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Anti-scaling magnetic slippery surfaces Ali Masoudi, Peyman Irajizad, Nazanin Farokhnia, Varun Kashyap, and Hadi Ghasemi ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 31 May 2017 Downloaded from http://pubs.acs.org on June 6, 2017

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ACS Applied Materials & Interfaces

Anti-scaling magnetic slippery surfaces Ali Masoudi, Peyman Irajizad, Nazanin Farokhnia, Varun Kashyap, and Hadi Ghasemi* Department of Mechanical Engineering, University of Houston, 4726 Calhoun Rd, Houston, Texas, 77204-4006, USA E-mail: [email protected] Keywords: (Magnetic slippery surfaces, scale resistant, salt nucleation, salt adhesion, magnetic gel)

Abstract

Scale formation is a common problem in a wide range of industries such as oil and gas, water desalination and food processing. Conventional solutions for this problem including mechanical removal and chemical dissolution are inefficient, costly, and sometimes environmentally hazardous. Surface modification approaches have shown promises to address this challenge. However, these approaches suffer from intrinsic existence of solid-liquid interfaces leading to high rate of scale nucleation and high adhesion strength of the formed scale. Here, we report a new surface called magnetic slippery surface in two forms of Newtonian fluid (MAGSS) and gel structure (Gel-MAGSS). These surfaces provide a liquid-liquid interface to elevate the energy barrier for scale nucleation and minimize the adhesion strength of the formed scale on the surface. Performance of these new surfaces in both static and dynamic (under fluid flow) configurations is examined. These surfaces show superior anti-scaling properties with an order of 1 ACS Paragon Plus Environment


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magnitude lower scale accretion compared to the solid surfaces and offer longevity and stability under high shear flow conditions. We envision that these surfaces open a new path to address the scale problem in the relevant technologies.

Introduction

Scale formation is a major problem in a broad spectrum of industries such as power generation 1–5

, oil and gas6–10 and desalination (in almost all processes such as multi stage flash11,12, multi

effect distillation13, nano filtration14, membrane distillation15,16, reverse osmosis14,17,18, forward osmosis19,20). Scale formation not only causes under-deposition corrosion21, affects efficiency and cost of operation21,22, but also in some cases could lead to complete shutdown of a plant6,23. Scaling phenomenon is the precipitation and accumulation of undesired solid materials in the aqueous systems (e.g. dissolved salts in water). A variety of chemicals exist naturally in water; among them, CaCO3 and CaSO4 are major scale contributors24. Both of these salts have inverse solubility behavior with increasing temperature and salts precipitate when the solution becomes supersaturated. Two conventional removal techniques to address scale problem in industry are mechanical and chemical approaches25,26 which have their own limitations6. Mechanical scale removal is inefficient and costly6,21, while in chemical approaches, handling waste and contaminating compounds is a big concern. On the other hand, prevention techniques are mostly focused on chemical inhibition, in which scale adhesion to the surface would be weakened by dosing of chemical additives27. Polyelectrolytes and organo-phosphorous compounds are two types of inhibitors extensively used for anti-scaling properties28–40. These inhibitors could prevent scale formation by distorting the crystal lattice to inhibit crystal nucleation and growth and dispersing 2 ACS Paragon Plus Environment

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the tiny grains in water41. Recently a new type of chemical inhibitor, polyamino polyether methylenephosphonate (PAPEMP), is developed for scale control in water desalination systems. This inhibitor is capable of controlling scale at extremely high supersaturations22. It has been shown that efficiency of chemical prevention techniques strongly depend on different parameters such as temperature and concentration of chemical additives.42 In general, employing chemical scale inhibitors would be helpful to some extend for prevention of scale formation, but serious environmental concerns have limited their implementation especially in sensitive applications1. Surface energy of the solid plays a significant role on scale formation and its further adhesion since it gives a direct measure of intermolecular or interfacial attractive forces43–45. So, another possible approach to alleviate scale formation problem is to tune solid surface energy with coatings or surface treatment techniques46–48. Low surface energy coatings such as selfassembled

monolayers

(SAM)49

and

autocatalytic

nickel-phosphorus

and

polytetra-

fluoroethylene (Ni-P-PTFE)50 have been used for scale reduction in heat exchangers. In recent years, development of bio-inspired surfaces with tunable properties has attracted attention in addressing scale formation problem46,51. For example, lubricant impregnation or liquid infusion inspired by Nepenthes Pitcher into a nano/micro textured surface have been used to fabricate a low surface energy surface with promising interfacial properties. These surfaces have shown high performance in anti-frosting52, anti-icing53–55, drag reduction56 and fouling reduction57,58, and scale resistivity performance46. In spite of their promising scale resistivity, lubricant impregnated surfaces should be used with caution because of liquid depletion due to evaporation, cloaking59, wicking of fluid to the porous structure of the formed scale and solubility60. So, the key limitation in implementation of these surfaces is their lack of durability especially under harsh environments, which they would face in most of their applications.

