Patent ID: 11965904
Assignee: ZHEJIANG UNIVERSITY
Field: Measurement (Instruments)
Classification: CPC G | IPC G

Claim 0:
1. A method for measuring a density based on circular magnetic levitation, comprising:
placing a sample to be measured in a medium solution located between two circular magnets to ensure that the sample to be measured is levitated in a set circular area between the two circular magnets;
measuring a levitation position of the sample to be measured in a magnetic field; and
calculating the density of the sample to be measured according to formula (I):, ρ
    s
   
   =
   
    
     ρ
     m
    
    +
    
     
      
       
        χ
        m
       
       -
       
        χ
        s
       
      
      
       g
       ⁢
       
        μ
        0
       
      
     
     ⁢
     
      (
      
       
        
         B
         r
        
        ⁢
        
         
          ∂
          
           B
           z
          
         
         
          ∂
          r
         
        
       
       +
       
        
         B
         z
        
        ⁢
        
         
          ∂
          
           B
           z
          
         
         
          ∂
          z
         
        
       
      
      )
     
    
   
  
  ;
 

wherein:
ρs is the density of the sample to be measured, g/cm3;
ρm is a density of the medium solution, g/cm3;
χs is a magnetic susceptibility of the sample to be measured, dimensionless;
χm is a magnetic susceptibility of the medium solution, dimensionless;
g is a gravitational acceleration, m/s2;
μ0 is a vacuum permeability, N/A2;
Br and Bz are respectively a radial magnetic field intensity and an axial magnetic field intensity at the levitation position;
r is a levitation radius of the sample to be measured in the medium solution being a distance from a center line of the two circular magnets to the sample to be measured; and
z is a levitation height of the sample to be measured in the medium solution being a distance from an upper surface of a lower magnet to the sample to be measured; and

wherein a distance between the two circular magnets satisfies:
(1) a curve expressed by a formula, B
     r
    
    ⁢
    
     
      ∂
      
       B
       r
      
     
     
      ∂
      r
     
    
   
   +
   
    
     B
     z
    
    ⁢
    
     
      ∂
      
       B
       r
      
     
     
      ∂
      z
     
    
   
  
  =
  0
 

 does not completely coincide with a center line of the two circular magnets; and
(2) a gradient of the curve expressed by an expression, B
    r
   
   ⁢
   
    
     ∂
     
      B
      r
     
    
    
     ∂
     r
    
   
  
  +
  
   
    B
    z
   
   ⁢
   
    
     ∂
     
      B
      r
     
    
    
     ∂
     z
    
   
  
 

 in r direction is greater than 0.