Single scattering characteristics of volume elements in coal clouds

G. Gouesbet; G. Grehan; B. Maheu

doi:10.1364/AO.22.002038

Applied Optics
Vol. 22,
Issue 13,
pp. 2038-2050
(1983)
•https://doi.org/10.1364/AO.22.002038

Single scattering characteristics of volume elements in coal clouds

G. Gouesbet, G. Grehan, and B. Maheu

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G. Gouesbet, G. Grehan, and B. Maheu, "Single scattering characteristics of volume elements in coal clouds," Appl. Opt. 22, 2038-2050 (1983)

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Abstract

Single scattering characteristics of volume elements in coal clouds are discussed and computed, with the aim of developing laser diagnosis methods in dense particle-laden flows, where multiple scattering phenomena become predominant. Results are provided for extinction efficiency factors, single scattering albedos, asymmetry parameters, forward scattering ratios, and phase functions (rigorous as well as modeled). Interest is focused on coal particles because of their present importance in connection with problems linked to the crisis of energy. Computations are carried out at three wavelengths covering 3 orders of magnitude (0.5145-μm Ar-ion laser; 10.6-μm CO₂ laser; 337-μm HCN laser) for diameters ranging from ~1 to ~100 μm.

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For 0.5145-μm Wavelength and 1.7–0.1i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.5732	0.53883	0.89835	0.96947
8	2.1447	0.54803	0.92627	0.96951
12	2.1110	0.55324	0.92724	0.96932
16	2.0919	0.55588	0.92762	0.96920
20	2.0794	0.55745	0.92779	0.96911
24	2.0705	0.55849	0.92788	0.96902
28	2.0637	0.55921	0.92793	0.96896
32	2.0583	0.55974	0.92795	0.96890
36	2.0540	0.56014	0.92795	0.96886
40	2.0504	0.56045	0.92795	0.96882
44	2.0473	0.56070	0.92794	0.96878
48	2.0447	0.56089	0.92793	0.96875
52	2.0424	0.56106	0.92792	0.96872
56	2.0403	0.56119	0.92791	0.96869
60	2.0385	0.56130	0.92789	0.96867
64	2.0369	0.56140	0.92788	0.96864
68	2.0355	0.56148	0.92787	0.96862
72	2.0342	0.56155	0.92785	0.96860

For 0.5145-μm Wavelength and 2.0–0.6i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.2319	0.56991	0.86679	0.94146
8	2.1496	0.58369	0.86989	0.94078
12	2.1152	0.58876	0.87042	0.94035
16	2.0956	0.59138	0.87050	0.94006
20	2.0826	0.59297	0.87045	0.93985
24	2.0732	0.59402	0.87037	0.93968
28	2.0662	0.59477	0.87028	0.93955
32	2.0606	0.59532	0.87019	0.93944
36	2.0560	0.59575	0.87010	0.93935
40	2.0522	0.59608	0.87002	0.93927
44	2.0490	0.59635	0.86994	0.93920
48	2.0463	0.59656	0.86987	0.93913
52	2.0439	0.59674	0.86980	0.93908
56	2.0418	0.59689	0.86974	0.93902
60	2.0399	0.59702	0.86968	0.93898
64	2.0382	0.59713	0.86962	0.93893
68	2.0367	0.59722	0.86957	0.93889
72	2.0353	0.59730	0.86953	0.93886

For 10.6-μm Wavelength and 1.7–0.7i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.2826	0.34258	0.32868	0.73458
8	2.8038	0.44861	0.70717	0.93391
12	2.6992	0.46918	0.79139	0.93886
16	2.5972	0.48702	0.82437	0.94472
20	2.5293	0.50168	0.84155	0.94643
24	2.4788	0.51292	0.85179	0.94718
28	2.4389	0.52171	0.85844	0.94804
32	2.4065	0.52873	0.86308	0.94799
36	2.3796	0.53449	0.86649	0.94841
40	2.3568	0.53930	0.86908	0.94834
44	2.3373	0.54338	0.87110	0.94848
48	2.3202	0.54690	0.87272	0.94850
52	2.3052	0.54995	0.87404	0.94847
56	2.2919	0.55263	0.87513	0.94852
60	2.2799	0.55501	0.87604	0.94845
64	2.2692	0.55712	0.87681	0.94848
68	2.2594	0.55903	0.87747	0.94842
72	2.2504	0.56074	0.87804	0.94841
76	2.2423	0.56230	0.87853	0.94839
80	2.2347	0.56372	0.87896	0.94834
84	2.2277	0.56502	0.87934	0.94833
88	2.2212	0.56622	0.87968	0.94828
92	2.2152	0.56732	0.87998	0.94826
96	2.2096	0.56834	0.88024	0.94822
100	2.2043	0.56929	0.88048	0.94819

