3.3 Particle transport and deposition

3.3.1 Effect of particle rebounds on particle deposition

Depositions and trajectories of soft PSL particles are shown in Fig.3-6.Diameters of the PSL particle and fiber are 2.0μm and 20.0μm,respectively.The face velocities (V),which means the air flow velocities of the simulation domain inlet ^[46,61],is chosen to be 2.0 m/s.There are 100 particles to be released one by one from the entrance in Fig.3-6(a),where each particle has a random initial position.The particles released in the case of Fig.3-6(b) have the same initial positions with that of Fig.3-6(a).The calculated normal critical velocities (V_in^*) for these PSL particles are 0.845 m/s and 1.208 m/s,as listed in Table 3-1.Particle-1 has a same initial position as Particle-1ⁿ,where the superscript n denotes the condition that considers the particle rebound,and so do Particle-2,Particle-2ⁿ,Particle-3 and Particle-3ⁿ.

Particle-2 and Particle-3 are immediately trapped once contact with solid surfaces of the fiber or existing deposited particle at locations of A and B,in Fig.3-6(a),respectively,when the particle rebound is not considered.

However,when the particle rebound is considered in Fig.3-6(b),Particle-2ⁿhas an initial position close to the fiber center line,thus has a normal incident velocity V_in (0.993 m/s in Table 3-1) larger than V_in^*(0.845 m/s in Table 3-1).It rebounds from the fiber surface at the location A,then flies away.Moreover,Particle-3ⁿfirstly collides with an existing deposited particle (location C) with the V_in of 1.484 m/s (V_in^*=1.208 m/s as shown in Table 3-1).After rebounding,it collides with another existing deposited particle with a new V_in of 0.689 m/s (in Table 3-1) which is smaller than the V_in^*(1.208 m/s in Table 3-1),and is trapped at location D lastly.

Correspondingly,Fig.3-7 shows that velocity components in both the x-direction and y-direction of Particle-2ⁿand Particle-3ⁿhave obvious jumps due to rebounds.Negative values indicate that they fly backward after rebounding on the solid surfaces of the fiber and existing deposited particle.Therefore,the particle rebound is one of essential particle behaviors,and is indispensable in the study of fibrous filtration.

3.3.2 Effects of face velocity on particle deposition

Fig.3-8 shows the particle depositions with the different face velocities (V) ranged from 0.5 m/s to 3.0 m/s.The adhered and escaped particles are counted in Fig.3-9.The particle diameter is chosen to be 2.0μm.There are 200 particles to be randomly

released in each case.Note that initial locations of these particles are identical for the four cases in Fig.3-8.The Stokes number (defined as S_tk= d_p²ρ_pV/(18μd_f)) is associated with the particle inertia and is used to characterize the particle movement.The calculated normal critical velocities (V_in^*as shown in Table 3-1) for particle-fiber collisions and particle-particle collisions are 0.845 m/s and 1.208 m/s,respectively.

It can be seen from Fig.3-8 that the number of adhered particles firstly increases when the face velocity increases from 0.5 m/s to 2.0 m/s,then it decreases as the face velocity further increases to 4.0 m/s.Fig.3-9 shows that the percentage of directly escaped particles keeps decreasing with the increase of the face velocity.

When the face velocity is 0.5 m/s,91.5%of the particles have a small inertia and are more likely to follow the air flow streamlines to directly escape from the fiber surface.The particle rebound does not occur in this case.As the face velocity increases to 2.0 m/s,39.5%of the particles collide with the solid surface due to their significant inertia.Moreover,11%of the particles will rebound from the solid surface and fly away,while the rest particles (28.5%) finally deposit on the fiber surface.As the face velocity further increases to 3.0 m/s,the particle rebound plays a more important role and 29%of the particles will rebound from the solid surface and fly away.So less deposited particles (11.5%) are observed in Fig.3-8(c).

When the face velocity is 4.0 m/s,42.5%of the particles collide with the solid surfaced and fly away,and few particles are deposited.At such a large face velocity,particles will be captured under two possible conditions.The first condition is that particles moving to the lateral sides of the fiber which have a relatively larger incident angle and a smaller V_in will lastly be trapped,as illustrated by Chernyakov et al ^[60].The second condition is that particles moving towards the fiber center will rebound several times and dissipate a lot of kinetic energy before adhering at last,just like the particles in the medial region shown in Fig.3-8(d).

