MICRO AI A MACHINE LEARNING TOOL FOR FAST CALCULATION OF LIFT COEFFICIENTS IN MICROCHANNELS Erfan Hamdi

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MICROAI: A MACHINE LEARNING TOOL FOR FAST

CALCULATION OF LIFT COEFFICIENTS IN MICROCHANNELS

Erfan Hamdi∗

Department of Mechanical Engineering

Sharif University of Technology

Tehran, Azadi St.

erfan.hamdi@mech.sharif.ir

Rasool Dezhkam∗

Department of Mechanical Engineering

Sharif University of Technology

Tehran, Azadi St.

rasool.dezhkam@sharif.edu

Amir Shamloo†

Department of Mechanical Engineering

Sharif University of Technology

Tehran, Azadi St.

shamloo@sharif.ir

Ali Mashhadian

Department of Mechanical Engineering

Sharif University of Technology

Tehran, Azadi St.

alimashhadian77@gmail.com

ABSTRACT

There have been multiple methods proposed to calculate lift coefﬁcients in microﬂuidic channels.

One of the most used methods is using Direct Numerical Simulation. DNS is a very accurate yet

computationally expensive method. DNS computations comprise most of the time consumed on

a microﬂuidic simulation done by commercial software. This paper proposes a user-friendly, fast,

and accurate AI-based webapp named microAI that can calculate the microﬂuidic lift coefﬁcients of

channels. We have also studied the effects of different types of activation functions and optimizers

in convergence and the ﬁnal function’s differentiability. microAI is deployed to huggingface and is

accessible at https://erfanhamdi.github.io/microAI/

Keywords Inertial Microﬂuidics ·DNS ·Machine Learning ·Web Application

1 Introduction

Inertial microﬂuidics as a method for cell separation is frequently used in Lab-On-a-Chip (LOC) and Lab-On-a-Disk

(LOD) platforms. Inertial cell separation belongs to the passive category of cell separation methods. There is no

external force for cell manipulation inside the microchannels, and particles will be separated because of differences

in density, shape, etc. On the other hand, external forces are applied to the ﬂuid or the particle in active methods

such as dielectrophoresis [Kwizera et al., 2021], magnetophoresis [Nasiri et al., 2022], acoustophoresis [Collins et al.,

2017], etc. However, passive methods like deterministic lateral displacement (DLD) [McGrath et al., 2014], Pinch Flow

Fractionation (PFF) [Yamada et al., 2004], and inertial methods [Di Carlo, 2009] unlike active methods, do not apply

any external force. Resulting in less complicated methods, they have always been one of the researchers’ choices for

particle sorting or separation. Lift and drag forces are the two main forces in the passive methods. The drag force

and the direction of the ﬂuid streamline are the same, and the movement of particles is mainly affected by this force.

However, the lift force is orthogonal to the ﬂow, resulting from pressure and surface stress differences around the

particle. This difference in lift force between various types of particles moves them to different positions in the width of

the channel.

Calculating the lift force applied to spherical particles has always been discussed [Saffman, 1965, Asmolov, 1999, Ho

and Leal, 1974, Bazaz et al., 2020]. Consequently, the lift force consists of four terms: Saffman, Magnus, Wall-induced,

∗Same Contribution

†Corresponding Author

arXiv:2210.11591v1 [physics.flu-dyn] 20 Oct 2022

microAI: A machine learning tool for fast calculation of lift coefﬁcients in microchannels

and Shear gradient lift force [Zhang et al., 2016]. The lag between the particles and the ﬂuid made by wall effects

[Saffman, 1965] induces Saffman force. Magnus force is the result of particle rotation. Pressure is higher on one side

of a rotating particle than on the other side; therefore, a lateral force is applied to the particle. Wall-induced lift force

is because of the wall effect. The ﬂow ﬁeld changes near the wall because of the particle, and a velocity gradient is

made, and as a result, a shear rate makes the particle rotate and move to the center of the channel to be far from the wall

[Michaelides, 2006]. Shear gradient lift force is applied to the particles because of the parabolic form of the velocity

proﬁle inside the channels. Therefore, the relative velocity is different on the two sides of the particles. Thus, a shear

gradient moves them toward the wall until wall-induced, and the shear gradient lift forces cancel each other [Feng et al.,

1994].