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Here we report a magnetic slippery surface in two forms of a Newtonian liquid (MAGSS)61,62 and a non-Newtonian liquid (Gel-MAGSS) with outstanding scale resistivity, self-healing and stability under high shear flows. In these surfaces, magnetic liquid–liquid interfaces are exploited to achieve these unprecedented characteristics. In these magnetic slippery surfaces, the magnetic field imposes a volumetric force on the ferrofluid film. This volumetric force opposes the differential surface energy forces and does not allow sinking/infusion of a droplet or liquid into the ferrofluid film. That is a liquid-liquid interface (ferrofluid-droplet/liquid) is formed instead of a solid-liquid interface (solid-droplet/liquid). This concept is shown both theoretically and experimentally by P. Irajizad et al.58. This liquid–liquid interface provides a low-energy interface for scale nucleation with Gibbs energy barrier close to the homogenous limit. Although the Newtonian form (MAGSS) is stable under shear flow conditions, some fluid depletion could occur in a long-time performance. This issue is solved by developing Gel-MAGSS, in which the polymer skeleton holds the ferrofluid and prevents wicking of ferrofluid by porous scale structure. The scale formation in both static and dynamic conditions is studied on these new developed surfaces. Experimental Section Materials: Calcium sulfate dihydrate (CaSO . 2H O) was purchased from alpha chemicals. Trichloro (1H,1H,2H,2H-Perfluoro-octyl) silane 97% and calcium sulfate hemihydrate

(CaSO . H O) 97% were purchased from Sigma Aldrich. Oil based ferrofluids APG 2140 and EFH1 were purchased from Ferrotec Inc. The polystyrene-block-poly (ethylene-stat-butadiene)block-poly-styrene (SEBS triblock copolymer, Kraton G-1650) was purchased from Kraton Inc. Development of MAGSS for static experiments: 2 ml of ferrofluid was applied on a 2.5 cm x 2.5 cm ferrite magnetic tape (McMaster Carr) with the thickness of 100 . The averaged 4 ACS Paragon Plus Environment

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magnetic field on the surface of magnetic tape was measured as 45 mT. Copper samples were made of 1/16” thick (Super-Conductive 101 Cu, McMaster Carr) and were prepared by a sand paper grade 400 to create a clean and smooth surface. Silicon samples were cut out of silicon wafers (Nova Electronic Materials). All surfaces were cleaned with DI water, propane and plasma cleaner. Development of Gel-MAGSS for dynamic experiments: For Gel-MAGSS, we mixed copolymer (SEBS triblock copolymer, Kraton G1650) with ferrofluid (Ferrotec EFH1) with two different weight ratios of 1 to 24 and 1 to 9 in a 50 ml glass beaker. Then, the compound was pre-swollen for 18-20 hrs, warmed up in an oven to 120 ℃ and kept for 2 hours. Hot mixture was placed on a hot plate at 110 ℃ and was stirred for 1 hr. The mixture was cooled down to room temperature, before annealing in oven at 50 ℃ for 20 hrs63,64,65. The final gel was cooled down to room temperature. We observed that for high weight ratio of copolymer to ferrofluid, the gel structure completely contained the ferrofluid inside without any thin liquid film on its surface. The formed structure is in elastic form rather than a gel structure, which would eliminate our desired liquid-liquid interface. On the other hand, for low weight ratio, we achieved a proper gel structure with a liquid-liquid interface. Static Experiments: All the substrates were suspended inside a glass beaker, which was filled with salt solution. The glass beaker was cleaned with a plasma cleaner (PDC-001 Harrick Plasma) and coated with trichloro (1H,1H,2H,2H-Perfluoro-octyl) silane inside the vacuum oven (MTI Corporation) to lower the surface energy and to prohibit preferential nucleation on beaker walls and bottom. Dynamic Experiments: To study anti-scaling properties of Gel-MAGSS under shear flow conditions, a hydraulic circuit was assembled, in which flow rate and temperature of fluid could



