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Separation and Purification Technology

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A self-cleaning piezoelectric PVDF membrane system for filtration of kaolinsuspensionDong Chena,⁎, Carlos Pomalaza-Ráezba Department of Civil and Mechanical Engineering, Purdue University Fort Wayne, 2101 E Coliseum Blvd, Fort Wayne, IN 46805, USAbDepartment of Electrical and Computer Engineering, Purdue University Fort Wayne, 2101 E Coliseum Blvd, Fort Wayne, IN 46805, USA

A R T I C L E I N F O

Keywords:Membrane foulingPiezoelectricVibrationMembrane cleaningPolyvinylidene fluoridePVDF

A B S T R A C T

Exploring innovative membrane material is an important approach to mitigate membrane fouling. This studyinvestigated a self-cleaning polyvinylidene fluoride (PVDF) piezoelectric membrane system which can vibrate atcontrolled frequencies, amplitudes and waveforms to mitigate membrane fouling. Among different PVDF films,the one of the highest content of β-phase PVDF was selected because of the greatest piezoelectric coefficient. Thefilm was pin punched to 0.14 ± 0.02mm holes for filtration purpose. The characteristic peaks of vibrationvelocity and amplitude were identified by measurements of a Scanning Laser-Doppler vibrometer with tiereddriving voltages. The piezoelectric membrane was tested in a dead-end filtration system fed with 0.5 g L−1 kaolinsuspension of 907.7 nm Z-average diameter at a constant filtration pressure of 34.5 kPa. The results indicatevibration velocity is more important than amplitude to choose the vibration frequency in order to optimizemembrane fouling control. The piezoelectric membrane with continued vibration driven by 24 V (peak-to-peak)and sine wave at the frequency of 1601 Hz (the peak of vibration velocity) yielded 87 ± 3% higher permeateflux than control test, compared to 30 ± 3% increase at the frequency of 664 Hz (the peak of vibration am-plitude). However, the antifouling effect was not apparent with intermittent vibration, possibly due to inter-rupted processes of cleaning and fouling prevention. The mechanistic explanation of cleaning suggests lift forcebrought by hydraulic shearing is more important than inertial lift force of vibration.

1. Introduction

Membrane filtration plays an essential role in solid/liquid separa-tion processes including removal of particles, colloids and ionic con-taminants in water, primarily depending on the sieving mechanism ofmembrane pores compared to the size of the contaminants and elec-trostatic interactions [1]. Membrane filtration offers great advantagesover conventional methods mostly because of fast separations and smallfootprint. Among various membrane materials, polyvinylidene fluoride(PVDF) is a popular one, because it has excellent durability, biologicalresistance, and chemical tolerance. It can withstand continuous freechlorine contact to any concentration [2]. Most PVDF membranes be-long to micro- and ultra-filtration [3]. However, PVDF based nanofil-tration [4] and reverse osmosis (RO) membranes [5] have been re-ported. In addition, the advancement of polymer science has enabledmodification of a PVDF membrane to be more hydrophilic by cross-linking, copolymerization, and coating with nonionic polymers, so thatthe membrane is less prone to fouling by organic matters [2,6].

Nevertheless, membrane fouling still remains as a major hurdle to

the advancement of membrane technology. The processes causingmembrane fouling include deposition, adsorption, and surface crystal-lization of limiting salts (for desalination nano filtration and reverseosmosis membranes only) [7,8]. The types of membrane fouling, clas-sified by the locations of foulants relative to the membrane includemembrane pore blocking (standard, intermediate, and complete poreblocking) [9], cake or gel layer formation, and concentration polar-ization. Among these mechanisms, concentration polarization is re-versible fouling, because it disappears once filtration pressure is nulledthanks to diffusion process [10]; the other types of fouling can be re-versible or irreversible mainly depending on the efficiency and extent ofcleaning vs. toughness of fouling (i.e. the affinity among foulants,foulants, and membrane). By definition, any fouling could not be re-covered by cleaning is called irreversible fouling, which finally con-tributes to the necessity of membrane replacement, the single largestoperating cost [11].

