the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Jun 2023
The viscosity and surface tension of supercooled levitated droplets determined by excitation of shape oscillations
Abstract. We report a new method for determining the viscosity and surface tension of supercooled liquid droplets using electrodynamic levitation and phase analysis of shape oscillations. The method uses a high frequency alternating electrical potential to excite shape oscillations in a levitated droplet, and the phase shift of the oscillations is used to simultaneously determine droplet viscosity and surface tension. The advantages over existing contactless methods include its applicability to atmospherically relevant temperatures, and the possibility to continuously monitor changes in real time. We demonstrate proof-of-concept measurement for supercooled water droplets and dilute sucrose solution droplets, and we anticipate that the technique could be used to measure viscosity values within the semi-solid range for droplets containing dilute organics. The technique is especially well-suited for investigation of the role of atmospheric processing on the viscosity and surface tension of solution droplets in equilibrium with a given or changing relative humidity.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2023-1160', Alison Bain, 21 Jun 2023
Very nice paper, I enjoyed reading it. I do have a couple questions that you might concider addressing in the manuscript.
First, with regard to the statement of potential for investigating smaller particles, do you have an estimate for the smallest radius that could be investigated with this technique? Would the decrease in scattering intenisty as particles size decreases put a lower limit on the size range that can be investigated? Or is the limit defined by the smallest droplet that can be trapped and sized in the EDB?
Second, in Fig. 6 when the surface tension falls as the droplets evaporate, how long are these evaporation experiments?
Third, would it be possible to use this technique for absorbing aerosol like brown carbon? Does the choice of the HeNe laser mean that the absorbance would be low enough at the laser wavlength to obtain a sufficient signal?
Citation: https://doi.org/10.5194/egusphere-2023-1160-CC1 -
AC1: 'Reply on CC1', Denis Duft, 23 Jun 2023
Dear Alison,
Thank you for your comment and questions! We will consider addressing them in a revised manuscript.
Comment 1:
First, with regard to the statement of potential for investigating smaller particles, do you have an estimate for the smallest radius that could be investigated with this technique? Would the decrease in scattering intenisty as particles size decreases put a lower limit on the size range that can be investigated? Or is the limit defined by the smallest droplet that can be trapped and sized in the EDB?
Reply:
Besides scattering intensity and EDB trapping range there are a couple of additional factors which may limit the size range towards smaller particles in this method. The loss in scattering intensity may be overcome partially by using a more powerful and/or focussed laser. The EDB trapping range is more difficult to assess as it depends on several factors. Our EDB was initially designed to levitate droplets in the D=10-100µm size range. We estimate that limitations will occur for our trap below around 5µm dia. Some other factors are:
- We determine the droplet size by analysing the spatial frequency of fringes in the angular light scattering. This method for size determination becomes much less accurate for droplets below D=2µm.
- The natural frequency of the L=2 shape oscillation is on the order of 1Mhz for D=4µm droplets. Droplets of that size require not only excitation in the MHz range but also a detector which allows a much higher sampling frequency than which is used in the current experiment (bandwidth limit 200kHz).
- The amplitude of the shape oscillation is, among other factors, proportional to the droplet size. This will make it more challenging to detect the phase of the oscillation in the scattered light for small droplets. However, it is known that phase sensitive detection techniques as lock-in amplification can extract the phase shift from signals with very small signal to noise ratio. So a priori this may ultimately not be a limiting factor.
Because all these factors become relevant in the low micrometre range, we anticipate that, without major modifications, the method will be restricted to droplet sizes larger than a few micrometres in diameter.
Comment 2:
Second, in Fig. 6 when the surface tension falls as the droplets evaporate, how long are these evaporation experiments?
Reply:
Fig. 6 shows measurements of the surface tension for one water and four sucrose solution droplets evaporating in the EDB. Each of these measurements was recorded over a time span of about 100 to 120s. The residence time of the droplets was mainly determined by the relative humidity (RH) in the EDB. The residence time can be extended or decreased by choosing either a higher or lower RH. We plan to investigate the effect of residence time and with it the possible adsorption of surfactants from the surrounding air on the surface tension once the relative humidity control system is installed.
