Estructura volumétrica

The SDOCT method enables the 2D cross-sectional visualization of PS microparticles flow inside the drying droplets. The experimental set-up and principle behind the operation of SDOCT coupled with low pressure chamber has been described fully in section 2.4.1. The room temperature was maintained at about 22.2±0.2°C (the variations seem to be quite small due good air conditioning in the laboratory) while the relative humidity at 57.4±4.6%. The SDOCT x-spacing (pixel size) is determined by the scanning length and the number of columns. The number of columns was varied from 200 to 1000 while the scanning length of up to 2.4mm producing a scanning rates between ~1.0 to 4.6 fps. For example for 1µL droplet with horizontal scan length of 1.8mm, depth range of 1.6mm and 500 columns produces horizontal x-spacing of 3.6µm/pixel at a scanning rate of ~2.0fps. SDOCT axial resolution is determined by the coherence length of the source, while SDOCT transverse resolution depends not only on the wavelength, but also the focal length and the diameter of the laser beam. Depending on the experiment such as the whole droplet, half a droplet or a small section of a droplet near the contact line, the parameter above was combined accordingly. The sequence of images was saved as video after processing them with Image J software.

To determine the PS microparticles velocities, two methods were employed one using the PIV/PTVlab tracking algorithm and manually using Image J software. To determine the PS microparticles velocity by Image J, displacements in a given number of frames were determined by tracking particle through their center-of- mass to determine the Cartesian coordinates [145, 146] as illustrated in figure 4.1 and 4.2.

Figure 4.1: Schematic illustration of a PS microparticle movement from position 1 to 2 through an instantaneous displacement d.

Figure 4.2: Determination of instantaneous displacements xx₂ x₁ and

1 2 y y y  

 of the same PS microparticle moving in 13 frames between coordinates



x₁,y₁



in (a) and



x₂,y₂



in (b). The short white arrow shows the direction of movement of a particle.

In figure 4.2, the actual PS microparticles are shown in an evaporating droplet between 13 frames. The PS microparticle considered in this case was tracked between coordinate



x₁,y₁



to



x₂,y₂



in order to determine the magnitude Instantaneous displacement |d|

 

x 2 

 

y2 . The magnitude of velocity for each particle at time interval t was determined according to equation (4.1).

 

 

t y x | V | 2 2 i _     (4.1)

The calibration factors for x and y coordinates were represented by the value of x- spacing and y-spacing respectively for a given experiment. The vertical component of velocity of the PS microparticles was determined by measuring the optical path length [145] rather than the physical path length due to the difference in refractive index between air (n=1) and water (n=133). Therefore the vertical component of the PS microparticles displacement was divided by the refractive index of water (n=1.33). For particles recirculating and/or moving through an air-liquid interface, their velocities has to be corrected as illustrated in figure 4.3 to include the effect of air-liquid interface displacement.

Figure 4.3: Schematic illustration of the effect fast descending air-liquid interface on the position of the particle. A particle from point 1 after time t is located at position 2 for fast descending interface and position 3 when the interface velocity is smaller than the particle velocity.

Form figure 4.3, initially a particle is located at position marked 1 and there are two possibilities this particle will be located later as the air-liquid interface descend.

One possibility is the particle to be located at position marked 3 when interface velocity is very small then the particle velocity and the corresponding displacement from point marked 1 will be _d'_{. However for high drying rate the}

air-liquid interface descends faster such that the particle is no longer located at position marked 3. The second possibility a particle will be located at position marked 2 and corresponding displacement from point marked 1 will be d. In figure 4.4 a droplet containing PS microparticles is considered similar to illustration in figure 4.3.

Figure 4.4: (a) A PS microparticle at the air-liquid droplet interface with coordinate



x1,y1



from contact line of coordinate



x0,y0



(b) Instantaneous displacement of

the same particle in part (a) for 23 frames at ~2.0 fps between coordinate



x₁,y₁



and



x_n,y_n



with respect contact line (the short white arrow show the direction of the particle) as the air-liquid interface moves.

The contact line is considered to be pinned at all-time whose coordinates are

time t₁ in the frame f₁ as shown in figure 4.4(a). Then the approximate magnitude of the distance |d₁| of this particle from the contact will be given according to equation (4.2).













2 0 1 2 0 1 1| x x y y d |     (4.2)

For a given number frames the same PS microparticle will have displaced from coordinate



x₁,y₁



to a new coordinate



x_n,y_n



as described in figure 4.3(b) and the corresponding distance from the contact line will be given by equation (4.3).













2 0 n 2 0 n n| x x y y d |     (4.3)

The PS microparticle displacement d for a given number frames taking into account of air-liquid droplet interface will be given as d d_n d₁ and the

instantaneous velocity t d V_i     

. An equation (4.2) and (4.3) holds only for small change in contact angle and applies only for small number of frames. Then similar PS microparticle was tracked for a number of frames until it disappeared to determine the instantaneous velocities and average them. Similar procedures were repeated for at least 8 PS microparticles in a droplet and other two droplets making a total of 24 instantaneous measurements for inward velocity. The calculations above allowed the outward flow, vertical and inward velocities to be determined as illustrated in figure 4.5. Another important image processing tool was the Z-projection using Image J software. The Z-Projection is the one in which an image stack is projected along an axis perpendicular to the plane of the image (Z-axis) [157]. The preferred

average intensity over all images in a given stack at corresponding pixel location. Using PIV/PTVlab tracking algorithm Z-projection was automatically generated at the end of each session for the number of frames considered.

Figure 4.5: Illustration of particle motion (a) inward velocity (b) outward velocity and (c) vertical velocity.

4.2.3 Kinematics of Droplets Drying by Optical Imaging

In document UNIVERSIDAD NACIONAL DE LA AMAZONIA PERUANA FACULTAD DE CIENCIAS FORESTALES TESIS (página 28-0)