# Environmental dust repelling from hydrophobic and hydrophilic surfaces under vibrational excitation

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Sep 1, 2020

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.

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

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