Because of the inherent nature of fouling problem to membranefiltration, exploring innovative technologies are necessary to decreasethe energy cost, increase the clean water productivity, and extend

https://doi.org/10.1016/j.seppur.2018.12.082Received 12 October 2018; Accepted 29 December 2018

⁎ Corresponding author.E-mail address: chend@pfw.edu (D. Chen).

Separation and Purification Technology 215 (2019) 612–618

Available online 31 December 20181383-5866/ © 2019 Elsevier B.V. All rights reserved.

T

membrane life. Chemical-free cleaning technologies are attractiveamong various fouling-control methods. In our prior study, an ultra-sonic probe system embedded in a membrane cell significantly reducedfouling caused by particles and natural organic matters [12–14], i.e.cleaning and fouling prevention were carried out simultaneouslywithout interruption of the filtration process. However, the techniquecould be further improved. For example, in previous studies the ultra-sonic source (i.e., ultrasonic transducer or probe) and the membranewere separated from each other, which reduced the available ultrasonicenergy reaching the membrane; and the membrane cell had to becarefully constructed to accommodate the ultrasonic transducer. Inaddition, the limited size of the ultrasonic transducer (diameter was25.4mm) only provided a small cleaning area of the membrane.Therefore, there is a room to further advance this technique by ex-ploring a vibrating piezoelectric membrane for self-cleaning and foulingcontrol.

In this study, piezoelectric membranes were investigated for foulingcontrol, i.e. a membrane material combining both of the filtrationfunction and piezoelectric property. An alternating current (AC) powersthe piezoelectric membrane to vibrate whenever cleaning is required.Two types of piezoelectric membranes have been reported before, i.e.PVDF [15–18] and lead zirconate titanate ceramic membrane [19,20].However, the vibration behaviors and characteristics have not beensystematically studied yet to our best knowledge, especially the vibra-tion frequency, which is a key factor to optimize membrane cleaning.

Moreover, in many of the prior studies [16,19,21] the configurations ofthe electrodes to drive membrane vibration were too bulky and toocomplicated to fit common membrane modules such as spiral woundand hollow fiber. The system in this study can overcome these problemsby using metallic coatings on both sides of the membrane to form anelectric field or capacitor, which can be wrapped into any shape to fitexisting membrane modules and pressure vessels. The main objective ofthis study was to investigate the efficiency of a piezoelectric membraneto control membrane fouling by suspended particles. The more specificobjectives were to, (i) modify and characterize the piezoelectric PVDFmembranes; (ii) examine the piezoelectric vibration spectra of themembrane; and (iii) explore and optimize the efficiency of fouling re-duction by controlled vibrations.

2. Materials and methods

2.1. Membranes and materials

Three types of PVDF membranes and film were examined in thisstudy. The first one was original 0.2-µm FluoroTrans® W PVDF mem-brane of 127-µm thickness from Pall. The second sample was the samemembrane but had been electrically poled by being sandwiched be-tween two copper plates under 15.75 (MVm−1) electric field providedby a high DC voltage supply (PS/FJ15P08.0 Glassman High VoltageInc.) in air at 85 ± 5 °C (see Fig. S1). Beyond this voltage gradient,

Nomenclature

a the acceleration due to vibration (m s−2)D vibration amplitude (m)f vibration frequency (s−1)Fi the inertial force (N)FL lift force (N)FY permeation drag force (N)J permeate flux of the membrane (mL s−1 cm−2)J0 clean water permeate flux of the virgin membrane

(mL s−1 cm−2)P acoustic pressure (Pa)Rm the resistance of the clean membrane (cm−1)

Rf the resistance of membrane foulants (cm−1)Rp particle radius (m)t time (s)TMP transmembrane pressure (Pa)U vibration velocity (m s−1)Z specific acoustic impedance of the medium (Pa sm−1)µ dynamic or absolute viscosity (Pa s)ν velocity of the permeate flux (m s−1)ρ density of water (kgm−3)ρp density of foulant particle (kgm−3)τWall shear stress at the membrane surface and pores (Pa)

caused by velocity gradient (du/dy)

Fig. 1. Diagram of the dead-end piezoelectric membrane filtration system.