For 10.6-μm Wavelength and 2.6–1.2i Index

Diam (μm)	Q_ext	a	g	ζ
4	3.2922	0.48647	0.26252	0.68661
8	2.9012	0.51055	0.61928	0.89092
12	2.7484	0.54068	0.70384	0.88959
16	2.6396	0.55933	0.73567	0.89982
20	2.5645	0.57173	0.75227	0.89977
24	2.5097	0.58079	0.76232	0.90052
28	2.4669	0.58786	0.76882	0.90184
32	2.4324	0.59352	0.77329	0.90082
36	2.4040	0.59815	0.77652	0.90175
40	2.3800	0.60204	0.77894	0.90103
44	2.3594	0.60536	0.78079	0.90126
48	2.3415	0.60824	0.78223	0.90109
52	2.3258	0.61076	0.78339	0.90082
56	2.3118	0.61299	0.78432	0.90091
60	2.2299	0.61497	0.78508	0.90054
64	2.2880	0.61676	0.78571	0.90061
68	2.2777	0.61837	0.78624	0.90035
72	2.2684	0.61984	0.78668	0.90028
76	2.2598	0.62118	0.78705	0.90017
80	2.2518	0.62241	0.78736	0.89999
84	2.2445	0.62355	0.78763	0.89996
88	2.2377	0.62460	0.78786	0.89977
92	2.2313	0.62557	0.78806	0.89973
96	2.2254	0.62648	0.78822	0.89960
100	2.2198	0.62733	0.78837	0.89951

For 337-μm Wavelength and 2.0–5.0i Index

Diam (μm)	Q_ext	a	g	ζ
4	0.11929 × 10⁻¹	0.50296 × 10⁻³	0.0	0.49938
12	0.40025 × 10⁻¹	0.12321 × 10⁻¹	−0.71869 × 10⁻²	0.49452
20	0.81040 × 10⁻¹	0.48337 × 10⁻¹	−0.19333 × 10⁻¹	0.48529
28	0.14343	0.10951	−0.35536 × 10⁻¹	0.47294
36	0.23637	0.19180	−0.53090 × 10⁻¹	0.45953
44	0.37275	0.28893	−0.68903 × 10⁻¹	0.44739
52	0.57193	0.39163	−0.80519 × 10⁻¹	0.43835
60	0.85823	0.48924	−0.86699 × 10⁻¹	0.43336
68	1.2506	0.57360	−0.87324 × 10⁻¹	0.43250
76	1.7416	0.64131	−0.82955 × 10⁻¹	0.43536
84	2.2765	0.69293	−0.74352 × 10⁻¹	0.44134
92	2.7600	0.73102	−0.62177 × 10⁻¹	0.44992
100	3.1038	0.75849	−0.46796 × 10⁻¹	0.46079

For 337-μm Wavelength and 2.0–5.0i Index

Diam (μm)	Q_ext	a	g	ζ
108	3.2757	0.77781	−0.28204 × 10⁻¹	0.47390
116	3.3020	0.79089	−0.59948 × 10⁻²	0.48948
124	3.2359	0.79907	0.20598 × 10⁻¹	0.50803
132	3.1283	0.80337	0.52538 × 10⁻¹	0.53022
140	3.0165	0.80464	0.90641 × 10⁻¹	0.55664
148	2.9247	0.80377	0.13498	0.58739
156	2.8661	0.80175	0.18418	0.62164
164	2.8454	0.79969	0.23499	0.65727
172	2.8588	0.79855	0.28278	0.69118
180	2.8951	0.79892	0.32306	0.72034
188	2.9386	0.80085	0.35320	0.74291
196	2.9739	0.80391	0.37314	0.75877