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be controlled. The test tube of flow was made of 3/4” copper pipe (Super-Conductive 101 Cu, McMaster Carr) in which, inner side has been coated with a thin layer (200 m) of magnetic gel. A flexible neodymium magnetic tape (McMaster Carr) was attached to outer surface of the pipe. The averaged magnetic field on the surface of magnetic tape was measured as 90 mT. The flow rate of saturated solution of calcium sulfate hemihydrate inside the pipe was 22 ml/s. The surface temperature of pipe was kept at 50±2 ℃. Results and Discussion Schematic of scale formation on a solid surface is shown in Figure 1a. Scale nucleation and growth affects geometry of the pipe and consequently pressure drop and flow rate of a fluid. As time goes on, scale may completely block the flow in a tube. In comparison, the surface with anti-scaling coating is shown, in which, nucleation and growth of scale is prevented to keep a constant flow rate in the flow system. The role of liquid-liquid interfaces on prevention of scale formation is shown in Figure 1b. In a saturated solution of calcium sulfate hemihydrate (CaSO4.1/2H2O), scale formation at the surface of Copper, Silicon, Polytetrafluoroethylene (PTFE) (solid-liquid interfaces) is shown after 48 hrs. Scale will completely cover the surfaces and grow as a function of time. In these surfaces, surface roughness and low Gibbs energy barrier accelerate heterogeneous scale nucleation and growth46. In contrast, in MAGSS, smooth and defect free liquid-liquid interface will resist heterogeneous nucleation of scale leading to anti-scale properties. In the classical nucleation theory66–68, nucleation rate at a fixed temperature T is given by ∆ ∗

= (− )

(1)

where is the kinetic constant, ∆ ∗ is the activation energy barrier for nucleation and

!

is

Boltzmann constant. Kinetic constant ( = "#$) depends on number of atomic nucleation sites 6 ACS Paragon Plus Environment

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per unit volume (N), Zeldovich non-equilibrium factor (Z), and rate at which atoms or molecules are added to the critical nucleus (#)67. The Gibbs energy barrier for heterogeneous nucleation is written as ∆ ∗ =

16 ' ()* -( , ) 3 ∆,

(2)

where () denotes the interfacial tension of saturated liquid-salt nucleolus, ∆, the volumetric free energy of phase-change and -( , ) is the geometrical factor, which is governed by the energy of the involved surfaces. The volumetric free energy for homogenous nucleation of calcium sulfate hydrates (∆, ), which is the difference of Gibbs free energy between the supersaturated state and equilibrium state, is written as69 /0 (34 5 )(67 8 ) ∆, = − 12 2 9:

(3)

Where (34 5 ) and (67 8 ) denote ion activity, R is the gas constant, T is the absolute temperature and 9: is thermodynamics solubility of calcium sulfate hydrate. In function ;

-( , ), value of m depends on surface energy of the involved surfaces and value of (= < ) =

depends on the radius of roughness at the surface (R), and the critical nucleolus radius (>? ), which is equal to

@A ∆B

(Supplementary information). As we will discuss later, in MAGSS we

tuned the value of m and x to elevate the value of f close to 1 and approach homogeneous nucleation limit. We examined anti-scaling performance of MAGSS in two experimental configurations: static and dynamic configurations. A schematic of the experimental setup for static experiments is shown in Figure 2a. The samples were suspended in the solution while scale forms on their surface. Scale formation and growth were studied for both calcium sulfate hemihydrate and calcium sulfate dihydrate (CaSO4.2H2O). Initially, we prepared saturated solution of both salts at 7 ACS Paragon Plus Environment


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the ambient temperature. The solubility of hemihydrate salt at ambient temperature is 72 mgl-1, while this value for dihydrate salt is 20 mgl-1. In static experiments, temperature of solutions through a heater (VWR 97042-614) was set to 80±2 ℃. We used both mechanisms of temperature-dependent solubility and evaporation to keep continuous supersaturation state and scale deposition on samples. As the solubility of both salts at 80 ℃ is lower than the ambient temperature, the prepared solutions experience supersaturation state at 80 oC. Furthermore, as time goes on, evaporation of water keeps the liquid in the supersaturation state at 80 oC. This state leads to continuous heterogeneous salt nucleation and growth on surface of the samples. For static experiments, we used Cu (surface energy of ≃ 1.95 8 )70, [100] silicon wafers (surface energy of 2.31 8 )71, Polytetrafluoroethylene (PTFE) (surface energy of

