Environmental dust repelling from hydrophobic and hydrophilic surfaces under vibrational excitation


Environmental dust mitigation from hydrophobic and hydrophilic surfaces under vibrational motion is investigated for the various tilt angle of the sample surfaces. A high speed recording system is used to assess dust particles’ behavior under the vibrational sonic excitations. The dust particles are examined incorporating scanning and optical microscopes, energy dispersive spectroscopy, and X-ray diffraction. The adhesion of the dust particles on hydrophilic and hydrophobic surfaces is evaluated using an atomic force microscope.

Figure 2a,b show SEM images of the dust while Fig. 2c provides the size distribution of the dust particles. The size and shape of dust alter considerably, and the average dust size is about 1.2 µm. The composition of dust changes slightly as the dust size changes (Table 1), i.e. dust size less than 1.2 µm has more oxygen content. X-ray diffraction of dust particles is depicted in Fig. 2d. The formation of NaCl and KCl compounds can be observed from an X-ray diffractogram. Since the elemental composition of these compounds does not satisfy the stoichiometric ratio, non- stoichiometric compounds of NaxCly and KmCln are formed in the dust particle. The non- stoichiometric ratio of elements in the compounds creates charges on the dust particles. Hence, small particles form cluster-like structures that are attached to the large dust particle surfaces (Fig. 3b). The surface free energy of the dust particles plays an important role in dust adhesion at the glass sample surfaces. To evaluate surface free energy of dust, the droplet contact angle technique is used in accordance with early study21. Three different liquids, namely water, glycerol, and ethylene glycol, are used to measure the contact angle of the droplet on the dust surface. Two methods are adopted to measure the contact angle of the liquids on dust. The Washburn technique22 is adopted firstly to measure the contact angle of fluids. In the second approach, small pellets are formed from the dust particles via brisk pressing and, later, the droplets are formed on the pellet surface. The contact angle measurements are carried out within ten seconds of the droplet formation to avoid the influence of droplet fluid diffusion into the pellet. Moreover, to evaluate the contact angle using the Washburn method, the dust particles are introduced into a glass tube with a 3 mm diameter, and the liquid bath is located under the tube. This arrangement allows the dust particles to draw-up the liquids under the capillary influence. The liquid mass increased per unit time in the tube is associated with the mass gain, which is formulated by Washburn as: (frac{{left( {Delta m} right)^{2} }}{Delta t} = frac{{C cdot rho^{2} gamma costheta }}{mu }), here Δm represents the mass gain, Δt represents the duration for the mass gain (flow time), C is the capillary constant of dust, ρ is the fluid density, θ is the contact angle, µ is the fluid viscosity. To estimate the capillary constant (C), n-hexane is used in the fluid bath. This is because n-hexane results in zero contact angle (θ= 0). Several tests are carried out to ensure the repeatability of the experiments and data. Hence, the capillary constant for dust is estimated to be between 5.82 × 10–16 and 6.54 × 10–16 m−5. The discrepancy in the capillary constant can be related to the dust particles’ shape and sizes, which can differ for each test. However, similar discrepancies are also reported in the literature when assessing the contact angle of powders23. The water droplet contact angle measured on the dust pellet is about is 38.2° ± 3° while it is estimated as 37.4° ± 3° from the Washburn method. Hence, both methods result in almost similar contact angle data. The surface free energy of dust can be obtained from the contact angle relations, i.e. (gamma_{L} left( {cos theta + 1} right) = 2sqrt {gamma_{S}^{L} .gamma_{L}^{L} } + 2sqrt {gamma_{S}^{ + } .gamma_{L}^{ – } } + 2sqrt {gamma_{S}^{ – } .gamma_{L}^{ + } })21,24,25, here, subscripts S and L corresponds to the solid and the liquid segments, respectively, γS is the free energy of the solid surface, γSL is the interfacial solid–liquid free energy, γL is the surface tension of droplet liquid, θ is the measured contact angle, γ+ and—γare the electron acceptor and electron donor parameters of the acid–base component of the solid and liquid surface free energy, respectively. Table 2 gives the Lifshitz-van der Walls components and electron-donor parameters adopted in the calculations21,24,25. The surface free energy of the dust estimated from the contact angle method is about 111.5 ± 7.5 mJ/m2. To ensure the correct measurements, the tests were conducted eight times and the estimated error based on the repeatability of the data is about 7%. On the other hand, the dust adhesion on sample surfaces