Journal of Engineering Mathematics

, Volume 61, Issue 1, pp 69-79

First online:

Fundamental solutions for micropolar fluids

  • Jian-Jun ShuAffiliated withSchool of Mechanical & Aerospace Engineering, Nanyang Technological University Email author 
  • , Jenn Shiun LeeAffiliated withSchool of Mechanical & Aerospace Engineering, Nanyang Technological University

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New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet, the two- and three-dimensional micropolar Stokes couplet, the three-dimensional micropolar Oseenlet, and the three-dimensional micropolar Oseen couplet. These fundamental solutions do not exist in Newtonian flow due to the absence of microrotation velocity field. The flow due to these singularities is useful for understanding and studying microscale flows. As an application, the drag coefficients for a solid sphere or a circular cylinder that translates in a low-Reynolds-number micropolar flow are determined and compared with those corresponding to Newtonian flow. The drag coefficients in a micropolar fluid are greater than those in a Newtonian fluid.


Micropolar fluids Fundamental solutions Oseen flow Point couple Point force Stokes flow