Subscriber access provided by LONDON METROPOLITAN UNIV
Article
Dropwise condensation on soft hydrophobic coatings Akshay Phadnis, and Konrad Rykaczewski Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03141 • Publication Date (Web): 28 Sep 2017 Downloaded from http://pubs.acs.org on October 3, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Dropwise condensation on soft hydrophobic coatings Akshay Phadnis1 and Konrad Rykaczewski1* 1. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, Arizona, 85287, USA *corresponding author email:
[email protected] Promoting dropwise condensation (DWC) could improve the efficiency of many industrial systems. Consequently, a lot of effort has been dedicated to finding durable materials that could sustainably promote DWC as well as finding routes to enhance the heat transfer rate during this phase change process. Motivated by previous reports of substrate softening increasing droplet nucleation rate, here we investigated how mechanical properties of a substrate impact relevant droplet-surface interactions and DWC heat transfer rate. Specifically, we experimentally quantified the effect of hydrophobic elastomer’s shear modulus on droplet nucleation density and shedding radius. To quantify the impact of substrate softening on heat transfer through individual droplets, we combined analytical solution of elastomer deformation induced by droplets with finite element modeling of the heat transfer process. By substituting these experimentally and theoretically derived values into DWC heat transfer model, we quantified the compounding effect of the substrate’s mechanical properties on the overall heat transfer rate. Our results show that softening of the substrates below a shear modulus of 500 kPa results in a significant reduction in the condensation heat transfer rate. This trend is primarily driven by additional thermal resistance of the liquid posed by depression of the soft substrate. Keywords: dropwise condensation, soft substrates, elastocapillarity
ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 24
1. INTRODUCTION Promoting dropwise condensation (DWC) could improve the efficiency of many industrial systems1–5 because it is associated with a 5 to 10-fold heat transfer rate increase as compared to the currently predominant filmwise mode.6 Besides of the search for a durable material that could sustainably promote DWC,3,7–15 a lot of attention has been recently dedicated to finding routes to even further enhance the heat transfer rate during this phase change process. A moderate level of enhancement has been demonstrated with use of chemically heterogeneous,16– 24
textured,25–30 and lubricant-impregnated substrates.8,11,12,31 In contrast, DWC heat transfer
enhancement using soft substrates that have mechanical properties in-between the extensively studied “hard solid” and liquid substrates has received limited attention. Encouragingly, Sokuler et al.32 demonstrated that softening of a hydrophobic elastomer surface enhances the initial condensation rate by increasing droplet nucleation density. Such materials can also alter dynamics of droplet impact onto33–40 and movement across surfaces.41–52 Furthermore, Jeong et al.53 and Barlett et al.54 recently demonstrated that inclusion of room temperature liquid metal nano/microdroplets (e.g. EGaIn or EGaInSn) in silicone matrix significantly increases thermal conductivity of the resulting composite (k~1 to 10 Wm-1K-1) without considerably altering its mechanical properties. Since silicones are hydrophobic, reasonable thickness coatings (~5 to 10 µm) made out of such soft composites could be used to promote DWC without introducing a significant parasitic thermal resistance. Motivated by these results, here we investigate how mechanical properties of a substrate impact relevant dropletsurface interactions and the overall DWC heat transfer rate. The overall DWC heat transfer rate is dictated by heat transfer through individual drops
( , ), critical embryo radius ( ), nucleation density ( ), and droplet shedding radius
2 ACS Paragon Plus Environment
Page 3 of 24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
( ).6,55,56 The nucleation density determines the threshold radius ( ) that segregates nanoscale (() and micro-to-macroscale ( ) droplet populations, while the droplet shedding radius determines how often the surface is refreshed for subsequent droplet growth cycle. In more quantitative terms, the total heat transfer per unit area of a condenser surface is given by: " = , +
/ .!
,
(1)
In this model formulation the value of the critical radius does not depend on surface
properties ( = 2# $ %/&'( )Δ# where # $ is the saturation temperature, Δ# is subcooling of
the substrate, % is liquid-vapor surface tension, &'( is the latent heat, and ) is the condensate liquid density). Similarly, softening of the substrate is not likely to affect the functional form of the droplet size distribution. Specifically, and should be well-represented through
classical models,6,55 which reasonably describe droplet populations on both solid and liquid surfaces.31 However, change in mechanical properties of the substrate will affect two of the three
boundary values of these size distributions, namely and . The value of will be altered
because it is defined by the droplet nucleation density ( = 1/,4 ). The value of , in turn, will be altered because of the formation of a solid wetting ridge around the droplet perimeter. The schematic in Figure 1 shows that this deformation occurs because of the combined effect of
the condensate liquid’s surface tension and Laplace pressure inside the drop.49,57–60 The depression of the substrate under the drop will also increase the thermal resistance posed by the liquid as well as the liquid-solid interfacial area, thus altering , .