becomes important for vibrational repelling. Some model studies have been introduced for adhesion of particles on surfaces26,27,28,29. Because of the roughness of the dust particles and the sod surface, the equation introduced by Rabinovich et al.29 is adopted to estimate the dust adhesion on the sample surfaces. Hence, the adhesion force between the particle and the surface can be expressed as (F_{Ad} = frac{{AR_{pd} }}{{12Z_{0}^{2} }}left( {frac{1}{{1 + frac{{R_{pd} }}{{1.48r_{s} }}}} + frac{1}{{left( {1 + frac{{1.48r_{s} }}{{Z_{0} }}} right)^{2} }}} right)), here A corresponds to the Hamaker cstant (A = 0.48 × 10–20 J for SiO230) and Zo represents the particle spacing, which can be considered as the separation spacing between the dust particle and the sample surface, Rpd is the particle size, and rs corresponds to the dust particle roughness parameter, which represents the ratio of the area of pillars on the dust surface over the projected area of dust surface. The roughness of the plain glass (hydrophilic) surface is about 1.2 nm (as obtained from AFM line scan, Fig. 3a) while that of the hydrophobized glass surface is about 156 nm (as determined from AFM line scan, Fig. 3b). The roughness parameter of the dust surface is determined from SEM images, which is within the range of 0.57—0.62. It is worth mentioning that several SEM images are produced to assess the roughness parameter, i.e. the variation in roughness parameter is because of the randomness in the texture of the dust particles as the dust particle size changes. Using the formula of Rabinovich et al.29, the adhesion force is estimated to be 4.4 × 10–11 N for 11 µm size dust particle after adopting the Hamaker constant A = 0.48 × 10–20 J, which is for silica30. Moreover, the adhesion force is also measured using the atomic force microscopy (AFM) probe in the contact mode. The AFM probe (tip) deflection is associated with the adhesion force in the form of ( F_{add} = ksigma Delta V)31, where k corresponds to the spring constant of the tip (N/m) σ is the slope, which is estimated through the ratio of the tip displacement (Δz) over the probe voltage (ΔV), i.e. Δz/ΔV in m/V) during the tip scanning on the surface where the dust particle is located. From the AFM probe calibration, the slope related to the tip deflection remains constant, which is  = 5.80275 × 10–13 N/mV. This gives rise to the adhesion force of 4.211 × 10–11 N for 11 µm size dust particles as located on the plain glass surface. The AFM measurement of the adhesion force for about 11 µm size dust on the glass surface is almost similar to that obtained from Rabinovich et al.29 equation (4.4 × 10–11 N). The adhesion force measurements are extended to include the dust particle located on the hydrophobic glass surface. The findings revealed that the adhesion force for the same size dust particle reduces to 2.234 × 10–11 N on the hydrophobic glass surface. Hence, the adhesion force for the dust particle on the hydrophobic surface reduces significantly. However, the adhesion force measurements are carried out for small size dust particles (~ 1.2 µm) while locating the small size dust particle on hydrophobic and hydrophilic sample surfaces. The force of adhesion obtained from the AFM probe for the hydrophilic surface is about 2.612 × 10–10 N and it becomes 6.321 × 10–11 N for the hydrophobic sample. Also, as the dust particles become small, the force of adhesion becomes high, i.e. as the dust particle size reduces from 11 to 1.2 µm, the force of adhesion increases almost three folds for the hydrophobic surface while this increase becomes almost six folds for the hydrophilic sample. The reduction in the force of adhesion on the hydrophobic surface is related to: i) reduced interfacial force (van der Waal forces) between the dust particle and hydrophobic surface because of the low surface free energy of the hydrophobized surface, and ii) increased surface roughness of the hydrophobized surface (156 nm as compared to 1.2 nm for plain glass surface), which reduces the contact area between the dust particle and the hydrophobized surface. Hence, the dust adhesion force on the hydrophobized glass surface becomes smaller than that of the hydrophilic glass surface. Moreover, the possible explanation for strong adhesion of the small dust particle (~ 1.2 µm) on hydrophobic and hydrophilic surfaces is associated with: i) forming of non-stoichiometric compounds (NaxCly and KmCln, where x ≠ y and m ≠ n, Table 1) on small size dust particles, which results in ionic forces while increasing interfacial force between the small dust particle and the glass surface, and ii) as dust particle reduces (≤ 1.2 µm), in general, dust surface becomes smoother than the large size particles while increasing adhesion force between the particle as the glass surface because of the increased contact area. This finding is also consistent with the results of the early work8.