For 337-μm Wavelength and 4.0–10.0i Index

Diam (μm)	Q_ext	a	g	ζ
4	0.32796 × 10⁻²	0.16349 × 10⁻²	−0.36621 × 10⁻²	0.49725
12	0.21033 × 10⁻¹	0.20966 × 10⁻¹	−0.32379 × 10⁻¹	0.47564
20	0.58785 × 10⁻¹	0.59852 × 10⁻¹	−0.80200 × 10⁻¹	0.43964
28	0.10916	0.12997	−0.12803	0.40357
36	0.17115	0.23938	−0.16276	0.37728
44	0.25748	0.37521	−0.18262	0.36208
52	0.38852	0.50986	−0.19067	0.35570
60	0.58653	0.62218	−0.19019	0.35568
68	0.86885	0.70620	−0.18363	0.36018
76	1.2364	0.76555	−0.17827	0.36795
84	1.6604	0.80652	−0.15837	0.37816
92	2.0812	0.83465	−0.14136	0.39033
100	2.4295	0.85399	−0.12188	0.40426

For 337-μm Wavelength and 4.0–10.0i Index

Diam (μm)	Q_ext	a	g	ζ
108	2.6601	0.86725	−0.99813 × 10⁻¹	0.41999
116	2.7685	0.87621	−0.74755 × 10⁻¹	0.43779
124	2.7807	0.88205	−0.46062 × 10⁻¹	0.45813
132	2.7332	0.88554	−0.12992 × 10⁻¹	0.48156
140	2.6593	0.88726	0.25050 × 10⁻¹	0.50855
148	2.5837	0.88769	0.68120 × 10⁻¹	0.53927
156	2.5227	0.88731	0.11528	0.57319
164	2.4853	0.88664	0.16427	0.60887
172	2.4745	0.88612	0.21168	0.64400
180	2.4869	0.88612	0.25380	0.67598
188	2.5146	0.88680	0.28781	0.70275
196	2.5472	0.88810	0.31265	0.72342

Comparison Between Values Obtained from van de Hulst and Our Computations for Various α and m

α	m	gvdh	gsupermidi
2	0.90–0i	0.577	0.57703
1	1.5–0i	0.199	0.19894
2	1.5–0i	0.626	0.62595
3	1.5–0i	0.734	0.73434
4	1.5–0i	0.750	0.75021
6	1.5–0i	0.644	0.64418
8	1.5–0i	0.453	0.45293
10	1.5–0i	0.743	0.74291

Table I

For 0.5145-μm Wavelength and 1.7–0.1i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.5732	0.53883	0.89835	0.96947
8	2.1447	0.54803	0.92627	0.96951
12	2.1110	0.55324	0.92724	0.96932
16	2.0919	0.55588	0.92762	0.96920
20	2.0794	0.55745	0.92779	0.96911
24	2.0705	0.55849	0.92788	0.96902
28	2.0637	0.55921	0.92793	0.96896
32	2.0583	0.55974	0.92795	0.96890
36	2.0540	0.56014	0.92795	0.96886
40	2.0504	0.56045	0.92795	0.96882
44	2.0473	0.56070	0.92794	0.96878
48	2.0447	0.56089	0.92793	0.96875
52	2.0424	0.56106	0.92792	0.96872
56	2.0403	0.56119	0.92791	0.96869
60	2.0385	0.56130	0.92789	0.96867
64	2.0369	0.56140	0.92788	0.96864
68	2.0355	0.56148	0.92787	0.96862
72	2.0342	0.56155	0.92785	0.96860

