# Elasto-Inertial Particle Focusing in Microchannel with T-Shaped Cross-Section
## 1 Introduction  
Microfluidic techniques for separating and manipulating particles or cells using various forces generated as fluid flows in a microchannel have been attracting increased attention over recent decades. These techniques can separate and manipulate particles without the use of external forces and are low-cost, have high processing efficiency and reduced sample consumption, and so have been used in various fields, such as medicine, chemistry and biology. Particle focusing and separation are important for preprocessing in biomedical analysis. Viscoelastic microfluidics has been widely used to manipulate particles and cells using nonlinear elastic forces without any external force [1; 2; 3; 4]. That is, particles can be focused and separated depending on their sizes in a viscoelastic fluid. Viscoelasticity causes elastic lift force on particles to drive them laterally to equilibrium positions, typically the center of the microchannel [5]. Compared with inertial focusing in a Newtonian fluid, true 3D particle focusing can be easily obtained in simple straight channels in a viscoelastic non-Newtonian fluid [6], due to the coupling of inertial effect and elastic effect (i.e., elasto-inertial focusing) [7; 8; 9]. Such elastic force results from an emergence of the first normal stress differences across the channel. Several studies on the first normal stress have been carried out to evaluate the effect of flow rate, channel geometry and corner angles on focusing patterns through numerical simulations and experiments [7; 9; 10; 11]. Recently, itwas found that the elastic force increases at the obtuse corner of a channel cross-section, so that the particle focusing increases prominently. [PERSON] et al. proposed a new complex straight channel to obtain a tighter focusing band for smaller particles and a wider range of flow rates than can be achieved with conventional straight channels [PERSON] et al. (2018). The complex microchannels with a reflex angle in the corner of the channel cross-section were fabricated using micro-milling and micro-molding, and the behavior of particles in viscoelastic fluids was explored through experiments and simulations. It was shown that the corner angle of the cross-sectional shape of the microchannel influenced the particle focusing. In general, microchannels can be easily fabricated using a polydimethylsiloxane (PDMS) replica molding process based on the classical soft-lithography technique, but their cross-sectional shapes are restricted to squares and rectangles due to the micro-mold shapes. Recently, microchannels with non-rectangular cross-sections, such as a circle, half-circle, triangle and trapezoid, have been presented [3; 11; 13; 14]. In a previous study [15], we fabricated microchannels with various cross-sectional shapes, such as a parallelogram, rhombus, pentagon and hexagon. They were fabricated using basic micro-electro-mechanical systems (MEMS) processes, such as photolithography, reactive ion etching (RIE) and anisotropic potassium hydroxide (KOH) wet etching of Si followed by self-alignment between the Si channel and PDMS mold. However, it is not easy to fabricate microchannels with a reflex angle in the corner part of the channel cross-section using a conventional soft-lithography technique. In the present work, we propose a novel yet simple fabrication method for a microchannel with a T-shaped cross-section, which is based on soft lithography, followed by self-alignment with two PDMS molds. We carried out experiments to confirm the elasto-inertial focusing position of particles for three kinds of microchannels with different sizes of T-shaped cross-sections in non-Newtonian fluid according to the flow rate and particle size. By taking images from the top and side parts of the microchannel, it was possible to confirm the position of the particles three-dimensionally.