Mathematical Models for the van der Waals Force and Capillary Force between a Rough Particle and Surface

The capability of predicting the adhesion forces between a rough particle and surface including the van der Waals force and capillary force is important for modeling various processes involving particle surface retention and resuspension. On the basis of the fractal theory describing the behavior of multiple roughness scales and the Gaussian roughness distribution, a set of mathematical models for the van der Waals force and capillary force is proposed. The proposed models provide the adhesion force predictions in good agreement with the existing experimental data and converge to the previous classical solutions of the adhesion forces between a smooth particle and surface as the roughness goes to zero. The influences of roughness for the combination of particle and surface, relative humidity (RH), contact angle, and Hurst exponent toward the adhesion forces are examined using the proposed models. The decline mode of the adhesion force with surface roughness and contact angle, as well as the increase mode with RH and the Hurst exponent are reasonably predicted by the proposed models. The comparison between the proposed models and those from the existing studies is also performed, which shows the similarities and differences between the proposed models and the existing models

Modeling and Experiments of the Adhesion Force Distribution between Particles and a Surface

Due to the existence of surface roughness in real surfaces, the adhesion force between particles and the surface where the particles are deposited exhibits certain statistical distributions. Despite the importance of adhesion force distribution in a variety of applications, the current understanding of modeling adhesion force distribution is still limited. In this work, an adhesion force distribution model based on integrating the root-mean-square (RMS) roughness distribution (i.e., the variation of RMS roughness on the surface in terms of location) into recently proposed mean adhesion force models was proposed. The integration was accomplished by statistical analysis and Monte Carlo simulation. A series of centrifuge experiments were conducted to measure the adhesion force distributions between polystyrene particles (146.1 ± 1.99 μm) and various substrates (stainless steel, aluminum and plastic, respectively). The proposed model was validated against the measured adhesion force distributions from this work and another previous study. Based on the proposed model, the effect of RMS roughness distribution on the adhesion force distribution of particles on a rough surface was explored, showing that both the median and standard deviation of adhesion force distribution could be affected by the RMS roughness distribution. The proposed model could predict both van der Waals force and capillary force distributions and consider the multiscale roughness feature, greatly extending the current capability of adhesion force distribution prediction

Sound parameters on acoustics agglomeration.

<p>Effect of frequency, intensity and residence time on agglomeration efficiency. (Reproduced from Liu et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref096" target="_blank">96</a>] for fly ash with bi-modal characteristics).</p

Filtration efficiency of MERV 8 and 13 filters.

<p>Relationship between filter efficiency and particle size [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref033" target="_blank">33</a>], including the size distributions of virus [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref152" target="_blank">152</a>], bacteria [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref153" target="_blank">153</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref154" target="_blank">154</a>] and fungi [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref151" target="_blank">151</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref155" target="_blank">155</a>].</p

Forces acting on fine particles (PM_2.5) in an acoustics field.

<p>Forces acting on fine particles (PM_2.5) in an acoustics field.</p

Experimental results on the filtration efficiencies of MERV 11 and 13 filters with and without acoustic agglomeration pre-conditioning.

<p>Filtration efficiency is expressed as the percentage drop in particle number concentration before the agglomeration zone and after the filter. With acoustic pre-conditioning, the filtration efficiency of the MERV 11 filter is increased by about 10%, bringing its filtration efficiency closer to that of the MERV 13 filter without acoustic pre-conditioning.</p

Schematic of experimental set-up.

<p>Experimental set-up simulating travelling airborne PM in an open-loop, draw-through wind tunnel (resembling a ventilation duct) with acoustic agglomeration pre-conditioning prior to a test filter that is typically used in ACMV systems.</p

Filter properties [157] and computed fan power to overcome filter pressure drop in Eq (2), assuming an overall fan efficiency of 0.15.

<p>Filter properties [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.ref157" target="_blank">157</a>] and computed fan power to overcome filter pressure drop in Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178851#pone.0178851.e002" target="_blank">2</a>), assuming an overall fan efficiency of 0.15.</p

Orthokinetic and hydrodynamic mechanisms.

<p>Due to differential fluid and inertia forces, particles become entrained at different amplitudes and phase in the oscillations of an acoustic field. Consequently, the relative motions between the different sized particles result in collisions.</p

Summary of relevant experimental works in acoustic agglomeration with reported performances.

<p>Summary of relevant experimental works in acoustic agglomeration with reported performances.</p