion medium, the method comprising:
directing the slurry at a slurry filter that filters the slurry;
estimating a first characteristic of the slurry with a control system using a flow rate of a filtrate through the filter and a slurry filtration pressure of the slurry;
wherein the first characteristic is a cake particle packing fraction of the slurry, and the step of estimating the first characteristic includes using the following formula:, ∅
    ⁢
    
     c
     2
    
   
   
    
     (
     
      1
      -
      
       ∅
       ⁢
       c
      
     
     )
    
    3
   
  
  =
  
   
    P
    
     S
     ⁢
     
      S
      v
      2
     
     ⁢
     μ
    
   
   ⁢
   
    dt
    dV
   
   ⁢
   
    1
    L
   
  
 

wherein (i) Øc is the cake particle packing fraction of the slurry; (ii), dt
  dV, is the inverse of the flow rate of the filtrate through the slurry filter; (iii) P is the slurry filtration pressure as measured by the pressure sensor; (iv) Sv is a particle surface area;
(v) L is a cake thickness of a cake layer; and (vi) μ is a viscosity of the dispersion medium; and
estimating a second characteristic of the slurry with the control system using a hypothetical model of random close packing, the second characteristic of the slurry being a particle agglomerate diameter; wherein the step of estimating the second characteristic includes estimating the second characteristic of the slurry also using the cake particle packing fraction; wherein the step of estimating the second characteristic includes estimating the particle agglomerate diameter of the slurry using the following formula:, D
   aggl
  
  =
  
   
    
     
      
       ∅
       RCP
       2
      
      
       
        (
        
         1
         -
         
          ∅
          RCP
         
        
        )
       
       3
      
     
     
      
       ∅
       C
       2
      
      
       
        (
        
         1
         -
         
          ∅
          C
         
        
        )
       
       3
      
     
    
   
   ⁢
   
    D
    part
   
  
 

wherein (i) Daggi is the particle agglomerate diameter of the slurry; (ii) ØRCP is a random close packing cake particle packing fraction; (iii) Dpart is a nominal particle size of the particles; and (iv) Øc is the cake particle packing fraction of the slurry.