粘弹性纤维在均匀变形流场中的悬浮动力学

本文以三珠二杆粘弹性铰接的珠链作为纤维的模型,用将珠链运动分解为准刚体运动和纯变形运动的方法,对粘弹性珠链纤维在均匀变形流场中的悬浮运动进行了研究。得到了纤维速度,加速度分布公式,纤维平均取向的角速度南纤维纯变形运动方程。并发现,在纤维质心运动方程中,集中在纤维质心上的各圆珠的斯托克斯阻力之矢量和就等于流体作用于纤维质心的斯托克斯阻力;在纤维相对于质心的动量矩方程中,力矩是准刚珠链纤维中各圆珠上相对于纤维质心的斯托克斯阻力矩之矢量和。特别是在不计纤维惯性、重力和浮力的条件下,当纤维刚直并作平面运动时,其角速度与同样条件下无限长径比椭球角速度的 Jeffery 公式完全一致。

DYNAMICS OF A VISCOELASTIC FIBER SUSPENDED IN HOMOGENEOUS FLOW FIELD

The arbitrary motion of a viscoelastic fiber modeled by a 3-bead-2-rod link suspendedin a homogeneous flow field whose velocity is linear in the Cartesian coordinates is developedby means of resolving the motion and deformation of the chain model into itsquasi-rigid-chain motion and pure deformation components.The formulation of its linearvelocity and acceleration distribuition,as well as its angular velocity and the equation of itspure deformation are thus obtained.It is found that in the dynamic equations of the center of mass,the total vector sum ofStokes' drags acting on the three beads is equal to Stokes' drag on their center of mass;in thelifferential equations of angular momentum with respect to the center of mass,the momentof forces is the vecter sum of the moment of Stokes' drags acting the three beads of thequasi-rigid-chain.Furthermore,the angular velocity of a straight rigid fiber with negligibleinertia,gravity and buoyancy forces and moving parallel to a fixed plane is in agreement withJeffery's well-known formula of angular velocity of an ellipsoidal particle with unfinite as-pect ratio under same conditions.