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electrical sparks happened and the membranes were damaged. Thethird type was a solid (non-porous) un-metalized piezoelectric PVDFfilm of 52-µm thickness from Measurement Specialties, Inc.

Ultrapure deionized (DI) water (R= 18.2MΩ·cm) was used in thisresearch. 0.5 g L−1 kaolin particles (CAS# 1332-58-7 from EMDMillipore) suspended in DI water was used as the foulant for membranefiltration tests. The suspension was sonicated in an ultrasonic bath for20min before filtration and particle size distribution analysis by aZetasizer (Nano ZS90 from Malvern). The determined Z-average dia-meter of the kaolin particles was 907.7 nm with polydispersity index of0.667 (see Fig. S3). The pH level of the suspensions was 7.8 ± 0.1.

2.2. Characterization of PVDF membranes

The crystalline phases of the PVDF membranes and film were de-termined by a x-ray diffractometer (XRD) (Philips APD3520) with Cu K-alpha radiation to determine the piezoelectric property.

The solid PVDF film was cut into 44.5-mm diameter to fit themembrane cell. Afterwards, it was sputter coated under vacuum with15-nm thickness and 38-mm diameter of gold on each side of the film tomake conductive layers, the edge was intentionally uncoated to providean insulation ring between each side of the film. Then the film was pinpunched homogeneously over the filtration area by a 0.12-mm dia-meter stainless steel needle to make it porous in order to serve as amembrane filter. The resulted membrane pore size was0.14 ± 0.02mm examined by a microscope. Although high-techmethod such as ion beam etching is available to convert solid films intoneat ultra- or micro- filtration membranes, cost is prohibitive (e.g. thequoted expense was over 10,000 US$ to etch 0.2-µm pores with 1 μmapart for an area of 1mm2).

A copper tape adherently connected to the Au coating on each sideof the membrane and extended outside the membrane cell (see Fig. S2)through the notches to connect to an analog function generator(Hewlett Packard 3311A). As a result, an electric field was formed todrive vibration of the membrane (see Fig. 1). The output frequency andvoltage of the function generator was monitored by a digital multi-counter (John Fluke 1910A) and a multi-meter (DMT 7), respectively.The output frequency of the function generator had minor fluctuationsaround± 5Hz. Although there are other alternative configurations toform an electric field such as placing an electric conductor on each sideof the membranes, coating has exceptional advantages like simplicity,flexibility and enabling the membrane to be wrapped into differentshapes to accommodate common membrane modules such as spiralwound, tubular, and hollow fiber ones.

The mechanical vibration spectra of the membranes were recordedby pseudo random scanning of a Polytec MSA-400 Scanning LaserDoppler vibrometer (SLDV). Laser Doppler vibrometry utilizes Dopplershift of a reflected laser beam from a vibrating sample to measure itsreal-time vibration velocity or amplitude [22]. A SLDV is ideal tocharacterize a piezoelectric membrane because of its high resolutionand precision to detect velocity (down to micron s−1) and amplitude (inpicometer) at multiple spots in a great scanning range of frequency.

During the measurement, a PVDF membrane held in the membranecell with an O-ring in place (same as filtration condition) was sitting inair on a vibration isolation concrete slab. The vibration was driven by afunction generator with sine wave of different frequencies and incre-mental driving voltages (i.e. 12.5, 25, 50, and 100 V peak-to-peak),which distinguished piezoelectric vibration from potential backgroundnoises, because greater driving voltages should yield increased velo-city/amplitude of characteristic piezoelectric vibrations. The recordedvibration spectra of velocity and amplitude were the average of 9 dif-ferent spots forming a squared matrix with 1.1 mm apart in the centralarea of the membrane with resolution of 4 Hz.