3.3.3 Effects of particle diameter on particle deposition

Particle depositions with different particle diameters ranged from 0.1μm to 2.4μm are shown in Fig.3-10.The adhered or escaped particles are counted in Fig.3-11.The face velocity is chosen to be 2.0 m/s.There are four types of particles to be released from the same initial locations,and each type has 200 particles.The calculated normal critical velocities (V_in^*) for particle-fiber collisions and particle-particle collisions with different particle diameters are listed in Table 3-2.

Fig.3-10 shows that the number of deposited particles is the largest when the particle diameter is 1.8μm among four types of particle diameters.Fig.3-11 shows that the percentages of deposited particles with different particle diameters (0.1μm,1.0μm,1.8μm and 2.4μm) account for 12%,6.5%,29%and 17.5%,respectively.

The small particles (0.1μm and 1.0μm) have a relatively larger V_in^*(as shown in Table 3-2).Therefore,no particle rebound occurs for 0.1μm and 1.0μm particles as shown in Fig.3-11.For 0.1μm particles,the Brownian diffusion is the dominating trapping mechanism ^[18] and the inertial impaction is very weak.So,particles that pass by the fiber have the chance to contact with the backside of the fiber and then are adhered,which is consistent with previous studies ^[18-19].For 1.0 μm particles,the trapping mechanisms due to Brownian diffusion and inertial impaction are both weak (S_tk=0.37) ^[18],so most particles (93.5%) follow the flow streams and escape away as shown in Fig.3-10(b).

As the particle diameter increases to 1.8μm,33%of particles collide with the solid surface due to the significant inertia (S_tk=1.12).But most of them (29%) are adhered to the solid surface,resulting in the largest number of deposited particles in Fig.3-10(c).However,as the particle diameter further increases to 2.4μm,the V_in^*(as shown in Table 3-2) becomes relatively smaller.Thus,the percentage of particles that rebound to escape (26%) is largest among four types of particle diameters.

3.3.4 Filtration efficiency of a single fiber

The filtration efficiencies of a single fiber for different particle diameters are shown in Fig.3-12.Previous analytical expressions of the single fiber efficiency (SFE) ^[62],considering the Brownian diffusion,interception,and inertial impaction are listed in Table 3-3.All calculations by analytical expressions use the ideal trapping model,which assumes that a particle is captured and has no further movement once the contact happens.Besides,such analytical expressions are derived considering the clean filtration stage,which assumes that particles are trapped only by a fiber but not by existing deposited particles.In this book,we investigate 200 particles for each particle diameter,which are randomly released from the entrance.Twenty times simulations are carried out for each case to obtain the mean,maximum and minimum values of its filtration efficiency.The face velocity is chosen to be 2.0 m/s.

Fig.3-12 shows that the filtration efficiency decreases as the particle diameter increases from 0.1μm to 0.6μm,then it increases when the particle diameter exceeds 0.6μm.Although considering the particle rebound in our model,the behavior of small particles is dominated by the Brownian diffusion and will not rebound after contacting with the fiber surface due to a large normal critical velocity V_in^*(Table 3-2,Fig.3-11).So the filtration efficiency for small particles agrees well with that by the analytical expression of SFE,which does not consider particle rebound essentially.

When the particle diameter exceeds 0.6 μm,the inertial impaction gradually becomes the primary trapping mechanism.Therefore,the filtration efficiency increases mainly due to the significant increase of particles inertia.It is also observed that the filtration efficiencies for the particle diameters ranged from 1.1μm to 1.7μm are higher than that by the analytical expression of SFE.Because when enough particles are trapped by the fiber surface and form some dendritic deposition structures,the subsequent particles will collide with both the fiber surface and existing deposited particles.Thus,there is an enhancing effect on the total filtration efficiency.

As the particle diameter continuously increases,the normal critical velocity (V_in^*) becomes small correspondingly (Fig.3-4).As the V_in^*reduces to be smaller than the normal incident velocity V_in,particles will rebound and escape away.Thus,the filtration efficiency becomes smaller than that by the analytical expression of SFE.Results indicate that the analytical expressions not considering particle rebound will overestimate the filtration efficiency for large particles (above 1.8μm in this work).