Analytical Solutions to the Generalized Couette Flow of a Microstretch Fluid in an Annulus

Abstract

In classical continuum mechanics, fluid particles are assumed to be material points. However, this assumption may lose its validity in micro-channels where the characteristic length is very small and/or in many applications where particle sizes are large, such as in polymer melts, suspensions, and biological fluids. In these cases, micro-motions such as rotation and deformation of fluid particles contribute to the macro motion of the fluid. In this study, the field equations of microstretch fluids are solved for the generalized Couette flow in an annulus, and exact analytical solutions are obtained for velocity, microrotation, and microstretch fields. Results are presented graphically for velocity, microrotation, and microstretch at various values of the pertinent parameters. Present solutions include velocity field solutions for the classical Newtonian fluid as a special case. For microstretch fluids, the velocity field takes on larger values compared to a Newtonian fluid. Increasing the micropolar parameters increases the velocity and microrotation fields while increasing the microstretch parameter increases the microstretch field.

Keywords

• Microstretch fluid
• Generalized Couette flow
• Analytical solution
• Coaxial cylinders

Mikrogermeli Bir Akışkanın Halka Kesitli Kanalda Genelleştirilmiş Couette Akımına ait Analitik Çözümler

Öz

Klasik sürekli ortamlar mekaniğinde akışkanı oluşturan parçacıkların maddesel nokta olduğu varsayılmaktadır. Ancak, karakteristik uzunluğun çok küçük olduğu mikrokanallarda ve/veya parçacık boyutlarının büyük olduğu, polimer eriyikler, süspansiyonlar ve biyolojik akışkanlar gibi birçok uygulamada bu varsayım geçerliliğini yitirmektedir. Bu durumlarda akışkan parçacıklarının dönmesi ve deformasyonu gibi mikro hareketleri önem kazanmakta ve akışkanın makro hareketine katkı sağlamaktadır. Bu çalışmada, mikrogermeli bir akışkanın alan denklemleri halka kesitli bir kanalda, genelleştirilmiş Couette akımı için çözülmüş ve hız, mikro açısal hız ve mikro genleme alanlarına ait analitik çözümler elde edilmiştir. Hız, mikro açısal hız ve mikro genleme alanları için elde edilen çözümler; parametrelerin farklı değerlerinde grafik olarak sunulmuştur. Elde edilen çözümler, klasik Newtonian akışkan için geçerli hız alanı çözümlerini özel hal olarak içermektedir. Mikrogermeli akışkanlarda, hız alanı, Newtonian akışkanlara kıyasla daha yüksek değerler almaktadır. Mikropolar parametrelerin artması, hem hız hem de mikro açısal hız alanlarını artırırken, mikro genleme parametresinin artması da mikro genleme alanını artırmaktadır.

Anahtar Kelimeler

• Mikrogermeli akışkan
• Eş eksenli iki silindir
• Analitik çözüm
• Genelleştirilmiş Couette akışı

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