0.017

8 )72, a non-magnetic liquid-infused surface, developed by a membrane with a pore size of 5 and silicon oil (CLEARCO USA, CAS # 63148 62 9) (surface energy of 0.017 8 ), and MAGSS (surface energy of 0.032 8 ). Figure 2b shows the scale formation of calcium sulfate hemihydrate on all the substrates as a function of time. As the solubility of calcium sulfate hemihydrate decreases abruptly with temperature (~0.092 g l-1 K-1)73,74, a large amount of scale was formed on solid substrates even after 24 hours (Figures 2b). Although the same supersaturation condition exist for the MAGSS surface, scale formation on MAGSS is almost completely suppressed. The existence of liquid-liquid interface in MAGSS leads to these promising anti-scaling properties. Note that a small amount of formed scale at the edge of MAGSS sample is caused by an incomplete coating of the sample by the magnetic liquid. We emphasize that all the samples were suspended in the same solution and tested simultaneously. At certain time intervals, samples were removed from the solution, air-dried to evaporate extra liquid on the surface and weighted (Scientech ZSA 210). The accumulated mass of formed scale


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on substrates is shown in Figure 2c. Values are normalized with the scale weight on silicon substrate as the reference sample. As shown, the scale mass on MAGSS is less than 10% of scale mass on Cu and Si substrates, and several times less than PTFE and silicon oil liquid-infused surface for all time intervals. We continued the static scaling experiments with calcium sulfate dehydrate only for Cu and Si as reference substrates. As discussed later, low precipitation rate of this salts does not allow to have a comparative results for other substrates. The temperature dependence of solubility of this salt in the temperature range of 20-80 ℃ is very small73,74. This temperature dependence is shown in Figure 3a and is compared with calcium sulfate hemihydrate. The difference between the solubility at 20 and 80 ℃ is approximately 1 mgl-1, while this value for hemihydrate salt is 62 mgl-1. Thus, the amount of formed scale should be much lower for calcium sulfate dihydrate. The formed scale in the dihydrate solution is shown for all the samples in Figure 3b. A low amount of scale was formed on the samples even after 96 hrs. As shown, formed scale cover surface of Cu and Si samples, but few scale particles are formed on MAGSS. As the accumulated scale on the surface for dihydrate solution is so small, we could not acquire reliable results on the mass of accumulated salts. Thus, we studied microstructure of formed scale on the samples through optical microscope (Nikon Eclipse LV100ND). These microstructures are shown in Figure 4 on different substrates for calcium sulfate dihydrate. As shown, scale forms a needle-like structure on both copper and silicon and covers the entire surface after 96 hours. In contrast, on MAGSS, only slight scale deposition is observed and a small fraction of surface has been covered with very tiny particles (Figure 4). Scanning electron microscopy (SEM) image of the individual needle-like structures is shown in supplementary information, Figure S1.



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Once anti-scaling characteristics of MAGSS were examined in the static configuration, we continued studying these surfaces under flow conditions. In MAGSS, the ferrofluid film is locked on the surface through volumetric magnetic force75. Stability of MAGSS under high shear flow of water and air is shown in our previous work58 (Supplementary videos 9 and 10). However, the induced shear stress in long-time performance can deplete the ferrofluid film and affect longevity of these surfaces. Thus, for dynamic conditions, we developed Gel-MAGSS. The development procedure of the gel structure is shown in Figure 5a and is discussed in the Experimental Section. These gel structures are stable with minimal evaporation rate. The developed gel-form is shown in Figure 5b. These gel structures can be developed in any desired geometries. We left these gels in the laboratory environments for more than several weeks and no change in their properties was detected. Furthermore, we studied mechanism of ferrogel formation as shown in Figure 6. In the gel formation procedure, the middle block of copolymer (Poly Ethylene Butadiene) (PEB) (Figure 6a) dissolves at high temperature in the ferrofluid carrier fluid (light hydrocarbon oil, Ferrotec EFH1). After cooling of the solution, PEB forms a swollen network. On the other side, ferrofluid acts as a precipitant for polystyrene (PS) end blocks, which aggregate to microphase separated micellar cores and form cross-linked points in the PEB network. In the gel structure, ferrofluid is located in the interstitial domain between the cross-linked micellar domains63. A schematic of gel structure is shown in Figure 6b. Furthermore, we cut a cross section of ferrogel and examined it with an optical microscope as shown in Figure 6c. The dark areas are trapped ferrofluid in the bright gel structure. A thin layer of the developed gel (~ 200 ) was cut to be used for dynamic experiments. For

dynamic scaling experiments, we assembled a hydraulic circuit as schematically shown in Figure 7a. As solubility of hemihydrate salt in the solution decreases as a function of


