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# DROPLET SIZE ESTIMATION WITH THE RAYDROP

## Estimate the size of your droplets with the Raydrop!

We developed a droplet calculator based on correlations obtained from numerical modeling [Dewandre et al., 2020] to help you predict the diameter of droplets. The estimation account for the Raydrop’s nozzle diameter, flow rate of the continuous phase, viscosities of both phases, and interfacial tension.

Save time and use our calculator to find the set of parameters that best fit your needs!

## What is the RayDrop?

The RayDrop is a microfluidic droplet generator composed of three main parts fully removable:

• An injection capillary composed of a nozzle available in 30µm, 60µm and 90µm size
• An extraction capillary available in 150µm, 300µm and 450µm size
• A body containing a chamber

## How does it work?

The RayDrop works as a co-flow focusing principle. The nozzle and outlet capillary are aligned in continuous phase chamber, the dispersed phase comes through the nozzle to create the microparticles into the continuous phase and exit by the outlet insert.

## Droplet calculator

Warning: desktop Only.

 Raydrop configuration 30-150µm 60-300µm 90-450µm γ (mN/m) μd (cP) μc (cP) Qd (µl/min) Qc (µl/min)

γ: interfacial tension;

µd: dispersed phase dynamic viscosity;

µc: continuous phase dynamic viscosity;

Qd dispersed phase flow rate;

Qc continuous phase flow rate

Note that the droplet size is slightly underestimated as the dispersed phase flow rate is not taken into consideration (Qd -> 0).

## Diameter estimation of water-in-oil droplets

Water-in-mineral oil and water-in-HFE-7500 were characterized using our calculator. Droplet size was determined as a function of the device geometry, fluid properties and flow rate of the continuous phase.

The graphs below summarize the results obtained with the two types of emulsions. Droplets with diameter ranging from 41 µm to 375 µm can be obtained.

Note that these predictions have been made in the limit of Qd 0 and underestimate the real droplet size for increasing values of Qd.

Droplet diameter as a function of the continuous flow rate using different capillary couples (30 – 150 µm, 60 – 300 µm, and 90 – 450 µm); λ: viscosity ratio, µd: dispersed phase dynamic viscosity; µc: continuous phase dynamic viscosity; Qd: dispersed phase flow rate; Qc: continuous phase flow rate, γ: interfacial tension.

Droplet diameter as a function of the continuous flow rate using different capillary couples (30 – 150 µm, 60 – 300 µm, and 90 – 450 µm); λ: viscosity ratio, µd: dispersed phase dynamic viscosity; µc: continuous phase dynamic viscosity; Qd: dispersed phase flow rate; Qc: continuous phase flow rate, γ: interfacial tension.

## Diameter estimation of water-in-oil droplets

Water-in-mineral oil and water-in-HFE-7500 were characterized using our calculator. Droplet size was determined as a function of the device geometry, fluid properties and flow rate of the continuous phase.

The graphs below summarize the results obtained with the two types of emulsions. Droplets with diameter ranging from 41 µm to 375 µm can be obtained.

Note that these predictions have been made in the limit of Qd 0 and underestimate the real droplet size for increasing values of Qd.

Droplet diameter as a function of the continuous flow rate using different capillary couples (30 – 150 µm, 60 – 300 µm, and 90 – 450 µm); λ: viscosity ratio, µd: dispersed phase dynamic viscosity; µc: continuous phase dynamic viscosity; Qd: dispersed phase flow rate; Qc: continuous phase flow rate, γ: interfacial tension.

Droplet diameter as a function of the continuous flow rate using different capillary couples (30 – 150 µm, 60 – 300 µm, and 90 – 450 µm); λ: viscosity ratio, µd: dispersed phase dynamic viscosity; µc: continuous phase dynamic viscosity; Qd: dispersed phase flow rate; Qc: continuous phase flow rate, γ: interfacial tension.

## The theoretical model behind our microfluidic droplet calculator

Our partner Secoya made use of numerical simulations to build the correlations used in the calculator. A system based on the continuity and Navier-Stokes equations is solved using finite element method (FEM) with moving boundaries.

The model was validated by comparing with experimental data, as shown in the figure below (Cac is the capillary number of the continuous phase).

It has next been used to predict the effect of several parameters such as viscosity ratio, flow rates and geometrical parameters (nozzle inclination angle, nozzle-capillary distance) on droplet formation.

Comparison between transient simulations (green lines) and experimental pictures for the formation of water drops in mineral oil. R: Equivalent radius of the meniscus preceding the pinch-off location Cac : capillary number of the continuous phase. Couple 1 consists of a nozzle of 30 µm diameter and a 150 µm diameter extraction capillary, and couple 2 of a nozzle of 90 µm diameter and a 450 µm diameter extraction capillary.

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