Adhesion strength of soot particles to cellulose ester membranes determined by centrifuge technique

Figures & data

Figure 1. Typical SEM photomicrographs of soot, with magnifications of (a) 1000 and (b) 5000 x.

Figure 2. Particle size distribution of the soot.

Figure 3. SEM micrographs of the cellulose ester membrane filters with a magnification of 5000 x. (a) Grade 0.2 µm; (b) Grade 0.8 µm.

Figure 4. AFM topographical images of the cellulose ester filter membrane with their specific roughness. (a) Grade 0.2 µm, roughness of 169 nm; (b) grade 0.8 µm, roughness of 334 nm.

Figure 5. Typical photomicrographs of the soot on the first zone (2 x 2 mm) of the cellulose ester membrane disks proof after detachment forces of 63.7; 1,593.2; 5,161.8 and 12,490.3 RCF (a to d), for the press-on force of 255.0 RCF and pore size of 0.2 µm.

Figure 6. Percentage of adhered soot particles as a function of detachment force for 0.2 μm and 0.8 μm cellulose ester membrane filter media (press-on forces of 63.7, 255.0, and 1,593.6 RCF.

Figure 7. Resulting detachment forces as a function of the percentage amount of soot powder particles remained on cellulose filter membranes, for press-on forces of 63.7, 255.0, and 1,593.6 RCF.

Table 1. Geometric median adhesion force (GMAF) and geometric standard deviation (SD-G) for the three soot particles fractions for cellulose ester membranes with pores sizes of 0.2 and 0.8 µm.

Pores Size (µM)	Press-On Force (RCF)	Diameter Ranges (µm)	Mean Diameter (µm)	GMAF (N)	SD-G (-)
0.2	63.7	11.1–17.0	13.55	4.16 x10^−8	0.20
		17.1–23.0	19.60	6.05 x10^−8	0.19
		23.1–29.0	25.64	8.52 x10^−8	0.17
	255.0	11.1–17.0	13.77	4.25 x10^−8	0.21
		17.1–23.0	19.89	8.24 x10^−8	0.20
		23.1–29.0	25.74	1.09 x10^−7	0.18
	1,593.6	11.1–17.0	13.89	5.30 x10^−8	0.21
		17.1–23.0	20.28	1.03 x10^−8	0.22
		23.1–29.0	25.27	1.47 x10^−7	0.21
0.8	63.7	11.1–17.0	13.85	2.63 x10^−8	0.18
		17.1–23.0	19.51	4.98 x10^−8	0.19
		23.1–29.0	25.82	8.10 x10^−8	0.16
	255.0	11.1–17.0	13.80	2.36 x10^−8	0.16
		17.1–23.0	19.68	7.83 x10^−8	0.18
		23.1–29.0	25.48	1.07 x10^−7	0.21
	1,593.6	11.1–17.0	14.09	2.15 x10^−8	0.18
		17.1–23.0	19.94	8.84 x10^−8	0.22
		23.1–29.0	24.91	1.32 x10^−7	0.20

Figure 8. GMAF as a function of the soot particles size range, for press-on forces of 63.7, 255.0, and 1,593.6 RCF and cellulose ester membrane of 0.2 µm and 0.8 µm.

Table 2. Surface tensions of the adhesion components.

Material	γ (mJ/m^2)	γ^d (mJ/m^2)	γ^p (mJ/m^2)
Cellulose acetate^(1)	45.90	32.31	13.59
Soot^(2)	35.00	16.48	18.52

(1) Brandrup, Immergut, and Grulke (1999); (2) Glass and Larsen (1994).

Table 3. Interfacial tension and the work of adhesion determined by using the Antonow rule, geometric, and harmonic means for the soot cellulose membrane system.

Interfacial Tension (γ12)
Geometric mean	Harmonic mean	Antonow rule
(mJ m^2)	(mJ m^2)	(mJ m^2)
3.02	5.89	10.90
Work of Adhesion
WMG (mJ m^−2)	WMH (mJ m^−2)		WRA (mJ m^−2)
77.88	75.01		70.00

Figure 9. Comparison of experimental data of the adhesion forces for soot-cellulose ester membrane (pore sizes of 0.2 μm and 0.8 μm) with estimates by JKR and DMT models; for press-on forces of 63.7, 255.0, and 1,593.6 RCF.

Table 4. k_c correction factors for the JKR and DMT models used to describe the adhesion forces of the soot/cellulose ester membrane system.

Press-On Centrifuge Force (RCF)	Adhesion Models
	JKR	DMT
63.7	0.017	0.013
255.0	0.022	0.016
1,593.6	0.026	0.020

Figure 10. Experimental results of the adhesion forces and the corrected theoretical values determined by JKR and DMT models as a function of the mean soot diameter; press-on forces of 63.7, 255.0, and 1,593.6 RCF and cellulose membranes of 0.2 µm and 0.8 µm pore sizes.

Brandrup, J. , E. H. Immergut , and E. A. Grulke . 1999. Polymer handbook . 4rd ed. Wiley.

 Google Scholar

Glass, A. S. , and J. W. Larsen . 1994. Coal surface properties. specific and nonspecific interactions for polar molecules and surface tensions for hydrocarbons at the surface of illinois no. 6 coal. Energy Fuels 8 (3):629–636. doi:https://doi.org/10.1021/ef00045a018.

 Google Scholar