Table II

For 0.5145-μm Wavelength and 2.0–0.6i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.2319	0.56991	0.86679	0.94146
8	2.1496	0.58369	0.86989	0.94078
12	2.1152	0.58876	0.87042	0.94035
16	2.0956	0.59138	0.87050	0.94006
20	2.0826	0.59297	0.87045	0.93985
24	2.0732	0.59402	0.87037	0.93968
28	2.0662	0.59477	0.87028	0.93955
32	2.0606	0.59532	0.87019	0.93944
36	2.0560	0.59575	0.87010	0.93935
40	2.0522	0.59608	0.87002	0.93927
44	2.0490	0.59635	0.86994	0.93920
48	2.0463	0.59656	0.86987	0.93913
52	2.0439	0.59674	0.86980	0.93908
56	2.0418	0.59689	0.86974	0.93902
60	2.0399	0.59702	0.86968	0.93898
64	2.0382	0.59713	0.86962	0.93893
68	2.0367	0.59722	0.86957	0.93889
72	2.0353	0.59730	0.86953	0.93886

Table III

For 10.6-μm Wavelength and 1.7–0.7i Index

Diam (μm)	Q_ext	a	g	ζ
4	2.2826	0.34258	0.32868	0.73458
8	2.8038	0.44861	0.70717	0.93391
12	2.6992	0.46918	0.79139	0.93886
16	2.5972	0.48702	0.82437	0.94472
20	2.5293	0.50168	0.84155	0.94643
24	2.4788	0.51292	0.85179	0.94718
28	2.4389	0.52171	0.85844	0.94804
32	2.4065	0.52873	0.86308	0.94799
36	2.3796	0.53449	0.86649	0.94841
40	2.3568	0.53930	0.86908	0.94834
44	2.3373	0.54338	0.87110	0.94848
48	2.3202	0.54690	0.87272	0.94850
52	2.3052	0.54995	0.87404	0.94847
56	2.2919	0.55263	0.87513	0.94852
60	2.2799	0.55501	0.87604	0.94845
64	2.2692	0.55712	0.87681	0.94848
68	2.2594	0.55903	0.87747	0.94842
72	2.2504	0.56074	0.87804	0.94841
76	2.2423	0.56230	0.87853	0.94839
80	2.2347	0.56372	0.87896	0.94834
84	2.2277	0.56502	0.87934	0.94833
88	2.2212	0.56622	0.87968	0.94828
92	2.2152	0.56732	0.87998	0.94826
96	2.2096	0.56834	0.88024	0.94822
100	2.2043	0.56929	0.88048	0.94819

Table IV

For 10.6-μm Wavelength and 2.6–1.2i Index

Diam (μm)	Q_ext	a	g	ζ
4	3.2922	0.48647	0.26252	0.68661
8	2.9012	0.51055	0.61928	0.89092
12	2.7484	0.54068	0.70384	0.88959
16	2.6396	0.55933	0.73567	0.89982
20	2.5645	0.57173	0.75227	0.89977
24	2.5097	0.58079	0.76232	0.90052
28	2.4669	0.58786	0.76882	0.90184
32	2.4324	0.59352	0.77329	0.90082
36	2.4040	0.59815	0.77652	0.90175
40	2.3800	0.60204	0.77894	0.90103
44	2.3594	0.60536	0.78079	0.90126
48	2.3415	0.60824	0.78223	0.90109
52	2.3258	0.61076	0.78339	0.90082
56	2.3118	0.61299	0.78432	0.90091
60	2.2299	0.61497	0.78508	0.90054
64	2.2880	0.61676	0.78571	0.90061
68	2.2777	0.61837	0.78624	0.90035
72	2.2684	0.61984	0.78668	0.90028
76	2.2598	0.62118	0.78705	0.90017
80	2.2518	0.62241	0.78736	0.89999
84	2.2445	0.62355	0.78763	0.89996
88	2.2377	0.62460	0.78786	0.89977
92	2.2313	0.62557	0.78806	0.89973
96	2.2254	0.62648	0.78822	0.89960
100	2.2198	0.62733	0.78837	0.89951