Figure 2

SEM micrograph of dust particles and dust particle distribution: (a) SEM micrograph of various sizes of dust, (b) SEM micrograph of various sizes dust, (c) size distribution of dust particles, and (d) X-ray diffractogram of dust.

Table 1 Elemental composition of dust particles (wt%).
Figure 3
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AFM images of plain and coated glass surfaces: (a) plain surface and (b) functionalized nano-silica particles deposited surface.

Table 2 Lifshitz-van der Walls components and electron-donor parameters used in the simulation21,24,25.

The vibrational sonic excitation of the plate results in plate oscillation, which causes the acceleration of the dust particles on the plate surface. The force balance for a dust particle on the vibrationally excited inclined plate surface along the surface line (τ-axis) yields the acceleration of a particle, i.e.:

$$ frac{{d^{2} h_{tau } }}{{dt^{2} }} = gsin delta – mu_{f} gcos delta – frac{3pi mu D}{m}frac{{dh_{tau } }}{dt} $$

(2)

Similarly, a particle acceleration normal to the surface (n-axis) becomes:

$$ frac{{d^{2} h_{n} }}{{dt^{2} }} = gsin delta – frac{{C_{D} rho left( {frac{{dh_{tau } }}{dt}} right)^{2} A}}{2m} – F_{ad} – mu_{f} gcos delta . $$

(3)

where m is the dust particle mass, (h_{tau }) and (h_{n}) are the dust particle relling height (displacement) along τ and n-axes, respectively ((h = sqrt {h_{tau }^{2} + h_{n}^{2} }), h is the particle displacement from the plate surface), t is time, g is gravity, CD is drag coefficient, Fad is the adhesion force, (mu_{f}) is friction factor, (delta) is inclination angle of the plate. The formulation of Eqs. (2) and (3) are given in Appendix 1. Equations (2) and (3) are solved numerically to obtain the dust particle displacement on the plate surface.

Similarly, the particle velocity along the surface (τ-axis) is:

$$ v_{tau } left( t right) = frac{{mgsindelta – mu_{f} mgcosdelta }}{3pi mu D} – C_{1} me^{{ – frac{3pi mu D}{m}t}} $$

(4)

The particle velocity along the surface (n-axis) is:

$$ v_{n} left( t right) = frac{{ – mgcosdelta – F_{ad} }}{3pi mu D} – C_{3} me^{{ – frac{3pi mu D}{m}t}} $$