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temperature, we increased surface temperature of the test tube by an attached local heater to provide a supersaturation condition for scale nucleation and growth73. We coated a part of the test tube with MAGSS and the rest of the tube was left as a bare copper surface. As the solution with temperature of 0 (=25 oC) passes the test tube with surface temperature of 50 oC, scale forms on the surface of test tube. We kept the Reynolds number at 2200 in these dynamic experiments (shear stress of 0.034 Pa). After 5 days, we compared the part of test tube covered by Gel-MAGSS and the bare copper part. As shown in Figure 7b, although the copper surface is completely covered by the formed scale, Gel-MAGSS has suppressed scale formation providing a promising anti-scaling surface. In some transient applications, fluid flow rate can fluctuate as a function of time. That is sometimes, there is a steady-state fluid flow in the tube, while in other times, the fluid remains stationary for a long time in the tube. In the Gel-MAGSS structures, the surface provides a combination of liquid-liquid and maybe small fraction of solid-liquid interface leading to some scale formation on the gel structure. However, the formed scale has very low adhesion strength to the gel structure. At high flow rates in dynamic experiments, the shear stress at the surface dominates the adhesion force of scale at the gel structure and does not allow accumulation of any scale on the surface. However, in stationary conditions, scale may form on the Gel-MAGSS surface. To study this stationary condition, we left the Gel-MAGSS structure under saturated salt of calcium sulfate hemihydrate at temperature of 50 oC under stationary conditions for 24 hrs. We found that some scale forms on the Gel-MAGSS surface as shown in Figure 8a. We initialized the flow of fluid on the surface and incrementally increased the flow rate to examine adhesion strength of the formed scale on the Gel-MAGSS. We found that at the shear stress of 23 mPa at the surface, the scale is completely removed from the surface as shown in Figure 8b (Supplementary Movie 1). This value corresponds to adhesion strength of the



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formed scale on gel-MAGSS. This suggests that even if scale forms on the Gel-MAGSS in a long-time performance, an increase of flow rate (enhanced shear stress) will remove the formed scale from the Gel-MAGSS structure. Note that the scale formed on the copper has formed a strong solid-solid bond and will not be removed through tuning the shear force. Only through mechanical scratching or chemical dissolution, we could remove scale from the copper surface. To show the critical role of liquid-liquid interfaces in anti-scaling properties, we examined physics of scale formation on MAGSS. The Gibbs energy barrier for scale formation is given in Equation 2. As mentioned, the energy barrier for heterogeneous nucleation depends on function f (m,x). Note that m equals to cos F, shown in Figure 9a. We developed an approach to find this value for scale nucleation on MAGSS (see supplementary information). As shown in Figure 9b, the value of f function for MAGSS is approximately 0.98 ± 0.02. That means, the liquid-liquid interface on MAGSS boost the energy barrier for heterogeneous scale nucleation approaching to the homogenous limit of salt nucleation. Conclusions We present a new paradigm of anti-scaling surfaces in which liquid-liquid interfaces are exploited to mitigate scaling problem. The liquid-liquid interface is developed through introduction of volumetric magnetic forces, which oppose the interfacial forces and does not allow formation of a solid-liquid interface. The developed surfaces boost the Gibbs energy barrier for salt nucleation and show minimal adhesion strength to the salt particles (23 mPa). The Gibbs energy barrier on these structures is approximately 0.98 ± 0.02 of that of homogenous nucleation limit. These anti-scaling surfaces are developed in two forms, Newtonian fluid and gel structure. Their superior performance with both calcium sulfate hemihydrate and calcium sulfate dihydrate are examined. Although the Newtonian form of these surfaces have exceptional


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anti-scaling properties in static conditions, for dynamic configuration (under shear flow), the gel form of these structures have been developed to achieve longevity and durability. These surfaces promise a new method to tackle the problem of scaling in flow systems in the energy fields, chemical processing plants and water desalination systems.



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a

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b

Copper

Silicon

LI Silicon Oil

PTFE

MAGSS

Figure 1. (a) Schematic of scale deposition at the solid-liquid interface is shown, while this formation at the liquid-liquid interfaces is suppressed. (b) Calcium sulfate hemihydrate scale formation on copper, silicon, PTFE, and liquid-infused silicon oil samples after 48 hours is shown, while liquid-liquid interface of MAGSS suppresses any scale formation. The scale bar is 5 mm.