Table V

For 337-μm Wavelength and 2.0–5.0i Index

Diam (μm)	Q_ext	a	g	ζ
4	0.11929 × 10⁻¹	0.50296 × 10⁻³	0.0	0.49938
12	0.40025 × 10⁻¹	0.12321 × 10⁻¹	−0.71869 × 10⁻²	0.49452
20	0.81040 × 10⁻¹	0.48337 × 10⁻¹	−0.19333 × 10⁻¹	0.48529
28	0.14343	0.10951	−0.35536 × 10⁻¹	0.47294
36	0.23637	0.19180	−0.53090 × 10⁻¹	0.45953
44	0.37275	0.28893	−0.68903 × 10⁻¹	0.44739
52	0.57193	0.39163	−0.80519 × 10⁻¹	0.43835
60	0.85823	0.48924	−0.86699 × 10⁻¹	0.43336
68	1.2506	0.57360	−0.87324 × 10⁻¹	0.43250
76	1.7416	0.64131	−0.82955 × 10⁻¹	0.43536
84	2.2765	0.69293	−0.74352 × 10⁻¹	0.44134
92	2.7600	0.73102	−0.62177 × 10⁻¹	0.44992
100	3.1038	0.75849	−0.46796 × 10⁻¹	0.46079

Table VI

For 337-μm Wavelength and 2.0–5.0i Index

Diam (μm)	Q_ext	a	g	ζ
108	3.2757	0.77781	−0.28204 × 10⁻¹	0.47390
116	3.3020	0.79089	−0.59948 × 10⁻²	0.48948
124	3.2359	0.79907	0.20598 × 10⁻¹	0.50803
132	3.1283	0.80337	0.52538 × 10⁻¹	0.53022
140	3.0165	0.80464	0.90641 × 10⁻¹	0.55664
148	2.9247	0.80377	0.13498	0.58739
156	2.8661	0.80175	0.18418	0.62164
164	2.8454	0.79969	0.23499	0.65727
172	2.8588	0.79855	0.28278	0.69118
180	2.8951	0.79892	0.32306	0.72034
188	2.9386	0.80085	0.35320	0.74291
196	2.9739	0.80391	0.37314	0.75877

Table VII

For 337-μm Wavelength and 4.0–10.0i Index

Diam (μm)	Q_ext	a	g	ζ
4	0.32796 × 10⁻²	0.16349 × 10⁻²	−0.36621 × 10⁻²	0.49725
12	0.21033 × 10⁻¹	0.20966 × 10⁻¹	−0.32379 × 10⁻¹	0.47564
20	0.58785 × 10⁻¹	0.59852 × 10⁻¹	−0.80200 × 10⁻¹	0.43964
28	0.10916	0.12997	−0.12803	0.40357
36	0.17115	0.23938	−0.16276	0.37728
44	0.25748	0.37521	−0.18262	0.36208
52	0.38852	0.50986	−0.19067	0.35570
60	0.58653	0.62218	−0.19019	0.35568
68	0.86885	0.70620	−0.18363	0.36018
76	1.2364	0.76555	−0.17827	0.36795
84	1.6604	0.80652	−0.15837	0.37816
92	2.0812	0.83465	−0.14136	0.39033
100	2.4295	0.85399	−0.12188	0.40426

Table VIII

For 337-μm Wavelength and 4.0–10.0i Index

Diam (μm)	Q_ext	a	g	ζ
108	2.6601	0.86725	−0.99813 × 10⁻¹	0.41999
116	2.7685	0.87621	−0.74755 × 10⁻¹	0.43779
124	2.7807	0.88205	−0.46062 × 10⁻¹	0.45813
132	2.7332	0.88554	−0.12992 × 10⁻¹	0.48156
140	2.6593	0.88726	0.25050 × 10⁻¹	0.50855
148	2.5837	0.88769	0.68120 × 10⁻¹	0.53927
156	2.5227	0.88731	0.11528	0.57319
164	2.4853	0.88664	0.16427	0.60887
172	2.4745	0.88612	0.21168	0.64400
180	2.4869	0.88612	0.25380	0.67598
188	2.5146	0.88680	0.28781	0.70275
196	2.5472	0.88810	0.31265	0.72342

Table IX

Comparison Between Values Obtained from van de Hulst and Our Computations for Various α and m

α	m	gvdh	gsupermidi
2	0.90–0i	0.577	0.57703
1	1.5–0i	0.199	0.19894
2	1.5–0i	0.626	0.62595
3	1.5–0i	0.734	0.73434
4	1.5–0i	0.750	0.75021
6	1.5–0i	0.644	0.64418
8	1.5–0i	0.453	0.45293
10	1.5–0i	0.743	0.74291

Single scattering characteristics of volume elements in coal clouds

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Applied Optics