2.3. The filtration system and tests

Fig. 1 shows the dead-end unstirred membrane filtration system. Allfiltration tests were carried out at 5.0 psi (34.5 kPa) driven by a com-pressed nitrogen gas cylinder and at room temperature 21.0 ± 0.5 °C.A one-gallon stainless steel pressure vessel containing 1.0 L of DI wateror kaolin suspension was connected to a 50-mL dead-end membranecell (Amicon 8050, Millipore) of 44.5 mm diameter. The membranepermeate flux (J) was periodically determined by gravimetric mea-surements during the filtration processes. The measured pure waterpermeate flux (J0) of the clean PVDF membrane was 114.19 gmin−1 at34.5 kPa.

3. Results and discussions

3.1. XRD measurements

Piezoelectric property reflects the responses of mechanical move-ment to electrical input or vise verse. As a result, the crystallinestructure of piezoelectric materials is of great importance. PVDF, one ofthe most popular membrane materials used in micro- and ultra-filtra-tion shows piezoelectric character or has the potential to be poled into apiezoelectric material with piezoelectric coefficient of about 30–40(pC N−1) [21,23–27]. As a result, PVDF provides the feasibility to cleanand prevent membrane fouling via self-vibration.

As shown in Fig. 2, β-phase of PVDF has a peak at 20.86° (2θ) for(1 1 0) (2 0 0) planes, generally consistent with other research results[28,29]. The 0.2 µm microfiltration membrane from Pall has both α(2θ=20.32° corresponding to (1 1 0) plane) and β crystalline phases.After electric poling at 15.75 (MVm−1) and 85 ± 5 °C, there was aminor increase in the intensity of β-phase (from 1157 to 1192 at 20.86°)and a slight decrease in the intensity of α phase (from 1219 to 1201 at20.32°). Although electric poling was conducted in heated silicone oil at85–90 °C instead of air to prevent electric sparks, the improvement inpiezoelectric property was marginal based on XRD examinations (datanot shown).

PVDF has a polar molecular structure. The hydrogen atoms arepositively charged and the fluorine atoms are negatively charged withrespect to the carbon atoms in the polymer. The net moment of a groupof molecules in PVDF film depends on the orientation of individualdipoles. There are five separate crystalline phases based on differentPVDF polymer chain conformations, including frequently studied α, β,and γ phases [29]. In the β-phase of PVDF, the molecules form a planarzigzag conformation with the dipole moments parallel in the unit cell[23,30,31]. Consequently, a given crystal lamella has a net polarizationequal to that of a single repeat unit [23]. Therefore, the β-phase ofPVDF exhibits the strongest piezoelectric response among the five

Degree (2θ)10 15 20 25 30 35

Inte

nsity

0

1000

2000

3000

4000

5000

6000

Solid filmOriginal 0.2 µm membranePoled 0.2 µm membrane

Fig. 2. XRD patterns of different PVDF membranes and film.

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crystalline phases [29]. However, α crystal form has a net dipole mo-ment with a component normal to the molecular axis but the chainspack to form an antipolar unit cell and hence nonpolar lamellae [31]. αcrystalline phase could be given a stable or permanent [30] polarizationby performing an electric-field-induced crystal modification (i.e., po-larization or poling) to a polar form (i.e. β-phase) at 85 °C and under 60(MVm−1) electric field, and thus exhibits piezoelectric characteristic[24]. This conversion was observed in this study, although the extentwas small.

3.2. Spectra of vibrations

SLDV measurements were carried out with the pin-punched PVDFmembrane, which had the greatest content of β-phase PVDF, thus thehighest piezoelectric coefficient [29]. The vibration spectra of the pin-punched PVDF membrane were recorded by a SLDV system. Incre-mental voltages from 12.5, 25, 50, to 100 V (peak-to-peak) were ap-plied to pinpoint characteristic vibrations from potential backgroundnoises. Fig. 3a and b shows the vibration velocity and amplitude withrespect to vibration frequency, respectively, in the frequency rangefrom zero to 4500 Hz.