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b

a

Copper

c Mass gain as a fraction of scale on silicon

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Silicon Copper Silicon PTFE LI Silicon oil MAGSS

PTFE

LI Silicon Oil

MAGSS 24 hours

48 hours

72 hours

Start

24 hours

48 hours

Figure 2. (a) Schematic of the experimental setup to examine scale formation in static conditions. (b) Calcium sulfate hemihydrate scale accumulation on copper, silicon, PTFE, and liquid-infused silicon oil and MAGSS samples after 24 and 48 hours. The scale bar is 6 mm. (c) Normalized mass of accreted scale on the selective substrates at different time intervals.



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a

b

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Copper

Silicon

MAGSS

Start

24 Hours

48 Hours

72 Hours

96 Hours

Figure 3. (a) The solubility of calcium sulfate dihydrate and calcium sulfate hemihydrate as a function of temperature is shown. While solubility of hemihydrate salt strongly depends to temperature, this solubility dependence for dihydrate salt is very small.73 (b) Deposition of calcium sulfate dihydrate on various solid samples at different time intervals are shown. Low dependence of solubility on temperature, results in low rate of scale formation. The scale bar is 6 mm.


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Copper

Silicon

MAGSS

Start

48 Hours

96 Hours

Figure 4. Microscopic structures and surface coverage of calcium sulfate dihydrate scale on Copper, Silicon, and MAGSS samples at different time intervals. The scale bar is 200 μm.

a

b

Magnetic gel

Figure 5. (a) The procedure for development of gel form of magnetic fluid for Gel-MAGSS is shown. (b) The final gel structure at room temperature. This structure can be developed in various geometries. The scale bar is 5 mm.



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a PS end block

b

PEB middle block PS end block

c Cross-linked Aggregated Micelle

Ferrofluid Gel structure

PS core PEB chains

Figure 6. (a) Structure of SEBS copolymer (b) Structure of formed ferrogel, which is composed of a swollen PEB network connecting aggregated micelles of PS. (c) Cross section of ferrogel structure. The dark regions show ferrofluid and the bright regions are the gel structure. The scale bar is 100 µm.


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a

b

Copper

Copper after 120 h

c

Gel-MAGSS

Gel-MAGSS after 120 h

Figure 7. (a) Schematic of the hydraulic circuit for flow experiment is shown. The test tube is at higher temperature (50 ℃) than the fluid (25 ℃) leading to supersaturation condition at the test tube walls. This supersaturation drives the scale formation process. (b) The scale formation on the surface of bare copper is shown after 120 hrs. The formed scale is strongly bonded to the surface and should be removed through mechanical or chemical dissolution approaches. (c) No scale is accreted on Gel-MAGSS after 120 hrs. The Reynolds number in these experiments is 2200. The scale bar is 10 mm.



a

b

Under fluid flow

Stationary fluid

Figure 8. (a) The formed scale of calcium sulfate hemihydrate on Gel-MAGSS after 24 hrs is shown under stationary conditions. (b) Once the fluid flow is initialized, the formed scale film is easily removed from the Gel-MAGSS and leaves a pristine surface. The adhesion strength of the scale on Gel-MAGSS is 23 mPa. The scale bar is 5 mm.

a

b MAGSS

f(m,x)

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m= -1 m= -0.9 m= -0.8 m= -0.7

x Figure 9. (a) Schematic of salt nucleolus on MAGSS is shown. The value of m in Equation 2 corresponds to cos F. Through a discussed approach in supplementary information, we determined the value of m as -0.86. (b) Geometrical function of -( , ) as a function of x for different values of m is shown. The value of -( , ) for MAGSS is approximately 0.986 approaching to homogenous nucleation limit (- = 1).


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ASSOCIATED CONTENT

Supporting Information. The method for determination of Gibbs energy barrier for scale nucleation on liquid-liquid interfaces. (PDF) Supplementary Videos 1. Scale removal under shear flow . (MP4)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Author Contributions H. G. conceived the idea. A. M. and P. I developed the surfaces and conducted the experiments. N. F. conducted the surface characterization experiments. V. K. helped on the dynamic scaling experiments. A. M. and H. G. wrote the manuscript and all the authors commented on the manuscript. H. G. directed the research.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors gratefully acknowledge funding support from the Air Force Office of Scientific Research (AFOSR) for grant FA9550-16-1-0248 with Dr. Ali Sayir as program manager.



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Antiscaling Magnetic Slippery Surfaces - ACS Publications - American

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