Inertial migration of a deformable particle in pipe flow

Abstract

We perform fully Eulerian numerical simulations of an initially spherical hyperelastic particle suspended in a Newtonian pressure-driven flow in a cylindrical straight pipe. We study the full particle migration and deformation for different Reynolds numbers and for various levels of particle elasticity, to disentangle the interplay of inertia and elasticity on the particle focusing. We observe that the particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline. We note that the migration dynamics and the final equilibrium position are almost independent of the Reynolds number, while they strongly depend on the particle elasticity; in particular, the migration is faster as the elasticity increases (i.e. the particle is more deformable), with the particle reaching the final equilibrium position at the centerline in shorter times. Our simulations show that the results are not affected by the particle initial conditions, position and velocity. Finally, we explain the particle migration by computing the total force acting on the particle and its different components, viscous and elastic.

Motion of a capsule in a curved tube

“…This is evident from recent numerical studies where migration of capsules and deformable particles in straight vessels was considered in the presence of inertia. Migration toward the vessel centreline was noted in Alghalibi, Rosti & Brandt (2019) and Hur et al (2011), while off-centre equilibrium was reported in Kilimnik, Mao & Alexeev (2011), Krüger, Kaoui & Harting (2014) and Shin & Sung (2011).…”

A pair of particles in inertial microfluidics: effect of shape, softness, and position

“…[46][47][48][49] Only recently, inertial microfluidics of deformable cells has caught attention. 20,[50][51][52][53][54][55][56][57][58] Using two-dimensional numerical simulations, Shin and Sung 51 showed that the final equilibrium position for a given value of capsule elasticity varies with the Reynolds number. In their following work 54 they identified different types of capsule dynamics such as tank-treading, swinging, and tumbling.…”

“…They also proposed that the inertial lift force in the vicinity of the channel center scales as a cube of capsule radius. More recently, Alghalibi and colleagues 58 investigated cross-stream inertial migration of a soft particle in pipe flow. Interestingly, they found that irrespective of the particle's softness and the flow rate, the particle always ends up at the channel center for an initial particle diameter of 0.2 times the pipe diameter.…”

Analogue tuning of particle focusing in elasto-inertial flow

“…This is due to the distorted first normal stress difference that builds up around the particle leading to an oscillatory stretching around the particle as shown in Fig. 5c, see also [57]. The final equilibrium position of the particle is also shown to be independent of its initial condition for both the Newtonian and the Non-Newtonian fluid, as shown in Fig.…”