# Measuring Surface and Interfacial Tension In Situ in Microdripping Mode for Electrohydrodynamic Applications

^{1}

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## Abstract

**:**

## 1. Introduction

_{low}) and very low, even zero, applied voltage (V = V

_{min}) [18,19,20,21,22,23]. Due to the relatively low influence of mechanical and electrical forces in this mode, drops are dispensed almost solely due to the interplay between S/IFT and gravity. With electromechanical stresses muted, at V

_{min}= 0, this mode is particularly suited for in situ measurement of S/IFT. Moreover, as one would intuitively expect, particle production frequency in this mode is relatively very low—from near zero Hz to low kHz. Another interesting consequence of the virtually nonexistent influence of V

_{min}is that there is no cone formation at the tip of the nozzle. Instead, as the solution flows through the assembly to the nozzle tip, the drop at the tip continues to grow primarily as a function of SFT, capillary diameter, and Q

_{low}until the weight (gravity) of the drop overcomes SFT. At this point, one part of the drop from the nozzle tip is dispensed, while the remaining solution relaxes to regain its original smaller shape at the tip of the nozzle. This mode is also characterized with near monodisperse particle sizes.

## 2. Materials and Methods

^{®}(2017a, MathWorks, Inc., Natick, MA, USA) modules were developed to derive time domain signals from the flux in the columnar sum of pixel intensities of light reflected from the dispensed drops in the captured frames. The algorithm then analyzes this signal to determine periodicity and frequency (Figure 2D).

#### 2.1. Computational Model

^{®}Fluent

^{®}(18.0, Ansys, Inc., Canonsburg, PA, USA) project runtime parameters.

#### 2.2. Signal Processing and Spectral Analysis

^{®}(2016, National Instruments, Austin, TX, USA) was processed using a custom MATLAB

^{®}program to confirm the periodicity of dispensed droplets and calculate droplet frequencies from the input signal comprising of a series of image frames. Briefly, the algorithm comprised of transforming 2D image frames to a 1D array of columnar intensity sums as a means to rapidly pinpoint the droplet’s position and size in each frame. The input signal, which is essentially an array of 2D image frames, is thus converted into an array of 1D arrays, which forms a convenient numerical proxy for the original fast frame video captured by the LabView

^{®}module. A visual representation of this array of 1D arrays is shown in the first panel in Figure 2D. Next, spectral density and period are computed by the algorithm using Welch’s method. Spectral density of a signal is simply the power of the signal at different frequencies. The algorithm starts by converting the input signal from the time to frequency domain to obtain the periodogram/spectrum. Compared to the standard periodogram spectrum and Bartlett’s method, Welch’s method reduces noise by compromising (reducing) frequency resolution. This is advantageous when the signal contains noise from imperfect or finite data and where noise reduction is desired. A visual representation of the Welch spectral density computed is shown in the second panel in Figure 2D. The algorithm also performs a confirmatory Fast Fourier-Transform (FFT) analysis. It is important to note that FFT is “conjugate symmetric” with a 2-sided spectrum function of both positive and negative frequencies (−Fs/2 to +Fs/2). The algorithm computes a 1-sided spectrum (with twice the amplitude) based on a 2-sided spectrum and signal length equal to the original signal. Absolute values of the complex-valued FFT are computed to extract the 1-sided magnitude and filter out phase data. A visual representation of the FFT is shown in the third panel in Figure 2D. Please refer to Supplementary Material section for LabView

^{®}and MATLAB

^{®}source files.

#### 2.3. Experimental

^{®}tubing (Saint-Gobain Corporation, La Défense, Courbevoie, France). For flow rates below 500 µL/min, a BeeHive

^{®}MD-1020 (Bioanalytical Systems, Inc., Lafayette, IN, USA) syringe pump was used, while a KDS-410 (kdScientific

^{®}, Holliston, MA, USA) was used for flow rates ranging from 500 µL/min to 20 mL/min. A high-speed Teledyne Dalsa Genie

^{®}CR-GM00-H6401 camera (300 fps, Teledyne DALSA, Waterloo, Ontario, Canada) fitted with extension tubes and a 10x macro lens and connected to a computer system running custom LabView (LabView

^{®}2016, Vision Acquisition Software

^{®}2017, and Vision Development Module

^{®}2016) and MATLAB (MathWorks

^{®}MATLAB

^{®}2017a) programs, was positioned 40 mm away from the needle tip, normal to which, a focused LED light source was also positioned 40 mm away from the needle. As noted earlier, to ensure a low Weber number, parameters such as nozzle diameter, flow rate, density, and viscosity must be appropriately configured. Droplet frequencies near 1–5 Hz minimize computational resources and also control experimental variance. In addition, care must be exercised to manage conditions such as atmospheric saturation, nozzle-plane leveling, and surrounding vibration. Tubing and apparatus must be examined to ensure that no contaminants are inadvertently introduced in the system. Furthermore, pumps must be calibrated and fine-controlled to ensure smooth and accurate dispensing of solution, which in turn, ensures a near-constant flow velocity. Ethanol (70% v/v) was purchased from Ricca Chemical Company (Arlington, TX, USA). Saline (0.9% NaCl with trace HCl or NaOH for pH adjustment) was purchased from Hospira (Lake Forest, IL, USA). Molecular biology grade chloroform (with 0.75% Ethanol preservative) and non-ionic surfactant Tween

^{®}20 (Polyoxyethylene-20-sorbitan Monolaurate) were purchased from Fisher Scientific (Fair Lawn, NJ, USA). All experiments were at least performed in triplicate. At least 3 measurements were made for all experimental observations.

