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PDMS 표면에서 충돌 액적의 점도에 따른 거동의 주기성

강동관1, 이상민2,#orcid

Periodicity of Droplet Impact Behavior by Liquid Viscosity on PDMS Surface

Dong Kwan Kang1, Sangmin Lee2,#orcid
Journal of the Korean Society for Precision Engineering 2022;39(11):857-862.
Published online: November 1, 2022

1 동의대학교 인공지능로봇연구소

2 동의대학교 기계자동차로봇부품공학부

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#E-mail: thinking@deu.ac.kr, TEL: +82-051-890-2300
• Received: May 26, 2022   • Revised: July 7, 2022   • Accepted: July 12, 2022

Copyright © The Korean Society for Precision Engineering

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • Periodicity behavior was observed after droplet collision in viscous solutions with controlled glycerol concentrations onto a PDMS surface. No periodic movement was observed in the droplets at glycerol concentrations of 50% or more. In contrast, the vertical diameter of the droplets increased and decreased periodically at glycerol solution concentrations of 40% or less. Moreover, there was little change in the periodicity of the impacting droplet movement, and the vibration frequency was measured at approximately 80 to 98 Hz in the entire range. The maximum droplet spreading factor after collision decreased significantly with increasing glycerol concentrations of 40% or more (Ohnesorge number 1.4 × 10-2 or more). The results suggest that the effect of viscosity became greater than that of the solution surface tension with increasing glycerol concentrations.
  • KEYWORDS: Droplet impact, Periodicity, Spreading, Viscosity
  • KEYWORDS: 액적 충돌, 주기성, 퍼짐, 점도

