page_title: Nonlinear frictiophoresis
section_title: Applications
hierarchical_section_title: Nonlinear frictiophoresis / Applications
caption_attribution_description: English: Velocity and displacement for optimal force Українська: Швидкість і зміщення під дією оптимізованої сили
context_page_description: Nonlinear frictiophoresis is the unidirectional drift of a particle in a medium caused by periodic driving force with zero mean. The effect is possible due to nonlinear dependence of the friction-drag force on the particle's velocity. It was discovered theoretically.,
  and is mainly known as nonlinear electrofrictiophoresis
  .
  At first glance, a periodic driving force with zero mean is able to entrain a particle into an oscillating movement without unidirectional drift, because integral momentum provided to the particle by the force is zero. The possibility of unidirectional drift can be recognized if one takes into account that the particle itself loses momentum through transferring it further to the medium it moves in/at. If the friction is nonlinear, then it may so happen that the momentum loss during movement in one direction does not equal to that in the opposite direction and this causes unidirectional drift. For this to happen, the driving force time-dependence must be more complicated than it is in a single sinusoidal harmonic.
context_section_description: In applications, the nature of force  in (5), is usually electric, similar to forces acting during standard electrophoresis. The only differences are that the force is periodic and without constant component.
  For the effect to show up, the dependence of friction/drag force on velocity must be nonlinear. This is the case for numerous substances known as non-Newtonian fluids. Among these are gels, and dilatant fluids, pseudoplastic fluids, liquid crystals.
  
  Dedicated experiments
  have determined  for a standard DNA ladder up to 1500 bp long in 1.5% agarose gel. The dependence found, see Fig. 6, supports the possibility of nonlinear frictiophoresis in such a system. Based on data in  Fig. 6, an optimal time course for driving electric field with zero mean, , has been found in, which ensures maximal drift for 1500 b.p. long fragment,
  see Fig. 7.
  The effect of unidirectional drift caused by periodic force with zero integral value has a peculiar dependence on the time course of the force applied.  See the previous section for examples. This offers a new dimension to a set of separation problems.
caption: Fig. 7 Time courses of optimal electric field, 
    
      
        
          E
          (
          t
          )
        
      
      {\displaystyle E(t)}
    
  , 
    
      
        
          E
          (
          t
          ±
          1
          s
          )
          =
          E
          (
          t
          )
        
      
      {\displaystyle E(t\pm 1s)=E(t)}
    
  , steady-state velocity, 
    
      
        
          
            v
            
              ∗
            
          
          (
          t
          )
        
      
      {\displaystyle v^{*}(t)}
    
  , and displacement, 
    
      
        
          X
          (
          t
          )
        
      
      {\displaystyle X(t)}
    
  . The drift value 
    
      
        
          
            
              
                
                  v
                  
                    ∗
                  
                
                (
                t
                )
              
              ¯
            
          
          =
          0.31
          μ
        
      
      {\displaystyle {\overline {v^{*}(t)}}=0.31\mu }
    
  m/s.
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