Table 1 shows the vibration frequencies of the peaks of velocity (V)and amplitude (D) of the tested membrane based on per driving voltageapplied. Here the vibration amplitude refers to the vibrating distancedisplaced from the equilibrium position. The greatest vibration velocityof (2.72 ± 0.14)× 10−6m s−1 V−1 occurred at 1601 Hz, followed by2734 Hz, 3781 Hz and 664 Hz, the four highest peaks of velocity. Incontrast, 664 Hz yielded the greatest vibration amplitude of(4.20 ± 0.56)× 10−10mV−1, while smaller peaks were found at1601 Hz, 2734 Hz and 3781Hz. In other words, the frequency is dif-ferent with respect to the greatest peaks of vibration velocity or am-plitude.

For a sinusoidal motion, the relationship between vibration ampli-tude (D) and velocity (U) can be expressed by the following equation,

=D U f/(2 ) (1)

where D is vibration amplitude, i.e., the vibration distance displacedfrom the equilibrium position; and f is vibration frequency. From Eq.(1), vibration amplitude is proportional to vibration velocity at thesame frequency. However, the relative importance of vibration ampli-tude vs. velocity to membrane cleaning and fouling prevention was tobe explored to optimize the efficiency.

3.3. Membrane filtration tests

The effect of vibration frequency on membrane cleaning and foulingprevention was investigated in this study. The results are illustrated inFig. 4. Four frequencies were tested with respect to the peaks of vi-bration velocity or amplitudes from 0 to 4500 Hz. Overall, the vibratingmembrane at all tested frequencies yielded greater permeate fluxes thanthe control test (i.e. without vibration). Among them, vibration at1601 Hz had the greatest permeate flux, followed by 2734Hz, whichenhancement of the permeate flux, i.e. the percentage of increasedpermeate flux over control test (no vibration) was 81 ± 3% and46 ± 2%, respectively at the end of 30min’s filtration. The normalpermeate flux at 664 Hz (of the maximum vibration amplitude) and3781 Hz was close to each other, i.e., 0.0851 ± 0.0018 and0.0840 ± 0.0010 respectively, slightly above the normal permeate flux(0.0675 ± 0.0018) of the control test at the end of the filtration periodof 30min. The corresponding enhancement was 26 ± 3% and25 ± 2%, respectively.

The model of resistance-in-series was used to quantify the foulantresistance Rf (cm−1) in membrane filtration [32].

=+

J TMPµ R R( )m f (2)

where, J is permeate flux of the membrane (mL s−1 cm−2). TMP meansthe transmembrane pressure (Pa). µ is dynamic or absolute viscosity ofthe permeate (Pa s). Rm is the resistance of the clean membrane (cm−1).In the equation, Rm can be calculated by measuring the clean waterpermeate flux of the virgin membrane (J0), when the foulant resistanceRf is zero.

Table 2 displays the calculated foulant resistance (Rf) and its nor-malized ratio to the clean membrane resistance (Rm). The resultsshowed that vibration reduced membrane fouling and improved thepermeate flux to varied extends. More specifically, the normalizedfouling resistance (Rf/Rm) was 13.82 ± 0.39 without vibration (con-trol test), the least improvement (Rf/Rm around 10.76 - 10.90 ) wasfound at 3781 and 664 Hz, while the greatest improvement occurred at1601 Hz (Rf/Rm=7.17 ± 0.12).

