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The mechanisms and properties of inertial microfluidics: from fundamental models to biomedical applications

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Abstract

With continuous efforts of researchers all over the world, the field of inertial microfluidics is constantly growing, to cater to the requirements of diverse areas like healthcare, biological and chemical analysis, materials synthesis, etc. The scale, automation, or unique physics of these systems has been expanding their scope of applications. In this review article, we have provided insights into the fundamental mechanisms of inertial microfluidics, the forces involved, the interactions and effects of different applied forces on the suspended particles, the underlying physics of these systems, and the description of numerical studies, which are the prime factors that govern designing of effective and practical devices.. Further, we describe how various forces lead to the migration and focusing of suspended particles at equilibrium positions in channels with different cross-sections and also review various factors affecting the same. We also focus on the effect of suspended particles on the flow of fluids within these systems. Furthermore, we discuss how Dean flows are created in a curved channel and how different structures affect the creation of secondary flows, and their application to mixing, manipulating, and focusing particles as fluid. Finally, we describe various applications of microfluidics for diagnostic and other clinical purposes, and discuss the challenges and advancements in this field. We anticipate that this manuscript will elucidate the basics and quantitative aspects of inertial fluid dynamic effects for application in biomedicines, materials synthesis, chemical process control, and beyond.

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Reproduced from the reference (Warkiani et al. 2015) with permission from the Royal Society of Chemistry

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Reproduced from the reference with permission from the reference Tay et al. (2021) Royal Society of Chemistry

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Abbreviations

\(p\) :

Acting pressure on the fluid element (Pa)

\(\vec{\Omega }\) :

Angular velocity of the suspended particle (rad/s)

\(\gamma\) :

Applied shear rate (1/s)

\(\overrightarrow {{U_{{\text{f}}} }}\) :

Average velocity of the fluid (m/s)

\({\text{Re}}\) :

Channel Reynolds number

\({\text{Re}}_{{\text{P}}}\) :

Particle Reynolds number

\(t_{{\text{p}}}\) :

Characteristic time of an experimental observation

\(\sigma_{xx}\) :

Component of normal stress along the flow direction

\(\sigma_{yy} , \sigma_{zz}\) :

Components of normal stress perpendicular to the flow direction

\({\text{De}}\) :

Dean number

\({\text{D}}\) :

Deborah number

\(\rho_{{\text{f}}}\) :

Density of the fluid (kg/m3)

\({\varvec{\sigma}}\) :

Deviatoric stress tensor

D :

Diameter of the circular cross section of the channel (m)

\(a\) :

Diameter of the suspended particle within the fluid domain (m)

\(\mu\) :

Dynamic viscosity of fluid (Pa.s)

\({\text{El}}\) :

Elasticity number

\(N_{1}\) :

First normal stress difference

\(\lambda\) :

Fluid relaxation time (s)

H :

Hydraulic diameter of the microfluidic channel (m)

\(I\) :

Identity tensor

υ :

Kinematic viscosity (m2/s)

\(u_{{\text{p}}}\) :

Linear velocity of the particle (m/s)

\(U_{{\text{D}}}\) :

Magnitude of secondary flow velocity

\(m_{p}\) :

Mass of the particle

\(m_{{\text{p}}}\) :

Mass of the particle in non-straight non-planar channel (kg)

\(L_{\min }\) :

Minimum channel length required for focusing of particles

\(I_{{\text{p}}}\) :

Moment of inertia of the particle

\(F_{{\text{L}}}\) :

Net inertial lift force (N)

\(f_{{\text{L}}}\) :

Non-dimensional lift coefficient

K :

Numerical constant in the equation for Saffman lift force (K \(\sim\) 81.2)

n :

Outward unit normal vector

\(\alpha\) :

Particle blockage ratio

\(\partial V_{{\text{P}}}\) :

Particle domain

\(\eta_{{\text{p}}}\) :

Polymer viscosity (Pa.s)

\(r\) :

Position vector

R :

Radius of curvature of the proposed microfluidic system (m).

\(v_{t}\) :

Relative velocity of fluid particle elements to suspended particles (m/s).

\(\overrightarrow {{F_{{{\text{LR}}}} }}\) :

Rotation induced lift force (N)

\(N_{2}\) :

Second normal stress difference

\(F_{{\text{D}}}\) :

Secondary flow drag or Dean drag (N)

\(F_{{{\text{LS}}}}\) :

Shear gradient force (N)

γ :

Shear rate (1/s)

\(S^{\prime}\) :

Surface area of the particle

S :

The cross-sectional area of the suspended particle (m2)

\(f_{{{\text{drag}}}}\) :

The viscous drag coefficient

\(F_{{\text{drag }}}\) :

The viscous drag force on the suspended particle (N)

\(t\) :

Time

\(u\) :

Velocity field

\(F_{{{\text{LW}}}}\) :

Wall lift force (N)

\({\text{Wi}}\) :

Weissenberg number

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Acknowledgements

Joydeb Mukherjee is thankful to Zydus Life science Limited for providing the opportunity to work on this topic. Deepa Chaturvedi would like to thank Department of Science and Technology (DST-Purse/1933).

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Authors and Affiliations

  1. Department of Chemical Engineering, Institute of Chemical Technology, Mumbai, 400019, India

    Shlok Mishra

  2. Department of Biological Science and Biotechnology, Institute of Chemical Technology, Mumbai, 400019, India

    Joydeb Mukherjee & Ratnesh Jain

  3. Department of Pharmaceutical Sciences and Technology, Institute of Chemical Technology, Mumbai, 400019, India

    Deepa Chaturvedi & Prajakta Dandekar

Authors
  1. Shlok Mishra
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  2. Joydeb Mukherjee
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  3. Deepa Chaturvedi
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  4. Ratnesh Jain
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  5. Prajakta Dandekar
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Contributions

1.Shlok Mishra: Writing the original draft 2. Joydeb Mukherjee: Writing, editing the original draft. 3. Deepa Chaturvedi: Writing the original draft. 4. Ratnesh Jain and Prajakta Dandekar Jain: Writing, editing the original draft.

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Correspondence to Prajakta Dandekar.

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Mishra, S., Mukherjee, J., Chaturvedi, D. et al. The mechanisms and properties of inertial microfluidics: from fundamental models to biomedical applications. Microfluid Nanofluid 27, 84 (2023). https://doi.org/10.1007/s10404-023-02692-x

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