(209b) Non Tumbling Particles In Simple Shear Flow

At low Reynolds number under no external forces or torques, the center of the particle translates with the fluid velocity and rotates based on its shape and the ambient fluid flow. In simple shear flow, the rotational component of the flow rotates the particle with the angular velocity of the fluid in the direction of vorticity and the extensional component of the flow acts to align the particle along the principal direction of the extensional flow. The shape of the particle determines the contribution of the extensional flow towards alignment. For spherical particle the contribution of the extensional flow goes to 0 and the particle rotates with the angular velocity of the fluid where as for thin (disks) and long (fibers) spheroidal particle, the contribution of extensional flow is significant and the particle in these limits rotates with a time period of rotation of 1/ r (disks) and r (fibers). Here, r is the aspect ratio of the particle defined as the ratio of length to diameter. Thus the complete alignment of the particle can only be achieved when the particle is a line (r = ∞) or a plane (r = 0). Shape of the particle can be used to tune the period of rotation but it is interesting that so far no finite aspect ratio particle shapes have been discovered which can completely stop rotating in simple shear flow despite Bretherton (1962) presenting some extreme shapes that can align about half a century ago.

In this talk, we present particle shapes at finite aspect ratio which stop tumbling in simple shear flow at low Reynolds number. This behavior is analogous to the behavior of nematic phase liquid crystals but unlike liquid crystal systems where intermolecular forces lead to alignment, in our system a single particle aligns based on its shape in the absence of any external interactions. Using scaling analysis, we present how certain asymmetry in shape can give rise to a torque on the particle in a direction opposite to the direction of vorticity that could be used to balance the torque from fluid motion which acts to rotate the particle in the vorticity direction. We will discuss the characteristic shapes that can lead to non tumbling behavior of the particle. Using boundary element method, we determine finite aspect ratio at which the transition occurs from the tumbling state to the aligned state for particles of different shapes. Finally, we discuss implications of aligned particle suspensions on fluid properties and material processing.