To determine the key parameter leading to membrane cleaning,Fig. 5a and b were plotted with the normalized fouling resistance as afunction of vibration amplitude or velocity under the peak frequency of664, 1601, 2734, and 3781Hz, respectively. Fig. 5a shows that there isnot a direct correlation between fouling resistance and vibration am-plitude. In other words, the greatest vibration amplitude of10.08 ± 1.34 nm at 664 Hz did not produce the most reduction ofmembrane fouling. In contrast, Fig. 5b illustrates a good correlationbetween fouling reduction and vibration velocity, i.e., a greater vibra-tion velocity provided a better cleaning or defouling effect, especiallywhen the vibration velocities were at higher levels, such as57.12 ± 4.08 and 65.28 ± 3.36 µm s−1 at 2734 and 1601 Hz, re-spectively, which reduced normalized membrane fouling ratio (Rf/Rm)to 9.15 ± 0.09 and 7.17 ± 0.12, correspondingly. At low velocitylevels, e.g. 42.00 ± 5.52 and 48.48 ± 3.36 µm s−1 produced at 664and 3781Hz, respectively, the defouling efficiencies were relatively lowand close to each other with Rf/Rm from 10.76 ± 0.25 to10.90 ± 0.15.

In addition to the tests of continuous vibration during the wholefiltration time, intermittent vibration was investigated as well for en-ergy saving purpose. As shown in Fig. 6, normal permeate flux declinedsharply in first 6min followed by a gradual decrease before being sta-bilized after 20min. When vibration at 1601 Hz started at 30min, thenormal permeate flux increased slightly from 0.067 to 0.069 or about3% increase. In agreement, insignificant changes of the permeate fluxwere observed when vibration turned off at 38min and turned on againat 47min. In other words, the enhancement of permeate flux broughtby intermittent vibration was not apparent compared to continuousvibration, possibly because of shorter time and less energy delivered forboth cleaning and fouling prevention (i.e. particles are likely difficult to

Vibration frequency (Hz)

0 1000 2000 3000 4000

Vib

ratio

n ve

loci

ty (m

/s)

0.0000

0.0001

0.0002

0.0003

0.0004

12.5 V25 V50 V100 V

Fig. 3. (a) Vibration velocity of the PVDF membrane measured by a SLDVunder tiered peak-to-peak driving voltages. (b) Vibration amplitude of thePVDF membrane measured by a SLDV under tiered peak-to-peak driving vol-tages.

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deposit on a vibration object), especially when the vibration was rela-tively weak with velocity in the range of µm s−1. In addition, the re-sonant vibration frequency might be shifted for a greatly fouled pie-zoelectric membrane compared to a clean one, which caused thecleaning less effective.

3.4. Cleaning mechanisms of a vibrating membrane

Because the kaolin particle size (Z-average diameter of 907.7 nm)was much smaller than the membrane pores (0.14 ± 0.02mm), themajor fouling mechanisms are standard pore blocking, cake layer for-mation, and concentration polarization for a dead-end filtration system.Standard pore blocking means the membrane is envisioned to consist ofa set of equal cylindrical pores. When the particles are much smallerthan the membrane pore, each particle arriving at the membrane de-posits onto the walls of internal pores, thus leading to a decrease of thepore diameter [9,33].

Control tests were also conducted for a filtration of DI water by aclean piezoelectric PVDF with or without vibration of the membrane.The difference of the clean water permeate flux with or without vi-bration was less than 2%, suggesting the possible changes of themembrane pore structures and viscosity of water are negligible due tovibration. The cleaning effects of vibration should play a dominant rolefor fouling reduction.

In addition, acoustic cavitation can be ruled out in the tested con-ditions. Because the acoustic pressure P can be calculated as,

=P UZ [34] (3)

where, U is vibration velocity; and Z is specific acoustic impedance ofthe medium, which is 413.3 (Pa s m−1) for air at 20 °C [34]. As a result,the maximum acoustic pressure produced by the vibrating membrane isless than 1 Pa, far less than the cavitation threshold in water (in therange of 104 Pa) [35].