ρ

Density

σ

Surface Tension

V

Velocity

D

Droplet Diameter

D0

Initial Droplet Diameter

Dmax

Maximum Droplet Diameter

μ

Kinematic Viscosity
액체 상태의 미소 액적(Microdroplet)이 고체 표면에 충돌하는 현상은 분무 도장(Spray Coating), 분무 냉각(Spray Cooling), 분부 코팅(Spray Coating) 등과 같은 다양한 산업 현장에서 일어나는 현상을 이해하기 위해 오래전부터 많이 연구되어 오고 있다[1,2]. 특히, 잉크젯 프린팅(Inkjet Printing) 기술과 같이 미소 액적을 정밀하게 전달하여 패턴을 형성하는 기술은 버려지는 재료의 양이 적어 경제적이며 공정이 단순하여 효율적인 제조 방법으로 인쇄 전자(Printed Electronics) 분야에서 많이 연구되고 있다.
최근에는 웨어러블 디바이스(Wearable Device)를 제작하기 위하여 고분자(Polymer) 기반의 유연한 기판에 전도성 잉크를 사용해 전극(Electrode) 패턴을 형성하는 연구가 진행되고 있다. Khan 외는 셀룰로스 아세테이트(Cellulose Acetate) 기판에 은 나노 입자 잉크(Ag Nanoparticles Ink)를 패터닝(Patterning) 후 폴리디메틸실록산(Polydimethylsiloxane, PDMS) 기반의 나노복합체(PDMS-Based Nanocomposite)와 교차 연결된 전극을 제작하였으며[3], Ling 외는 PEDOT:PSS (Poly(3,4-Ethylene Dioxythiophene) Polystyrene Sulfonate) 잉크를 사용하여 투명하며 유연성을 가진 나노 종이 기반 터치 센서(Nano Paper-Based Touch Sensor)를 구현하였다[4].
미소 액적의 충돌 현상은 액적의 표면장력, 점성과 같은 유체역학적인 특성뿐 아니라, 충돌하는 표면의 거칠기(Roughness)나 젖음성(Wettability), 액적의 운동 에너지(Kinetic Energy) 등에 따라 그 현상이 달라진다[5,6].
기존의 미소 액적의 충돌 현상은 견고한(Rigid) 기판(Substrate)에서 액적의 충돌 현상에 대해서 많이 연구되어 왔다. 하지만 최근 웨어러블 디바이스와 같은 유연한 전자 소자들의 제작에 프린팅 기술이 많이 응용되면서, 부드러운(Soft) 기판 혹은 유연 박막 위에서 액적의 충돌 현상에 대한 관심이 커지고 있다[7]. 위와 같은 표면은 액적 충돌에 의해 기판이 변형하거나 진동할 수 있다. 특히 잉크젯 프린팅 방식으로 유연한 표면에 출력하고자 할 때에는 충돌한 액적의 움직임이 기판 자체의 움직임과 결합하여 출력 품질에 영향을 미칠 수 있으므로[8], 액적의 안정적인 증착을 위해서 유연한 표면의 움직임뿐만 아니라 액적의 움직임의 주기성 또한 확인이 필요할 것이다.
본 연구에서는 PDMS (Polydimethylsiloxane) 재료 표면에서 액적의 점도에 따른 충돌 이후 거동의 주기성을 관찰하였다. PDMS는 웨어러블 디바이스 및 유연 소자 제작에 보편적으로 사용되는 재료로 이를 기반으로 다른 기능성 물질들을 표면에 프린팅하여 소자를 제작하는 방법들이 많이 연구되고 있다[9]. 또한, 액적의 충돌 후 움직임을 분석하기 위해서 초고속 카메라를 이용하여 일정 높이에서 자유낙하한 액적의 충돌 과정을 촬영하였고 이미지 분석을 통해서 액적의 움직임을 정량적으로 분석하였다. 동일한 방법으로 액적의 점도를 증가시켜가며 액적의 충돌 이후 움직임을 수직 방향과 수평 방향의 시간에 따른 지름 변화를 분석하여, 지름 변화의 주기성에 용액의 점성이 미치는 영향을 실험적으로 확인하였다.
Fig. 1은 액적 충돌 실험 장치의 구성을 나타낸 개념도이다. 본 연구에서는 초순수(Deionized Water)에 글리세롤(Glycerol)을 첨가하여 다양한 점도의 용액을 준비하였으며, 무게 비율로 0-90%까지 글리세롤을 첨가하였다. 글리세롤 수용액은 실린지 펌프(Fusion200, Chemyx Inc.)와 플라스틱 니들(25-Gage, 내경~0.53 mm)을 사용하여 일정한 높이(~110 mm)에서 일정한 크기의 액적으로 자유낙하되도록 하였다. 액적의 충돌 전, 후의 과정은 초고속 카메라(FASTCAM MiniAX, Photron)를 통해 10,000 FPS (Frame per Second)의 속도로 기록하였으며, 디지털 영상 분석 기술(Digital Image Processing, MATLAB®)을 이용하여 액적의 움직임을 정량적으로 분석하였다.
Fig. 1

A diagram of the experimental setup for observing droplet collision behavior

KSPE_2022_v39n11_857_f001.jpg
동일한 실험 조건에서 글리세롤 농도 별 충돌 현상을 5회 이상 반복 측정하였으며, 각 농도 별 충돌 액적의 부피와 속도를 이미지 분석을 통해서 측정하였으며, 측정 결과는 Fig. 2에 나타냈다. 충돌 액적의 평균 속도는 약 1.45±0.01 m/s으로 글리세롤의 농도가 증가하더라도 비슷한 속도로 측정되었다. 하지만, 충돌 액적의 부피는 대략 7-10 μL 범위에서 측정되었으며, 글리세롤 농도가 증가할수록 부피가 감소하는 경향을 보였다. 글리세롤 농도가 증가할수록 혼합 용액의 밀도는 증가하게 되며, 표면장력은 오히려 감소하게 된다. 따라서 동일한 니들 크기에서 액적이 매달릴 수 있는 부피는 글리세롤 농도가 증가할수록 감소하게 되어 충돌 액적의 부피가 다소 감소한 것으로 보인다.
Fig. 2

Volume and velocity of falling droplets versus glycerol concentration of liquid solution