## 3. Results

^{®}20 aqueous solutions similar to published profiles but, as anticipated, at relatively higher values of SFT [34,35,36].

## 4. Discussion

_{i}is local mean interface curvature for i, and ${\alpha}_{i}$ is volume-fraction of i. Equation (4) shows that SFT source-term for a cell is proportional to the average density in the cell. For two-phase systems, volume-fraction-averaged density becomes:

_{3}), an organic solvent with high density but low dynamic viscosity; (ii) 70 v/v % ethanol (etOH), with low density but high viscosity; (iii) water.

## 5. Conclusions and Outlook

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Approximate regimes of electrohydrodynamic atomization (EHDA) modes shown as a function of applied voltage (V) and flow rate (Q).

**Figure 2.**Schematic illustration of the modified EHDA setup for in situ (

**A**) surface tension (SFT) and (

**B**) interfacial tension (IFT) measurements. In both cases, a light-emitting diode (LED) light source is pointed slightly below the tip of the EHDA nozzle, while a charge-coupled device (CCD) camera captures images at a minimum 200 frames per second (fps). (

**C**) An image of a dispensed drop captured by the camera. (

**D**) Three panels showing the signal derived from captured image sequence (video) in the time domain, where dS/dt is the derivative of signal intensity with respect to time, which highlights peak intensities at drop locations, Welch’s power spectral density (WSD) and fast Fourier-transform (FFT) in the frequency domain. Both WSD and FFT indicate that the signal is not only periodic, given that almost all the power is in the fundamental frequency and its multiples (harmonics), but that the fundamental frequency is 2.13 Hz, which is close to the average drop rate.

**Figure 3.**Computational fluid dynamics (CFD) domain, adaptive mesh, and drop kinetics simulation. (

**A**) Domain showing tip of the nozzle and non-adaptive mesh. (

**B**) Mesh adaptation function. (

**C**) Volume fractions from a detaching drop in two-phase simulations of dispensed drops.

**Figure 4.**Estimating SFT and IFT. (

**A**) Frequencies from CFD numerical solutions for discrete S/IFT values were interpolated, labeled “CFD,” and adjusted, “Adj”, −4% for Water–Air and +1.5% for other interfaces. Bold dashed lines indicate published [32,33] range of S/IFT for respective interfaces. (

**B**) S/IFT derived by cross-referencing in situ recorded “drop-kicks” frequencies against corresponding “Adj” frequencies from CFD numerical solutions. Aside from a few outliers, resulting S/IFT were in agreement with published ranges, particularly for Chloroform–Water IFT. Flowrate (Q) for CHCl3–Air SFT was 3 mL/min, all others were at 5 mL/min.

**Figure 5.**Effect of surfactants and additives on SFT. (

**A**) Frequencies from CFD numerical solutions for a wider range of discrete Water–Air SFT values interpolated, labeled “CFD,” and adjusted, “Adj,” −4%. (

**B**) “Drop-kicks” frequencies cross-referenced against Water–Air “Adj” frequencies to derive SFT for Water–Air and various micromolar concentrations of aqueous Tween

^{®}20 solutions. Bold dashed lines indicate published ranges [34,35,36] of SFT. SFT decreased with increasing concentrations of Tween

^{®}20 but at relatively higher than published values. This was anticipated considering that established methods measure SFT at boundaries with asymmetrically high concentrations of surfactants which lower SFT.

Simulation | Material | Density (kg/m^{3}) | Viscosity (kg/m·s) | Velocity (m/s) | Time Step (s) |
---|---|---|---|---|---|

Water-Air | Water | 998.2 | 0.001003 | 0.083 | 5 × 10^{−6} |

Air | 1.225 | 1.7894 × 10^{−5} | |||

Ethanol-Air | 70% Ethanol | 880 | 0.0025 | 0.0415 | 1 × 10^{−6} |

Air | 1.225 | 1.7894 × 10^{−5} | |||

Chloroform-Air | Chloroform | 1490 | 0.000563 | 0.0415 | 5 × 10^{−6} |

Air | 1.225 | 1.7894 × 10^{−5} | |||

Chloroform-Water | Chloroform | 1490 | 0.000563 | 0.0415 | 1 × 10^{−6} |

Water | 998.2 | 0.001003 | |||

Air | 1.225 | 1.7894 × 10^{−5} |

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**MDPI and ACS Style**

Budhwani, K.I.; Pekmezi, G.M.; Selim, M.M.
Measuring Surface and Interfacial Tension In Situ in Microdripping Mode for Electrohydrodynamic Applications. *Micromachines* **2020**, *11*, 687.
https://doi.org/10.3390/mi11070687

**AMA Style**

Budhwani KI, Pekmezi GM, Selim MM.
Measuring Surface and Interfacial Tension In Situ in Microdripping Mode for Electrohydrodynamic Applications. *Micromachines*. 2020; 11(7):687.
https://doi.org/10.3390/mi11070687

**Chicago/Turabian Style**

Budhwani, Karim I., Gerald M. Pekmezi, and Mohamed M. Selim.
2020. "Measuring Surface and Interfacial Tension In Situ in Microdripping Mode for Electrohydrodynamic Applications" *Micromachines* 11, no. 7: 687.
https://doi.org/10.3390/mi11070687