Comment 3:
Third, would it be possible to use this technique for absorbing aerosol like brown carbon? Does the choice of the HeNe laser mean that the absorbance would be low enough at the laser wavlength to obtain a sufficient signal?
Reply:
The HeNe-laser was mainly chosen for its high-quality laser beam profile rather than its specific emission wavelength as our test liquids, water and sucrose solutions, are very weak absorbers throughout the visible region. Nevertheless, our method of optically detecting the shape oscillations is tolerant to some degree of absorption. We have not yet performed a comprehensive study on absorbing materials; however, based on a quick check using Mie-theory, we have estimated that absorption up to an imaginary refractive index of about k<=10-3 should be okay. This estimate is valid only if the droplet does not become opaque due to photochemical reactions induced by absorption of the laser light. If this is the case there still might be a short time window with enough signal. Also, the intensity of the laser light might be decreased to reduce the speed of degradation.
Combining this with the fact that the absorbance of brown carbon is typically stronger in the UV and shorter wavelength of the visible region, it may very well be possible to study brown carbon aerosol using the HeNe-laser.
Citation: https://doi.org/10.5194/egusphere-2023-1160-AC1
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AC1: 'Reply on CC1', Denis Duft, 23 Jun 2023
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RC1: 'Comment on egusphere-2023-1160', Anonymous Referee #2, 04 Jul 2023
Review of Singh et al. 2023
This paper describes a method for characterizing the surface tension and viscosity of levitated particles in an electrodynamic balance by analysis of the phase offset of the shape oscillations of the particle with respect to an external driver. This method builds off existing “single-shot” methods for characterizing these properties that induce these oscillations via coalescence. The authors provide data for model systems that show reasonable agreement to literature, and provide an extensive supporting information document detailing the method development and analysis procedures. Overall this is a very compelling method to probe important physicochemical properties of particles.
In my responses below I highlight some information that could be provided more clearly, in addition to some other queries and suggestions.
- What is the driver voltage amplitude and how is the appropriate magnitude of this chosen?
- What is the uncertainty in the particle size, and how much of this translates to uncertainty in viscosity and surface tension? Equations 6 and 7 both show dependencies on R^2 or higher, indicating some significant propagation of error. The authors chose to use the phase function approach, which for large particles can yield reasonable accuracy when comparing measured spectra to Mie theory simulations. There are several approaches to sizing using these data, as described in the SI. Thus, it would be convenient to describe how the angular scattering pattern is used in the main text along with the estimated uncertainty.
- I would suspect that when the droplet is driven at a frequency resonant with a mode of oscillation that the amplitude of the oscillation would increase significantly, leading to a higher scattered signal from the droplet. Using a dual-phase lock-in, the amplitude of the scattering and the phase of the signal, both as a function of frequency, could be analyzed as the driver frequency is swept. Has amplitude information been measured and/or analyzed to identify the resonant frequency? This would presumably directly yield omega_0 for an underdamped oscillation, but perhaps not yield sufficient information on the damping constant for viscosity analysis.
- What are the limits of viscosity that can be probed with this method. The viscosity values reported here are all many orders of magnitude lower than what is typically considered to be a viscous particle. Is there a limit on the viscosity that can be measured due to the limited response of a more viscous particle to any kind of shape deformation? Is this connected with the deviation of the measure viscosity in this approach from the literature range (Figure 3 for example)?
- In the same vane, what are the limits of surface tension that can be measured? Would surfactant coated particles be accessible?
- Were measurements performed on particles that spanned a range of charge states? When calculating the charge according to the SI, no gas flow drag factor is reported. How does the gas flow in the chamber affect the force balance? How big is the uncertainty in the charge and how much does this contribute to the calculation of surface tension and viscosity?
- What is the timescale for evaporation in the measurements shown in Figure 6? Does the decrease in surface tension arise from the adsorption of know contaminants from an external source (i.e. are there lubricant oils that might be outgassing, low purity gas cylinders, etc.), or are these present in the particle and become more concentrated at the surface as evaporation occurs?
- How large are the oscillations in the particle shape?
- What size range of particles can be explored using this technique? Being able to access particles that span a wide range of surface-volume ratios would facilitate an exploration of surface partitioning and the influence of surfactant depletion etc.
