Dynamics of rigid and soft particles in a cross-slot flow at finite inertia

Abstract

Sepsis is a life-threatening aberrant immune response to an infection, resulting in irreversible organ damage. Timing is critical because mortality increases dramatically with delayed diagnosis, as much as 8% per hour of treatment delay. Early intervention in sepsis is essential in reducing morbidity and mortality.

In 2012, researchers developed a flow cytometry method capable of characterising large cell populations based on their deformability; this method is commonly tagged as deformability cytometry in the literature. The critical element of this technique is the cross-slot flow which causes the deformation of cells due to high tensile stresses. Under finite inertia and height-towidth channel ratio, a spiral vortex is formed at the fluid intersection. Later improvements led to integrating deformability cytometry in an inertial microfluidic platform capable of analysing white blood cell deformability and providing a likelihood band for sepsis in patients in less than 10 minutes. Despite the crucial application of cross-slot flows, most published works concern proof-of-concept studies and fundamental studies of the vortex dynamics in a cross-slot flow.

Motivated by the applicability of cross-slot flows in early sepsis diagnosis, the thesis uses computer simulations to study the transient dynamics of spherical rigid and soft particles in cross-slot flows under finite inertia. The influence of the properties of a particle and its mechanisms of motion are revealed for vortical cross-slot flows. Furthermore, the influence of the vortex on the transient behaviour of a soft particle is also identified by comparing crossslot flows with and without the vortex formation. The current thesis proposes and uses three macroscopic metrics to characterise the shape of particle trajectories in the junction.

The entry position in the junction plays the dominant role in the transient dynamics and largely determines the motion of a rigid particle in the junction under steady vortex conditions. A particle interacts longer with the vortex when it enters the junction from positions closer to the mid-plane. The vortex imposes a characteristic spiral trajectory on the particle’s motion, the shape of which depends stronger on the lateral than vertical entry position in the junction, as the employed metrics showed. Larger particles reside longer in the junction and tend to leave the junction without performing the characteristic spiral trajectory. The influence of the particle-to-fluid density ratio is evident only when the particle interacts longer with the vortex. The analysis revealed that two competing mechanisms determine the transient motion of a rigid in the junction under steady vortex conditions: i) the acceleration and ii) the revolution of a rigid particle as it moves downstream.

The study for the soft particle confirmed that rigid and soft particles share the main mechanism of motion in the junction and the same trends when particle size varies, but it also revealed that particle softness alters the transient behaviour of a particle. A soft particle enters the main vortical flow for a broader range of initial positions because the deformation of the particle leads to different interaction with the vortex. The transient deformation of a soft particle is determined primarily by the normal stresses acting on it due to the flow expansion. However, the shear stress on the yz-plane (inlet-height plane) causes a soft particle to follow more slanted spiral trajectories than a rigid one. The spatial and time variations of the particle deformation in the junction are observed due to the high strain rate zones of the fluid.The investigation revealed that steady vortex conditions should be favoured for applications that require particle or cell deformation, such as deformability cytometry.

The current thesis sets the foundations of the rigid and soft particle dynamics in cross-slot flows under steady vortex conditions. It reveals the effects of crucial particle properties on the transient behaviour of rigid and soft particles in the junction and factorises their behaviour into metrics based on their trajectories. Moreover, the thesis identifies the dependency of the transient deformation of a soft particle from a steady vortex and illustrates that steady vortex conditions lead to larger particle deformation than cross-slot flows without a vortex. This thesis should help improve the design of devices operating under steady vortical cross-slot flows targeted for deformability measurements.