KSPE_2022_v39n11_857_f002.jpg
충돌 표면은 두께 약 3 mm의 PDMS 재료를 이용하였으며, 가장 보편적인 Dow Corning 사의 Sylgard 184를 이용하여 Prepolymer와 Curing Agent를 10 : 1로 섞은 후 70°C에서 24시간 경화하는 방법으로 제작하였다.
액적 충돌 현상은 액적이 가지는 운동 에너지와 액체의 표면장력 및 점성력의 상호작용으로 나타나게 되며, 이를 정량적으로 구분하기 위해서 주로 웨버 수(Weber Number, We)나 오네소지 수(Ohnesorge Number, Oh)를 이용하며[10,11], 각각의 무차원 수는 식(1)과 같이 정의할 수 있다.
(1)
We=ρV2Dσ,Oh=μρσD
여기서 ρ는 액적의 밀도, V는 속력, D는 액적의 지름을 뜻하며, σ는 표면장력, μ는 점성계수를 나타낸다. 웨버 수는 액체의 표면 장력과 운동에너지의 비로 웨버 수가 클수록 운동에너지가 큰, 즉 관성력(Inertia Force)이 크게 작용한다는 것을 의미한다. 마지막으로 오네소지 수는 액체 표면 장력에 의한 모세관력(Capillary Force)과 점성력의 비로 오네소지 수가 클수록 점성력의 영향이 큰 것을 의미한다. 본 실험에 사용한 글리세롤 수용액의 농도 별 웨버 수와 오네소지 수를 계산하기 위해서, 용액의 밀도, 표면장력, 점도는 문헌에 알려진 대표적인 값을 이용하였으며[12], 이를 이용하여 계산한 무차원 수는 Table 1에 정리하였다.
Table 1

Dimensionless number (Re, Oh) calculated based on the volume and velocity of each droplet concentration

Table 1
Glycerol concentration [wt.%] We Oh
90 104 3.8 × 10-1
80 97 8.8 × 10-2
70 93 5.7 × 10-2
60 88 2.3 × 10-2
50 88 1.8 × 10-2
40 82 1.4 × 10-2
30 76 9.3 × 10-3
20 77 4.1 × 10-3
10 74 2.5 × 10-3
0 68 2.5 × 10-3
Fig. 3은 글리세롤 농도 별 액적의 충돌 과정을 고속카메라로 촬영한 연속 이미지들을 보여주고 있다. PDMS 표면에 충돌한 액적은 관성에 의해 최대로 퍼져나가며, 이후 반발력에 의해 액적이 다시 움츠러드는 과정을 확인할 수 있었다. 글리세롤 농도가 낮은(40% 이하) 경우에는 움츠러든 이후에도 액적의 높이가 증가와 감소가 반복되는 주기적인 움직임을 확인할 수 있었으며, 글리세롤 농도가 높은(50% 이상) 경우에는 액적 높이의 주기적인 움직임은 거의 관찰되지 않았다. 이는 액적의 점도가 증가하여 충돌 이후 움직임에서 점성력(Viscous Force)의 영향이 커지게 되면서, 점성에 의한 감쇠 효과(Damping Effect)가 커져 주기적 움직임이 감소한 것으로 보인다.
Fig. 3

Sequential images of collision droplets with varying glycerol concentrations on the PDMS surface

KSPE_2022_v39n11_857_f003.jpg
충돌 이후 액적의 거동을 정량적으로 분석하기 위해서, 충돌 이전 액적의 지름(D0)을 기준으로, 충돌 이후 액적의 지름(D)과 액적의 높이(H)의 상대적인 변화량을 계산하였다(Fig. 4). 충돌 이후 액적의 지름은 표면의 접촉 지름이 아니라 액적 형상의 최대 넓이를 액적의 수평 방향 지름으로 정의하였다.
Fig. 4

Using a digital image processing technique, calculating the diameter and height of a collision droplet

