Study of the measurement for the diffusion coefficient by digital holographic interferometry

Shi Zhang; Maogang He; Ying Zhang; Sanguo Peng; Xinxin He

doi:10.1364/AO.54.009127

Applied Optics
Vol. 54,
Issue 31,
pp. 9127-9135
(2015)
•https://doi.org/10.1364/AO.54.009127

Study of the measurement for the diffusion coefficient by digital holographic interferometry

Shi Zhang, Maogang He, Ying Zhang, Sanguo Peng, and Xinxin He

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Shi Zhang, Maogang He, Ying Zhang, Sanguo Peng, and Xinxin He, "Study of the measurement for the diffusion coefficient by digital holographic interferometry," Appl. Opt. 54, 9127-9135 (2015)

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Abstract

In the measurement of the diffusion coefficient by digital holographic interferometry, the conformity between the experiment and the ideal physical model is lacking analysis. Two data processing methods are put forward to overcome this problem. By these methods, it is found that there is obvious asymmetry in the experiment and the asymmetry is becoming smaller with time. Besides, the initial time for diffusion cannot be treated as a constant throughout the whole experiment. This means that there is a difference between the experiment and the physical model. With these methods, the diffusion coefficient of KCl in water at $0.33 mol / L$ and 25°C is measured. When the asymmetry is ignored, the result is $1.839 \times 10^{- 9} m^{2} / s$ , which is in good agreement with the data in the literature. Because the asymmetry is becoming smaller with time, the experimental data in the latter time period conforms to the ideal physical model. With this idea, a more accurate diffusion coefficient is $2.003 \times 10^{- 9} m^{2} / s$ , which is about 10% larger than the data in the literature.

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Method	Characteristics Used in the Measurement		The Way for Determination
MGH-1	Width of the peak in the phase difference profile	/	$t_{0}$ and $D$ are determined simultaneously
MGH-2	Extreme difference of the peaks in the phase difference profile	Shape of the phase difference profile	$t_{0}$ and $D$ are determined, respectively

$t_{1}^{count}$ min	$t_{2}^{count}$ min	$w_{1}$ pixels	$w_{2}$ pixels	$w^{p}$ pixels	$Δ w$ pixels	$δ w$ %
40	80	96.95	120.12	108.53	11.59	10.68
40	85	99.12	120.91	110.02	10.90	9.90
40	90	101.66	124.06	112.86	11.20	9.93
40	95	103.75	125.74	114.74	11.00	9.58
40	100	106.15	128.09	117.12	10.97	9.37
40	105	108.21	129.63	118.92	10.71	9.01
40	110	110.68	131.65	121.17	10.48	8.65
40	115	112.77	134.26	123.52	10.74	8.70
40	120	114.84	135.29	125.06	10.23	8.18
40	125	116.93	136.59	126.76	9.83	7.75
40	130	118.06	138.68	128.37	10.31	8.03
40	135	120.66	140.48	130.57	9.91	7.59
40	140	121.90	141.31	131.61	9.70	7.37
40	145	123.93	142.89	133.41	9.48	7.11

$t_{1}^{count}$ min	$w_{1}$ pixels	$w_{2}$ pixels	$w^{p}$ pixels	$Δ w$ pixels	$δ w$ %
$Δ t = 40 \min$
40	96.95	120.12	108.53	11.59	10.68
45	103.71	126.27	114.99	11.28	9.81
50	110.90	133.36	122.13	11.23	9.20
55	118.26	137.19	127.72	9.47	7.41
60	124.91	144.10	134.51	9.59	7.13
65	130.21	147.96	139.09	8.87	6.38
70	136.80	152.22	144.51	7.71	5.34
$Δ t = 70 \min$
40	110.55	131.59	121.07	10.52	8.69
45	118.15	140.26	129.20	11.05	8.56
50	124.76	144.33	134.55	9.79	7.27
55	131.24	148.28	139.76	8.52	6.10
60	136.25	155.34	145.80	9.54	6.54
65	144.23	159.53	151.88	7.65	5.04
70	148.99	163.44	156.21	7.23	4.63
75	155.30	167.10	161.20	5.90	3.66
80	157.84	171.30	164.57	6.73	4.09
85	166.49	176.52	171.51	5.02	2.93
90	168.64	179.85	174.24	5.61	3.22

	Initial Values		Fitting Results
Fitting Step	$t_{0}$ min	$D \times 10^{- 9} m^{2} / s$	$t_{0}$ min	$D \times 10^{- 9} m^{2} / s$	$F_{1} {pixels}^{2}$
1	0	1.8	0	1.336	34.93
2	7	1.8	8.35	1.545	11.94
3	14	1.8	14.59	1.753	2.36
4	14.59	1.86	15.70	1.799	1.36
5	15.70	1.86	16.67	1.839	0.73
6	16.67	1.86	17.16	1.858	1.09
7	15.70	1.839	17.28	1.863	1.02

$t_{1}^{count}$ min	$H / 2$ rad	$A_{1}$ rad	$A_{2}$ rad	$A_{3}$ rad	$A_{4}$ rad	$A_{5}$ rad	$A_{6}$ rad	$A_{7}$ rad	$A_{8}$ rad	$A_{9}$ rad	$A_{10}$ rad	$A_{Δ t = 40}$ rad
40	12.783	58.474										56.951
45	11.351	58.067	59.287									56.731
50	10.210	57.706	58.795	60.444								56.513
55	9.300	57.519	58.505	60.000	58.640							56.439
60	8.618	57.868	58.779	60.158	58.902	58.367						56.872
65	7.990	57.873	58.714	59.989	58.829	58.334	56.648					56.952
70	7.512	58.368	59.157	60.352	59.264	58.800	57.220	56.209				57.505
75	7.054	58.518	59.257	60.377	59.357	58.923	57.442	56.495	54.489			57.709
80	6.596		58.863	59.909	58.957	58.551	57.169	56.285	54.414	51.847		57.419
85	6.294			60.453	59.546	59.160	57.843	57.001	55.218	52.774	52.080	58.080
90	5.809				57.999	57.642	56.429	55.653	54.009	51.757	51.118	56.648
95	5.626					58.756	57.582	56.832	55.243	53.064	52.446	57.794
100	5.271						56.704	56.001	54.514	52.475	51.897	56.902
105	5.080							56.619	55.187	53.224	52.668	57.487
110	4.755								54.132	52.296	51.776	56.283
115	4.487									51.684	51.194	55.443
120	4.393										52.406	56.564
The average of $A / rad$		58.049	58.920	60.210	58.937	58.567	57.129	56.387	54.651	52.390	51.948	56.958
Initial time $t_{0} / \min$		13.47	12.47	10.95	12.33	12.92	14.92	16.20	18.90	22.61	23.66	14.56

This Work			Data in the Literature
$D / \times 10^{- 9} m^{2} / s$	$D / \times 10^{- 9} m^{2} / s$	Deviation from the Data in Literature	Author (time)	Method
1.839	1.842	−0.16%	Harned and Nuttall (1949) [24]	Conductance measurement
	1.839	0	Harned and Nuttall (1949) [24]	Onsager–Fuoss theory
	1.841	−0.11%	Gosting (1950) [25]	Gouy interference
	$1.864 \pm 0.037$	−1.34%	Szydlowska and Janowska (1982) [26]	Holographic interferometry
	$1.86 \pm 0.02$	−1.13%	Ruiz-Bevia et al. (1985) [15]	Holographic interferometry

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Applied Optics