(5)

where

$$ C_{1} = frac{{left( {gsin delta – mu_{f} gcos delta } right)m}}{3pi mu D} – v_{1} ;quad C_{2} = frac{{C_{1} m}}{3pi mu D};quad C_{3} = frac{{left( { – gcos delta – frac{{F_{ad} }}{m}} right)m}}{3pi mu D} – v_{2} quad {text{and}}quad C_{4} = frac{{C_{3} m}}{3pi mu D} $$

here vτ(t) and vn(t) are the particle velocities along τ and n-axes ((v_{p} = sqrt {v_{tau }^{2} + v_{n}^{2} }), vp is the particle displacement from the plate surface), respectively, t is the time, and Fad is the adhesion force of the particle on the surface. It is worthy to mention that the initial acceleration of the dust particles is evaluated from the vibration of the plate and formulation is provided in the Appendix. Figure 4a,b show temporal behavior of displacement and velocity of the dust particles obtained from the experiment and predicted from the analytical solution for 1.732 mm clustered dust particles and various inclination angles of the plate. It should be noted that τ and n-axes are laid in normal to the plate surface and the data obtained from the simulations and experiments are obtained according to the axes. Hence, the τ, n-axes simulation results are presented in Fig. 4a,b. In addition, the dust particles repelled from the surface form clustered-like structures because of the adhesion of the dust particles (among them, Fig. 4a). Since the glass sample is fixed on the oscillating plate subjected to the vibrational sonic excitation, the height of the clustered dust particles repelled from the plate surface is measured relative to the plate surface for all periods of plate oscillation. The displacement of the clustered dust particles along the τ-axis remains almost zero at the inclination angle of the plate is zero (δ= 0°) and small increase obtained from the experiment is associated with the experimental errors. As the inclination angle increases, the clustered dust particles displace along the τ-axis and the displacement enhances as the plate inclination angle increases further. Hence, the gravitational influence and vibrational sonic excitation of the clustered particles along with n and τ-axes enhance the dust displacement with an increasing inclination angle. It should be noted that the clustered particles repelled from the inclined surface under the vibrational sonic excitation follow a trajectory, which composes of τ and n-axes compounds. In the case of n-axis displacement of the clustered dust particles, the particle follows the oscillation of the plate under the vibrational sonic excitation. As time progresses, particle displacement along n-axis location enhances. The analytical findings are in good agreement with those obtained from the experiments. The displacement of the dust particles, which are shown in Fig. 4a, is obtained reference to the position of the glass sample surface. In this case, the plate undergoes an oscillatory motion due to vibrational sonic excitation with a frequency of the excitation of 30 Hz. It is worth noting that several tests are carried out at different frequencies and amplitudes of the vibrational excitations in order to find the optimum parameters for maximum dust removal rate, which bases on the total area cleaned from the dust on hydrophobic surface (Fig. 5). The sonic frequency of 30 Hz at 5 mm plate displacement amplitude is found to be favorable. This corresponds to peak plate velocity and acceleration of 0.0.9 m/s and 185.3 m/s2 respectively. At low frequencies (i.e. 0–20 Hz) dust removal was difficult due to low excitation energy and very short dust particle lifting height. While at high