KSPE_2022_v39n11_857_f004.jpg
Fig. 5는 글리세롤 농도별 충돌 이후 시간에 따른 액적의 지름의 상대적인 변화를 분석한 결과이다. 액적의 지름은 충돌 초기 최대로 퍼짐으로써 지름 변화량의 최댓값을 보이고, 이후 움츠러드는 움직임을 보였으며, 30% 이하의 낮은 글리세롤 농도에서는 미세한 지름 증가/감소의 변화가 보였으나, 주기성은 확인되지 않았다. 그리고 액적의 지름은 충돌 이전의 지름 대비 1.2배의 크기로 수렴하였다. 반면, 40% 이상의 글리세롤 농도에서는 일정하게 감소하는 경향을 보였으며, 이때 액적의 지름은 충돌 이전의 지름 대비 약 1.5배의 크기로 수렴하는 것을 확인할 수 있었다.
Fig. 5

Relative droplet diameter (D/Do) over time after collision with various glycerol concentrations

KSPE_2022_v39n11_857_f005.jpg
또한, 액적 지름 변화량의 최댓값은 수평 방향으로 퍼져나가는 액적의 최대 퍼짐 지수(Maximum Spreading Factor)로 식(2)와 같이 표현할 수 있다.
(2)
β=DmaxD0
여기서 Dmax는 충돌 후 최대 지름을 나타내며, 측정 결과 글리세롤 농도 별 최대 퍼짐 지수와 각 농도에서 계산된 오네소지 수를 Fig. 6에 나타냈다. 글리세롤이 포함된 용액에서 농도가 증가할수록 최대 퍼짐 지수가 감소하는 경향을 확인할 수 있었다. 최대 퍼짐 지수는 글리세롤 농도 40% 이상에서 크게 감소하는 것으로 보인다. 즉 오네소지 수가 1.4 × 10-2 이상인 범위에서 퍼짐 지수의 감소가 크게 나타나는 것으로 관찰되었다[13]. 또한, 글리세롤 농도가 0-10%인 구간에서 최대 퍼짐 지수가 약간 증가하는 경향을 보이는데, 이는 두 글리세롤 농도에서 오네소지 수의 변화는 거의 없지만, 웨버 수가 증가한 것으로 계산되었다. 따라서 점성력 효과는 비슷한 수준에서 관성력의 영향이 다소 증가하여 이에 비례해 퍼짐성이 약간 증가한 것으로 보인다. 이후 글리세롤 농도가 증가할수록 점성력의 효과가 증가하면서 최대 퍼짐 지수는 감소한 것으로 보인다.
Fig. 6

Maximum spreading factor (β) and ohnesorge number versus glycerol concentration of the liquid solution

KSPE_2022_v39n11_857_f006.jpg
Fig. 7은 충돌 이후 시간에 따른 액적의 수직 방향의 지름, 즉 높이의 상대적인 변화를 측정한 결과이다. 글리세롤 농도가 40% 이하로 낮은 경우에는 충돌 초기 최대로 퍼져나가면서 높이는 최대로 줄어들어 최솟값을 보였으며, 이후 연속적으로 움츠러듦에 의해 최댓값을 보였다. 이후 액적의 높이는 증가와 감소를 반복하는 주기적인 움직임을 확인할 수 있었다. 반면, 글리세롤 농도가 50% 이상의 경우에는 최대로 퍼짐에 의한 최소 높이 값을 보인 이후 최종 높이로 수렴해가는 경향을 보였으며, 이 과정에서 주기적인 높이 변화는 확인되지 않았다.
Fig. 7

Relative droplet height (H/Do) over time after collision with various glycerol concentrations

KSPE_2022_v39n11_857_f007.jpg
따라서, 주기적인 움직임을 보인 40% 이하의 낮은 글리세롤 농도에 대해서 진폭과 진동 주기를 측정하였으며, 그 결과 높이 변화 값의 최대 진폭과 진동 주파수를 Fig. 8에 나타냈다. 진동 주파수는 시간에 따른 높이 변화의 각 피크 값들의 시간평균(Average of Peak-to-Peak Time)으로 계산된 주기의 역수(Reciprocal Number)로 정의하였다[14]. 계산된 액적의 진동 주파수는 80.2-98.3 Hz 범위로 계산되었으며, 평균 88.26±5.59 Hz 값으로 계산되었다. 이는 액적의 형상에 따른 이론적인 공진주파수(Resonance Frequency)를 계산한 결과 80-82 Hz와 비슷한 범위로 측정된 것을 확인할 수 있었다[15]. 이론적인 공진주파수는 액적의 형상(부피)과 밀도, 표면장력이 고려된 값으로, 이에 대한 변화는 주파수 변화에 영향이 크지 않다는 것을 알 수 있다.
Fig. 8