To understand the cleaning and fouling prevention mechanisms ofthe self-vibrating membrane, force balance analysis has been con-ducted. A particle deposited on the membrane surface or pores ex-periences a permeation drag force, FY (N) during the dead-end filtra-tion. Assuming laminar flow (low Reynolds number) of the permeateflow, the permeate drag force can be quantified by the Stokes equation[14,36,37],

=F µR6Y p (4)

Vibration frequency (Hz)

0 1000 2000 3000 4000

Vib

ratio

n am

plitu

de (m

)

0

2e-8

4e-8

6e-8

8e-8

12.5 V25 V50 V100 V

Fig. 3. (continued)

Table 1Vibration frequencies of the velocity and amplitude peaks of the tested mem-brane.

Frequency ofvibration peaks(Hz)

Vibration velocity pervoltage (m s−1 V−1)

Vibration amplitude pervoltage (m V−1)

664 (1.75 ± 0.23)× 10−6 (4.20 ± 0.56)× 10−10

1601 (2.72 ± 0.14)× 10−6 (2.70 ± 0.14)× 10−10

2734 (2.38 ± 0.17)× 10−6 (1.39 ± 0.10)× 10−10

3781 (2.02 ± 0.14)× 10−6 (0.85 ± 0.06)× 10−10

Filtration time (min)

0 5 10 15 20 25 30

Nor

mal

per

mea

t flu

x (J

/J0)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Vibration off 664 Hz vibration1601 Hz vibration 2734 Hz vibration 3781 Hz Vibration

Fig. 4. Normalized permeate flux of the PVDF membrane for filtration of0.5 g L−1 kaolin suspension under different vibration frequencies. The filtrationpressure was 34.5 kPa. pH was 7.8 ± 0.1. The driving voltage of vibration was24 V (peak-to-peak).

Table 2Fouling resistance under different vibration frequencies.

Vibration frequency 0 (no vibration) 664 Hz 1601 Hz 2734Hz 3781 Hz

Rf (cm−1) (3.62 ± 0.10)× 109 (2.82 ± 0.06)×109 (1.88 ± 0.03)× 109 (2.40 ± 0.02)×109 (2.86 ± 0.04)× 109

Rf/Rm 13.82 ± 0.39 10.76 ± 0.25 7.17 ± 0.12 9.15 ± 0.09 10.90 ± 0.15

Vibration amplitude (nm)

0 2 4 6 8 10 12

Nor

mal

ized

foul

ing

resi

stan

ce (R

f /R

m)

6

8

10

12

14 no vibration

3781 Hz

2734 Hz

664 Hz

1601 Hz

Fig. 5. (a) Normalized fouling resistance (Rf/Rm) of the PVDF membrane withrespect to vibration amplitude. (b) Normalized fouling resistance (Rf/Rm) of thePVDF membrane with respect to vibration velocity. The membrane was fedwith 0.5 g L−1 kaolin suspension under filtration pressure at 34.5 kPa. pH was7.8 ± 0.1. The driving voltage of vibration was 24 V (peak-to-peak).

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where, μ is the absolute or dynamic fluid viscosity (Pa s); Rp is theparticle radius (m); and ν is the velocity of the permeate flux (m s−1).Neglecting molecule-molecule interactive forces, for example electro-static and hydrophobic interactions, FY makes the particle deposit onthe membrane surface and pores, and thus causes membrane fouling[14].

On the other hand, the likely cleaning mechanisms of a vibratingmembrane include dynamic shearing brought by velocity gradient andinertial force of vibration. When the piezoelectric membrane vibrates, itproduces waves in the surrounding media such as water and air. Thevibration was audible near the membrane unit area during this study.The absorption of vibration waves by water molecules results in waterflowing along the propagation direction of the waves (e.g. acousticstreaming) [38]. As a result, the flowing water brings a velocity gra-dient (du/dy) and thus shearing stress (τWall = μ(du/dy) for in-compressible Newtonian fluid) acting on the particles deposited on thevibrating membrane surface and pores. Therefore, the ability of vibra-tion to remove and to prevent deposition of particles at the membranesurface and pores can be measured by the lift force (FL) (N) [14,36,37],

=FRµ

6.088LWall p1.5 3 0.5

(5)

where, τWall is the shear stress at the membrane surface and pores (Pa);and ρ is the density of water (kgm−3).