Citation: https://doi.org/10.5194/egusphere-2023-1160-RC1 - AC2: 'Reply on RC1', Denis Duft, 12 Sep 2023
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RC2: 'Comment on egusphere-2023-1160', Anonymous Referee #1, 18 Jul 2023
Review on Singh et al.: “The viscosity and surface tension of supercooled levitated droplets determined by excitation of shape oscillations”.
The authors develop a new technique for measuring viscosity and surface tension of levitated droplets in an electrodynamic balance (EDB) by superimposing a high frequency, high voltage field across the DC electrodes of the EDB. This field stimulates shape oscillations of the droplet, which can be detected by monitoring light scattering. The phase shift of these oscillations relative to the excitation field - when scanning the excitation field over a sufficient frequency range - allows deducing viscosity and surface tension of the droplet.
The new technique is a very interesting alternative to methods previously used; the paper is well written and supported by adequate figures and is definitely of interest to the readership of AMT.
I am very pleased recommending publication as is.
The only comment I would like to ask the authors to consider is that they explain/estimate in more detail the limitations of the technique in both upper viscosity values and range of surface tension are.
Technical comments:
I was particularly interested in understanding the upper limit for the viscosity. In order to gain a better feeling for the behavior of the phase shift, I put some numbers into eq. (7) to estimate the natural angular frequency, ω0, namely (R=50 µm, σ=70 mN/m, ρ=1000 kg/m3, Q= 0.8 pC) and came up with 47 kHz. Using eq. (6) with a viscosity of 2 mPa s, I calculate a γ of roughly 4000. Putting those numbers into eq. (5), I cannot reproduce something similar to what is shown in Fig. 2. Most likely this is a mistake on my side, but the authors could provide in the SI some numbers on, ω0 and provide a plot where they show the expected phase shift assuming log spaced viscosity data keeping all other parameters constant.
Fig. S4: Please explain what is causing the apparent decrease in droplet charge after 70 s in a bit more detail. What is the size of the particle at this time of evaporation? Is this reaching the stability limit of the EDB or is the DC-feedback loop to keep the droplet in the center of the EDB no longer working?
Connected to the data shown in Fig. S4: How is the flow in the EDB affecting the determination of Q based on the applied DC-field? Does the drag force cause a systematic uncertainty here?
Citation: https://doi.org/10.5194/egusphere-2023-1160-RC2 - AC3: 'Reply on RC2', Denis Duft, 12 Sep 2023
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2023-1160', Alison Bain, 21 Jun 2023
Very nice paper, I enjoyed reading it. I do have a couple questions that you might concider addressing in the manuscript.
First, with regard to the statement of potential for investigating smaller particles, do you have an estimate for the smallest radius that could be investigated with this technique? Would the decrease in scattering intenisty as particles size decreases put a lower limit on the size range that can be investigated? Or is the limit defined by the smallest droplet that can be trapped and sized in the EDB?
Second, in Fig. 6 when the surface tension falls as the droplets evaporate, how long are these evaporation experiments?
Third, would it be possible to use this technique for absorbing aerosol like brown carbon? Does the choice of the HeNe laser mean that the absorbance would be low enough at the laser wavlength to obtain a sufficient signal?
Citation: https://doi.org/10.5194/egusphere-2023-1160-CC1 -
AC1: 'Reply on CC1', Denis Duft, 23 Jun 2023
Dear Alison,
Thank you for your comment and questions! We will consider addressing them in a revised manuscript.
Comment 1:
First, with regard to the statement of potential for investigating smaller particles, do you have an estimate for the smallest radius that could be investigated with this technique? Would the decrease in scattering intenisty as particles size decreases put a lower limit on the size range that can be investigated? Or is the limit defined by the smallest droplet that can be trapped and sized in the EDB?
Reply:
Besides scattering intensity and EDB trapping range there are a couple of additional factors which may limit the size range towards smaller particles in this method. The loss in scattering intensity may be overcome partially by using a more powerful and/or focussed laser. The EDB trapping range is more difficult to assess as it depends on several factors. Our EDB was initially designed to levitate droplets in the D=10-100µm size range. We estimate that limitations will occur for our trap below around 5µm dia. Some other factors are:
- We determine the droplet size by analysing the spatial frequency of fringes in the angular light scattering. This method for size determination becomes much less accurate for droplets below D=2µm.