frequencies, (i.e. 40–50 Hz), the dust particles are repelled at a very high rate that could affect the integrity of the glass sample and other accessories. Hence, the experiments are carried out at this frequency. Figure 6a,b show the plate displacement and the plate velocity with time. The frequency of the plate remains the same as the vibrational excitation frequency (30 Hz, Fig. 4a). The maximum amplitude (displacement) of the plate increases in the early period (t ≤ 0.042 s), which is related to the initial response of the plate to the vibrational excitation. However, as time progresses, the maximum amplitude of the plate oscillation becomes the same. Since both ends of the glass sample are fixed on the oscillating plate, the mode of oscillation of the glass sample remains the same as that of the plate. In the case of the clustered dust velocity (Fig. 4b), predictions agree well with the experimental data. In addition, the clustered dust particles almost follow the frequency of the plate. Hence, it reaches the maximum almost in the middle of the repelling height and reduces to zero as the clustered dust attains the maximum height. During the fall of repelled clustered dust particles, velocity becomes negative showing the falling clustered dust particles towards the sample surface. The velocity of the repelling dust increases slightly with the tilt angle of the plate. As the plate oscillation increases, the peak velocity of the clustered dust also increases. This behavior may be attributed to the reorientation of the clustered dust particles upon falling on the sample surface before excited by the vibrational motion of the plate, i.e. reorientation of the dust particles alters the adhesion of the clustered dust on the sample surface. Figure 7a,b show the dust particles displacement along τ, and n-axis for hydrophobic and hydrophilic surfaces at different inclination angles of the sample surface. The data presented in Fig. 7a,b are obtained from the high speed camera. The clustered dust displacement along τ-axis remains considerably small; however, the hydrophobic surface demonstrates large displacement along the n-axis from the surface. As the inclination angle of the surface increases, the clustered dust particles displacements in both τ and n-axes increase due to gravitational effect. The hydrophobic surface demonstrates a larger displacement of the clustered dust particles for all inclination angles as compared to that of the hydrophilic surface. This is mainly because of the pinning of the clustered dust particles, due to higher adhesion force, on the hydrophilic surface. As previously discussed by Quan et al.8, dust adhesion force on the hydrophobic surface is low because of lower surface energy associated with the highly rough (textured) surface. As the repelled dust falls back onto the sample surface, during the excitation period, the clustered dust adheres at the sample surface while reducing dust displacement on the sample surface under the vibrational excitation. In the case of the clustered dust particles velocity on the hydrophobic and hydrophilic surfaces (Fig. 7b), the clustered dust particles reach higher repelling velocity for the hydrophobic surface than the hydrophilic surface. The maximum repelling velocity for the hydrophobic surface becomes almost two-fold of the hydrophobic surface. The clustered dust behavior on the hydrophobic surface differs significantly in terms of repelling; hence, the use of the hydrophobic surface provides high velocity repelling of the clustered dust particles from the sample surfaces.