In addition to the lift force FL, the inertial force (Fi) (N) of vibrationcontributes to membrane cleaning and fouling prevention as well. Theinertial force of vibration is proportional to the mass of a foulant

particles [39].

F aRi p p3

(6)

where, ρp is the density of a foulant particle (kg m−3); and a is theacceleration due to vibration (m s−2). For sine wave, the acceleration acan be written as,

=a f D ft4 sin(2 )2 2 (7)

where, t is time (s). The equation of Fi shows the inertial force increaseswith vibration frequency, vibration amplitude D, and foulant particle’sdensity and size.

Overall, the vibrating membrane causes lift force due to shearingalong with an inertial force acting on the membrane surface and pores,which contribute to the major cleaning mechanisms. When the com-bination of these two forces is greater than the permeation drag forceFY, the foulant particle can be dislodged from the membrane surfaceand pores [40]. Consequently, the membrane is cleaned. However, thefiltration results that a better cleaning efficiency occurred at a greatervibration velocity suggest that the lift force FL brought by shearingplayed a more important role than the inertial force Fi of vibration.Therefore, the frequency of the greatest vibration velocity should beadopted for membrane fouling control. This observation is also inagreement with the aspect of energy transfer, because the maximumenergy of a vibrating membrane delivers to the membrane cell is ½mU2

at the equilibrium position, where the vibration amplitude is zero.Obviously the greater the velocity, the more energy is delivered to theadjacent water and foulants on the membrane, and thus a bettercleaning effect was observed.

4. Conclusions

Piezoelectric membranes were systematically investigated in theaspects of crystalline phases, vibration spectra, filtration performance,fouling control and cleaning mechanisms in this study. The PVDFsample of the greatest content of β-phase PVDF was chosen to maximizevibration for membrane fouling control. Because the membrane poresize is much bigger than kaolin particles, the main fouling mechanismsinclude standard pore blocking, cake layer formation, and concentra-tion polarization. The spectra of piezoelectric vibration velocity andamplitude were recorded by a SLDV system with tiered driving vol-tages. The results of filtration tests show that vibration velocity is moreimportant than vibration amplitude to choose the vibration frequency,in order to optimize the cleaning and fouling prevention effect of theself-vibrating membrane. Compared the cleaning mechanisms broughtby lift force of hydraulic sharing and inertial force of vibration, theformer one is more important. It is in agreement with the greatest dy-namic energy transferred to surrounding water and foulants at the peakof vibration velocity.

Acknowledgements

This research project is supported by funding from the NationalScience Foundation CBET program, United States (Award # 1548016).The authors gratefully acknowledge the support from the Office ofSponsored Programs at Purdue University Fort Wayne (PFW), UnitedStates. XRD measurements and sputter coating were carried out in theArgast Family Imaging and Analysis Labs at PFW. Devin Kalafut,Maurice Ralston, Peter Wirges, Gabrielle Carlston, Bryan Daugherty,Wyatt Decker, Prakshesh Patel, and Darnell Parris are recognized fortheir assistance with the project.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.seppur.2018.12.082.

Filtration time (min)0 10 20 30 40 50 60

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0.40

Vibration off Vibration on

Fig. 6. Normalized permeate flux of the PVDF membrane for filtration of0.5 g L−1 kaolin suspension under vibration frequency of 1601 ± 2Hz. Thefiltration pressure was 34.5 kPa. pH was 7.8 ± 0.1. The driving voltage ofvibration was 24 V (peak-to-peak).

Vibration velocity (µm/s)

06040

Nor

mal

ized

foul

ing

resi

stan

ce (R

f /R

m)

6

8

10

12

14

664 Hz 3781 Hz

2734 Hz

1601 Hz

no vibration

Fig. 5. (continued)

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617

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