Accordingly, here we focus on quantifying how mechanical properties of the substrate
change the values of , , and , . Specifically, we measure and of condensate on silicone substrates with elastic modulus altered through varied cross-linking density. To
quantify the impact of mechanical properties on , , we combine analytical solution of 3 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 24
elastomer deformation induced by droplets with finite element based heat transfer model. By substituting these experimentally and theoretically derived values into the DWC model (Equation 1), we quantify the effect of the substrate’s elastic modulus on the overall heat transfer rate.
Figure 1. An axisymmetric schematic illustrating forces imposed by a droplet on a soft substrate and its resulting deformation.
2. METHODS 2.1 Materials To quantify the effect of the shear modulus of the substrate, G, on droplet nucleation density and departure size, we fabricated 350 µm thick PDMS (Sylgard® 184, Dow Corning) slabs with varied base to cross-linker ratios. Specifically, we used base to cross-linker ratios of 10:1, 20:1 and 33:1 by weight which correspond to G=75 kPa, 220 kPa, and 500 kPa, respectively.48 We note that for a moving liquid front such as perimeter of a condensing droplet, the height of the substrate deformation is determined using the shear modulus, rather than Young’s modulus, ., of
the substrate (for isotropic and incompressible material like PDMS with Poisson’s ratio / = 0.5,
2 3 ./2/ + 1 3 ./3.46 The samples were poured into a mold made out of 350 µm thick
4 ACS Paragon Plus Environment
Page 5 of 24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
silicon wafers and cured at 60 °C for 1 hour. All of the resulting silicone substrates were highly hydrophobic with contact angles above 105° and contact angle hysteresis below ~15° (see the supporting information for more information). For a “hard” reference substrate with comparable wetting properties, we used a silicon wafer (G=50 GPa) coated with fluorosilane ((Tridecafluoro1,1,2,2-Tetrahydrooctyl)Trichlorosilane, Gelest Inc.)
2.2 Condensation experiments
In order to measure and , we conducted condensation experiments with horizontal and
vertical sample orientation. The experiments were conducted in a modified environmental chamber (Electro-tech Systems 5518) with air temperature of 22±0.2 °C and 99±1% relative humidity. The condensation process was initiated by decreasing the sample temperature by 5 °C below dew point using a water-cooled Peltier cooler connected to a programmable temperature controller (PTC10 Stanford Research System). The controller receives temperature feedback from the copper-constantan thermocouple (0.003” dia, Omega) attached to the PDMS surface. We imaged condensation on the horizontally oriented samples every 5 seconds using a high magnification optical microscope (Axio Zoom.V16) with an objective lens of 2.3x/0.57 FWD and 10.6 mm focal length (Zeiss PlanNeoFluar Z) that is integrated with the chamber using a custom extension.61 Additionally, we imaged the condensation process on vertically oriented samples with a digital camera (DFK23UP031, ImagingSource) at 15 fps. We analyzed all the resulting images using ImageJ. Specifically, we measured the projected base contact area of
droplets and, if the droplets were not circular, calculated the radius of the equivalent circle, 5 . We then calculated the equivalent radius of the droplet using corresponding static contact
angle, using = 5 /67. We analyzed at least 15 droplets per sample to calculate the
5 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 24
average radius. These values are reported with uncertainty determined using student’s t-test with 99.7% confidence interval. For nucleation density calculation, we used Particle count and Measure functions in ImageJ to measure the number of droplets and area, respectively. Four different measurements were done on each sample. These values are reported with uncertainty corresponding to 95% confidence interval. More details on the experimental setup are available in the Support Information.
2.3 Modeling of heat transfer across individual droplets on soft substrates
In order to simulate how the deformation of the substrate geometry impacts heat transfer, we combined Yu et al.’s58 analytical substrate deformation model with finite element model of heat conduction. As explained earlier, the combined action of Laplace pressure and surface tension deforms the substrate. A two-dimensional quasi-steady model of substrate deformation has been developed using linear momentum balance:
∇9 = 0
with the following boundary conditions: 9:: =
>