The maximum relative droplet height (Hmax/Do) and oscillation frequency of droplet by glycerol concentration

KSPE_2022_v39n11_857_f008.jpg
본 연구에서는 PDMS 재료 표면에서 액적의 점도에 따른 충돌 이후 거동의 주기성을 관찰하였으며, 그 결과 글리세롤 농도가 50% 이상인 용액의 액적에서는 주기적인 움직임이 확인되지 않았지만, 40% 이하의 글리세롤 농도의 액적에서는 수직 방향 지름의 증감이 주기적으로 발생한 것을 확인할 수 있었다. 또한, 40% 이하의 농도에서는 농도에 따른 충돌 액적의 움직임의 주기성 변화는 거의 없었으며, 전체 범위에서 진동 주파수는 대략 80-98 Hz로 측정되었다.
향후 액적의 주기성과 충돌 표면의 주기성의 상관관계를 넓은 범위에서 확인해 보기 위해서, 인장력을 이용하여 강성이 조절된 유연 박막의 표면에 충돌하는 액적의 거동에 대한 연구를 진행해 나갈 계획이다.
이 논문은 정부(과학기술정보통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임(No. NRF-2020R1F1A1050735).
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Dong Kwan Kang
KSPE_2022_v39n11_857_bf001.jpg
B.S. dgree in Division of Mechanical, Automotive, Robot Components Engineering, in Dong-Eui University. His research interest in MEMS and flexible sensors.
Sangmin Lee
KSPE_2022_v39n11_857_bf002.jpg
Assistant Professor in Division of Mechanical, Automotive, Robot Components Engineering, Dong-Eui University. His research interest is MEMS and microfluidic system.

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Periodicity of Droplet Impact Behavior by Liquid Viscosity on PDMS Surface
J. Korean Soc. Precis. Eng.. 2022;39(11):857-862.   Published online November 1, 2022
DOI: https://doi.org/10.7736/JKSPE.022.070
Download Citation

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Periodicity of Droplet Impact Behavior by Liquid Viscosity on PDMS Surface
J. Korean Soc. Precis. Eng.. 2022;39(11):857-862.   Published online November 1, 2022
DOI: https://doi.org/10.7736/JKSPE.022.070
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Periodicity of Droplet Impact Behavior by Liquid Viscosity on PDMS Surface
Image Image Image Image Image Image Image Image
Fig. 1 A diagram of the experimental setup for observing droplet collision behavior
Fig. 2 Volume and velocity of falling droplets versus glycerol concentration of liquid solution
Fig. 3 Sequential images of collision droplets with varying glycerol concentrations on the PDMS surface
Fig. 4 Using a digital image processing technique, calculating the diameter and height of a collision droplet
Fig. 5 Relative droplet diameter (D/Do) over time after collision with various glycerol concentrations
Fig. 6 Maximum spreading factor (β) and ohnesorge number versus glycerol concentration of the liquid solution
Fig. 7 Relative droplet height (H/Do) over time after collision with various glycerol concentrations
Fig. 8 The maximum relative droplet height (Hmax/Do) and oscillation frequency of droplet by glycerol concentration

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Periodicity of Droplet Impact Behavior by Liquid Viscosity on PDMS Surface
Glycerol concentration [wt.%] We Oh
90 104 3.8 × 10-1
80 97 8.8 × 10-2
70 93 5.7 × 10-2
60 88 2.3 × 10-2
50 88 1.8 × 10-2
40 82 1.4 × 10-2
30 76 9.3 × 10-3
20 77 4.1 × 10-3
10 74 2.5 × 10-3
0 68 2.5 × 10-3
Table 1 Dimensionless number (Re, Oh) calculated based on the volume and velocity of each droplet concentration

Table 1

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