- The natural frequency of the L=2 shape oscillation is on the order of 1Mhz for D=4µm droplets. Droplets of that size require not only excitation in the MHz range but also a detector which allows a much higher sampling frequency than which is used in the current experiment (bandwidth limit 200kHz).
- The amplitude of the shape oscillation is, among other factors, proportional to the droplet size. This will make it more challenging to detect the phase of the oscillation in the scattered light for small droplets. However, it is known that phase sensitive detection techniques as lock-in amplification can extract the phase shift from signals with very small signal to noise ratio. So a priori this may ultimately not be a limiting factor.
Because all these factors become relevant in the low micrometre range, we anticipate that, without major modifications, the method will be restricted to droplet sizes larger than a few micrometres in diameter.
Comment 2:
Second, in Fig. 6 when the surface tension falls as the droplets evaporate, how long are these evaporation experiments?
Reply:
Fig. 6 shows measurements of the surface tension for one water and four sucrose solution droplets evaporating in the EDB. Each of these measurements was recorded over a time span of about 100 to 120s. The residence time of the droplets was mainly determined by the relative humidity (RH) in the EDB. The residence time can be extended or decreased by choosing either a higher or lower RH. We plan to investigate the effect of residence time and with it the possible adsorption of surfactants from the surrounding air on the surface tension once the relative humidity control system is installed.
Comment 3:
Third, would it be possible to use this technique for absorbing aerosol like brown carbon? Does the choice of the HeNe laser mean that the absorbance would be low enough at the laser wavlength to obtain a sufficient signal?
Reply:
The HeNe-laser was mainly chosen for its high-quality laser beam profile rather than its specific emission wavelength as our test liquids, water and sucrose solutions, are very weak absorbers throughout the visible region. Nevertheless, our method of optically detecting the shape oscillations is tolerant to some degree of absorption. We have not yet performed a comprehensive study on absorbing materials; however, based on a quick check using Mie-theory, we have estimated that absorption up to an imaginary refractive index of about k<=10-3 should be okay. This estimate is valid only if the droplet does not become opaque due to photochemical reactions induced by absorption of the laser light. If this is the case there still might be a short time window with enough signal. Also, the intensity of the laser light might be decreased to reduce the speed of degradation.
Combining this with the fact that the absorbance of brown carbon is typically stronger in the UV and shorter wavelength of the visible region, it may very well be possible to study brown carbon aerosol using the HeNe-laser.
Citation: https://doi.org/10.5194/egusphere-2023-1160-AC1
-
AC1: 'Reply on CC1', Denis Duft, 23 Jun 2023
-
RC1: 'Comment on egusphere-2023-1160', Anonymous Referee #2, 04 Jul 2023
Review of Singh et al. 2023
This paper describes a method for characterizing the surface tension and viscosity of levitated particles in an electrodynamic balance by analysis of the phase offset of the shape oscillations of the particle with respect to an external driver. This method builds off existing “single-shot” methods for characterizing these properties that induce these oscillations via coalescence. The authors provide data for model systems that show reasonable agreement to literature, and provide an extensive supporting information document detailing the method development and analysis procedures. Overall this is a very compelling method to probe important physicochemical properties of particles.
In my responses below I highlight some information that could be provided more clearly, in addition to some other queries and suggestions.
- What is the driver voltage amplitude and how is the appropriate magnitude of this chosen?
- What is the uncertainty in the particle size, and how much of this translates to uncertainty in viscosity and surface tension? Equations 6 and 7 both show dependencies on R^2 or higher, indicating some significant propagation of error. The authors chose to use the phase function approach, which for large particles can yield reasonable accuracy when comparing measured spectra to Mie theory simulations. There are several approaches to sizing using these data, as described in the SI. Thus, it would be convenient to describe how the angular scattering pattern is used in the main text along with the estimated uncertainty.