All of the mentioned lift forces have a closed form, which enables us to calculate them separately. However, Direct

Numerical Solution (DNS) is a method that calculates the total lift force, comprised of all forms of the lift force

depending on the particle size, particle position, and channel Reynolds number. This method, developed by Di Carlo et

al., calculates the lift force in any arbitrary coordinate across the cross-section [Di Carlo et al., 2009]. As we used the

DNS method in our previous work [Mashhadian and Shamloo, 2019], we concluded that although DNS is the most

accurate method for inertial lift calculation, it is time-consuming and computationally expensive. Hence, utilizing

Artiﬁcial Intelligence (AI) methods can help researchers have almost the same accuracy and reduce the computational

cost [Su et al., 2021].

Deep Learning is a class of Machine Learning methods that can learn Representations of the input data by stacking

multiple layers of Perceptron [LeCun et al., 2015]. These methods have resulted in breakthroughs in many ﬁelds and

tasks, such as image classiﬁcation [Krizhevsky et al., 2017], natural language processing [Brown et al., 2020] and highly

accurate prediction of protein structure [Jumper et al., 2021] which is a signiﬁcant breakthrough in bioengineering.

Due to the high computational cost of conventional methods available in commercial packages, the iterative process of

coming up with solutions for new problems has been experiencing difﬁculties in scientiﬁc ﬁelds. With faster processing

units such as GPUs and more data, using AI as a surrogate model has become more feasible [McBride and Sundmacher,

2019, Mohammadzadeh and Lejeune, 2022]. The progress made in high-throughput microﬂuidics has resulted in vast

amounts of data. Processing this data using conventional methods no longer results in a good performance.

AI methods have been deployed in many microﬂuidic applications to address that need. In a great review, [Riordon

et al., 2019], have classiﬁed the ways that Deep Learning has been used in microﬂuidic applications based on the type

of input data and the desired output data from unstructured-to-unstructured [Chen et al., 2016] which cell classiﬁcation

is a type of, to Image-to-Image types of application for cell segmentation [Zaimi et al., 2018]. Design and controlling of

the microﬂuidic devices is an expert dependent process which can be of a burden to wide adoption of microﬂuidics in

other scientiﬁc ﬁelds. This gap can also be bridged by usage of user-friendly and easy to use machine learning methods

[McIntyre et al., 2022].

One of the signiﬁcant obstacles to using AI-based methods is the lack of credible data. [Su et al., 2021] generated

a database on lift coefﬁcients in microﬂuidic channels using a computationally expensive DNS method for three

types of cross-sections. They then developed an MLP Neural Network to predict lift coefﬁcients across 3 shapes of

microﬂuidic channel cross-section. Using the same architecture, they trained the neural network on each cross-section

shape separately. The provided model required to be retrained each time for inferring on new data.

In this work, we have trained a single network on the whole dataset provided by [Su et al., 2021]. We have studied

the hyperparameters using a Bayesian optimization [Snoek et al., 2012] method with a hyperband [Li et al., 2017]

stopping criteria to ﬁnd the best architecture speciﬁc to the predeﬁned need. We have also conducted a thorough study

on the effects of Non-linearities and optimizers used. After validating the results with the experimental studies in the

literature, we developed an API for the trained model with an easy-to-use user interface to reduce the need for machine

learning expertise in order to use surrogate models for faster design iterations in inertial microﬂuidics applications. The

developed webapp called microAI is deployed to the huggingface platform to be easily accessible to the community.