Figure 4
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(a) Clustered dust particles displacement obtained from experiment and analytical solution along τ, and n axes on glass surface for different inclination angle of glass samples. (b) Clustered dust particles velocity obtained from experiment and analytical solution along τ, and n axes on glass surface at different inclination angle of glass samples.

Figure 5
figure5

Variation of dust removed from hydrophobic surface with for 35°inclination angle of surface: (a) frequency and (b) amplitude of vibrating plate.

Figure 6
figure6

Plate displacement and velocity: (a) plate normal displacement under vibrational sonic excitation, and (b) plate normal velocity during excitation.

Figure 7
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(a) Clustered dust particles displacement with time obtained from experiment along τ, and n axes on glass surface for hydrophilic and hydrophobic surfaces at different inclination angle of glass samples. (b) Clustered dust particles velocity with time obtained from experiment along τ, and n axes on glass surface for hydrophilic and hydrophobic surfaces at different inclination angle of glass samples.

Figure 8a,b show side views of the location of the clustered dust particles obtained from high speed recorded data for different inclination angles of the hydrophilic and hydrophobic glass samples at different times. The clustered dust particles reach the maximum height, which is normal to the sample surface, at about 0.09 s, which corresponds to 2.52 duration of the vibrational excitation. Since the frequency of vibrational excitation is 30 Hz, the corresponding cycle period is 0.0333 s. However, some clustered dust particles remain on the surface due to the high adhesion on the sample surface. In addition, some clustered dust particles, which are repelled from the surface falls back onto the sample surface during the vibrational excitation, which is particularly apparent for horizontally located glass sample (δ = 0). Hence, the external force generated on the dust particle by the plate motion due to vibrational excitation is not sufficient to overcome the adhesion of some clustered dust particles on the sample surface. Some of the dust particles, which may have fewer compounds with non-stoichiometric elemental composition, have weak adhesion on the glass sample surfaces. These dust particles can repel from the sample surface under the vibrational excitation of the plate. As the inclination angle increases, the clustered dust repelled from the sample surface increases; therefore, the dust particles pinning under the gravitational influence reduces by the value equal to the sign of the angle of the inclined plate. As comparing the dust clusters repelling from the hydrophobic and hydrophilic surfaces, the displacement height of the repelled dust clusters remains larger for the hydrophobic surface as compared to the hydrophilic surface. In addition, the number of dust particles remains on the sample surface during repelling becomes considerably less for the hydrophobic surface than that of the hydrophilic surface. This is mainly associated with the dust adhesion on the sample surface, which is almost three-fold higher for the hydrophilic surface than the hydrophobic surface. In order to assess the amount of dust residues on the glass samples surface, high speed optic camera is used to take the images of the dusty sample surfaces during vibrational excitation. Figure 9a,b show time frames of the high speed optical images of the top view of the sample surfaces with the presence of dust particles at different plate angles for hydrophilic and hydrophobic cases, respectively. The dust residues on the horizontally located sample surface are considerably larger than those of the inclined surfaces, which is true for hydrophilic and hydrophobic surfaces. However, the amount of dust residues on the surface remains considerably low for the hydrophobic surface, which is more apparent for the large inclination angle of the samples. The approximate weight of the clustered dust particles with a size of 200 µm is about 1.15 × 10–7 N and the repelling force of the same size of the clustered dust is about 1.44 × 10–7 N. Since the repelling force remains larger than the gravitational force for the clustered dust removal from the sample surface, the pinning force of the clustered dust, because of adhesion, becomes critically important for the dust residues, which are not repelled from the sample surfaces. Hence, as the pinning force, due to adhesion of the clustered dust on the sample surface, becomes larger than the repelling force than the dust remains on the sample surface. The influence of the clustered dust pinning can be observed via comparing the amount of the dust residues on the inclined surface of hydrophilic and hydrophobic samples. This situation can be observed from Fig. 9a,b, in which the top views of the hydrophilic and hydrophobic sample surfaces are shown. In addition, few of small dust particles remain on the sample surfaces after the excitations. Figure 10 shows SEM micrograph of small size dust residues on the hydrophobized glass surface. The dust resides have sharp edges/corners, which can anchor on the coated surface and can create a clustering effect while preventing dust repelling from the surface under the vibrational excitation. The percentage of the area where dust is removed via repelling from the sample surface is also determined. Figure 11a,b show the temporal behavior of the area percentage at different inclination angles of the sample for hydrophilic and hydrophobic sample surfaces, respectively. The area percentage represents the ratio of the surface area of the dust particles repelled (removed) over the total sample surface area. In general, the increase of the area percentage of dust removed from the sample surface follows almost linear behavior with time. The slope of the area percentage of dust removal from the surface increases as the inclination angle of the surface increases, which becomes more apparent for the hydrophobic sample surface. The area percentage of dust removed from the hydrophobic surface reaches almost 80% after 0.36 s of vibrational excitation. However, in the case of the hydrophilic surface, the percentage of dust removal from the sample surface remains significantly low, which becomes less than 20% after 0.36 s of the vibrational excitation for all inclination angles. Consequently, adhesion of dust particles first forms clustered-like structures on the surface and the repelling those clustered-like structures from the surface remains extremely difficult due to the adhesion of those structures onto the sample surfaces.

Figure 8
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(a) Clustered dust particles repelled from hydrophilic glass surface at different inclination angle of the surface and times. Line shows sample surface. (b) Clustered dust particles repelled from hydrophobic glass surface at different inclination angle of the surface and times. Line shows sample surface.

Figure 9
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(a) Optical images of clustered dust particles on hydrophilic glass surface at different inclination angle of the surface and times. Line shows sample surface. (b) Optical images of clustered dust particles on hydrophobic glass surface at different inclination angle of the surface and times. Line shows sample surface.

Figure 10
figure10

SEM micrograph of dust residues on hydrophobic glass surface after vibrational excitations.

Figure 11
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Percentage of dust removed from surfaces at various inclination angles of samples: (a) hydrophobic surface, and (b) hydrophilic surface.



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