- I would suspect that when the droplet is driven at a frequency resonant with a mode of oscillation that the amplitude of the oscillation would increase significantly, leading to a higher scattered signal from the droplet. Using a dual-phase lock-in, the amplitude of the scattering and the phase of the signal, both as a function of frequency, could be analyzed as the driver frequency is swept. Has amplitude information been measured and/or analyzed to identify the resonant frequency? This would presumably directly yield omega_0 for an underdamped oscillation, but perhaps not yield sufficient information on the damping constant for viscosity analysis.
- What are the limits of viscosity that can be probed with this method. The viscosity values reported here are all many orders of magnitude lower than what is typically considered to be a viscous particle. Is there a limit on the viscosity that can be measured due to the limited response of a more viscous particle to any kind of shape deformation? Is this connected with the deviation of the measure viscosity in this approach from the literature range (Figure 3 for example)?
- In the same vane, what are the limits of surface tension that can be measured? Would surfactant coated particles be accessible?
- Were measurements performed on particles that spanned a range of charge states? When calculating the charge according to the SI, no gas flow drag factor is reported. How does the gas flow in the chamber affect the force balance? How big is the uncertainty in the charge and how much does this contribute to the calculation of surface tension and viscosity?
- What is the timescale for evaporation in the measurements shown in Figure 6? Does the decrease in surface tension arise from the adsorption of know contaminants from an external source (i.e. are there lubricant oils that might be outgassing, low purity gas cylinders, etc.), or are these present in the particle and become more concentrated at the surface as evaporation occurs?
- How large are the oscillations in the particle shape?
- What size range of particles can be explored using this technique? Being able to access particles that span a wide range of surface-volume ratios would facilitate an exploration of surface partitioning and the influence of surfactant depletion etc.
Citation: https://doi.org/10.5194/egusphere-2023-1160-RC1 - AC2: 'Reply on RC1', Denis Duft, 12 Sep 2023
-
RC2: 'Comment on egusphere-2023-1160', Anonymous Referee #1, 18 Jul 2023
Review on Singh et al.: “The viscosity and surface tension of supercooled levitated droplets determined by excitation of shape oscillations”.
The authors develop a new technique for measuring viscosity and surface tension of levitated droplets in an electrodynamic balance (EDB) by superimposing a high frequency, high voltage field across the DC electrodes of the EDB. This field stimulates shape oscillations of the droplet, which can be detected by monitoring light scattering. The phase shift of these oscillations relative to the excitation field - when scanning the excitation field over a sufficient frequency range - allows deducing viscosity and surface tension of the droplet.
The new technique is a very interesting alternative to methods previously used; the paper is well written and supported by adequate figures and is definitely of interest to the readership of AMT.
I am very pleased recommending publication as is.
The only comment I would like to ask the authors to consider is that they explain/estimate in more detail the limitations of the technique in both upper viscosity values and range of surface tension are.
Technical comments:
I was particularly interested in understanding the upper limit for the viscosity. In order to gain a better feeling for the behavior of the phase shift, I put some numbers into eq. (7) to estimate the natural angular frequency, ω0, namely (R=50 µm, σ=70 mN/m, ρ=1000 kg/m3, Q= 0.8 pC) and came up with 47 kHz. Using eq. (6) with a viscosity of 2 mPa s, I calculate a γ of roughly 4000. Putting those numbers into eq. (5), I cannot reproduce something similar to what is shown in Fig. 2. Most likely this is a mistake on my side, but the authors could provide in the SI some numbers on, ω0 and provide a plot where they show the expected phase shift assuming log spaced viscosity data keeping all other parameters constant.
Fig. S4: Please explain what is causing the apparent decrease in droplet charge after 70 s in a bit more detail. What is the size of the particle at this time of evaporation? Is this reaching the stability limit of the EDB or is the DC-feedback loop to keep the droplet in the center of the EDB no longer working?
Connected to the data shown in Fig. S4: How is the flow in the EDB affecting the determination of Q based on the applied DC-field? Does the drag force cause a systematic uncertainty here?
Citation: https://doi.org/10.5194/egusphere-2023-1160-RC2 - AC3: 'Reply on RC2', Denis Duft, 12 Sep 2023
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Mohit Singh
Stephanie Helen Jones
Alexei Kiselev
Thomas Leisner
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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