2 Methods

2.1 Direct Numerical Simulation

Point Particle Model (PPM) is widely adopted in the literature for determining particle trajectory [Bazaz et al., 2020] by

removing the surface tension effect. Therefore, the lift force caused by the surface tension is not considered. The PPM

assumption can be utilized when the particle size is considerably smaller than the channel dimensions. Otherwise, the

effect of the lift force is not negligible because of the considerable pressure gradient and shear stress on the particle

surface which makes the particles rotate in the ﬂow. This rotation is one of the main reasons for the lateral displacement

of the particles.

microAI: A machine learning tool for fast calculation of lift coefﬁcients in microchannels

In this study, a Direct Numerical Solution (DNS) is used to consider the effect of lift force even in PPM. DNS method

for lift force calculation has an iterative procedure that is shown in Figure 1. First, the initial coordinate of the particle is

set and then, the initial velocities are set for the rotating sphere. Second, an FEM-based solution is used for determining

the ﬂow ﬁeld and then the forces and moments applied to the particle are calculated. After calculating the linear and

angular accelerations, the linear and angular velocity can be extracted by using an appropriate time step and they are

used as an initial velocity for next iteration. This iterative process is continued while the calculated momentum in y and

z direction and the force in the x direction decrease to less than

10−18

N.m and

1.5×10−11

N, respectively. Finally,

the lift force is calculated in the initial position that is a function of the particle size (

d/H

) in which

is the particle

diameter and

is the height of the channel, particle position inside the channel (

2y/H, 2z/H

) and Reynolds number

of the channel by using the ﬂow density

, maximum cross-section velocity

Umax

and dynamic viscosity of the ﬂow

, and channel height

as the characteristic dimension of the channel (

ρUmax H

). It should be noted that the particle

center should always have a distance from the walls equal to its radius. Therefore, compared to PPM, the DNS method

considers the volume of the particle, and the total lift force is calculable in this method. A ﬂowchart showing how the

DNS method is used to calculate the lift force coefﬁcients and the dimensions notation used in this work can be seen in

Figure 1.

(a) Flowchart showing the steps of the Di-

rect Numerical Solution (DNS) method.

(b) A particle with diameter d inside the microchannel.

Figure 1: Direct Numerical Solution method for calculating the lift coefﬁcients inside a microchannel.

2.2 Machine Learning

First, we describe the way that microAI could be used. After describing the dataset, we explain the network hyperpa-

rameters, the method used to sweep the hyperparameter space, and the ﬁnal structure of microAI.

2.3 microAI usage

The frequent need for lift coefﬁcient for designing inertial microﬂuidic channels to calculate the particle trajectory

resulted in the decision to have a fast, accurate, accessible, and easy-to-use application to save hundreds of hours

from the scientiﬁc community. The webapp was developed using gradio [Abid et al., 2019]. Gradio is an open-source

python library that facilitates the creation of API with methods and functions for adding input spaces such as text

boxes, radio buttons, and sliders and removes the need for rewriting these functions from scratch. Another beneﬁt of

using gradio is its facility for deploying on the huggingface platform. Huggingface is a free and open-source hosting

platform for machine learning models to bring them from just models in papers to functioning objects that can be

accessed and used by the community. microAI was developed using pyTorch and can be accessed from this URL:

https://erfanhamdi.github.io/microAI/

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MICROAI:AMACHINELEARNINGTOOLFORFASTCALCULATIONOFLIFTCOEFFICIENTSINMICROCHANNELSErfanHamdiDepartmentofMechanicalEngineeringSharifUniversityofTechnologyTehran,AzadiSt.erfan.hamdi@mech.sharif.irRasoolDezhkamDepartmentofMechanicalEngineeringSharifUniversityofTechnologyTehran,AzadiSt.rasool.dezhkam@sha...

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MICRO AI A MACHINE LEARNING TOOL FOR FAST CALCULATION OF LIFT COEFFICIENTS IN MICROCHANNELS Erfan Hamdi

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