Table SI Dimensionless surface charge density/ surface potential relationship for a spherical colloidal particle immersed in a 3:1 type electrolyte solution
/ 2.5
280.1803
280.2501
(0.0249)
280.1434
(-0.0132)
280.2147
(0.0123) / 4.5
504.3051
504.5058
(0.0398)
504.2084
(-0.0192)
504.3627
(0.0114) / 6.5
728.6723
729.0252
(0.0484)
728.5353
(-0.0188)
728.7200
(0.0065) / 7.5
841.2050
841.6161
(0.0489)
841.1033
(-0.0121)
841.2740
(0.0082) / 8.5
954.4057
954.7749
(0.0387)
954.4690
(0.0066)
954.3189
(-0.0091) / 9.5
1069.178
1069.354
(0.0165)
1069.755
(0.0540)
1068.865
(-0.0293)
/ 2.5
127.3528
127.4510
(0.0771)
127.3240
(-0.0226)
127.3866
(0.0265) / 4.5
229.2607
229.5315
(0.1181)
229.1966
(-0.0280)
229.3011
(0.0176) / 6.5
331.7346
332.1789
(0.1339)
331.7037
(-0.0093)
331.7181
(0.0123) / 7.5
383.7388
384.2033
(0.1210)
383.8474
(0.0283)
383.6266
(-0.0050) / 8.5
437.1887
437.5148
(0.0746)
437.7071
(0.1186)
436.8646
(-0.0741) / 9.5
493.9988
493.7924
(-0.0418)
495.6197
(0.3281)
493.1979
(-0.1621)
/ 2.5
30.02900
30.17231
(0.4772)
30.01825
(-0.0358)
30.04338
(0.0479) / 4.5
54.42035
54.76085
(0.6257)
54.43662
(0.0299)
54.40272
(-0.0324) / 6.5
81.06752
81.48523
(0.5153)
81.35343
(0.3527)
80.85435
(-0.2299) / 7.5
97.20426
97.51048
(0.3150)
97.95591
(0.7733)
96.71247
(-0.2630) / 8.5
118.1873
118.2327
(0.0384)
119.9408
(1.484)
117.1370
(-0.8887) / 9.5
149.0306
148.8331
(-0.1325)
152.6427
(2.424)
146.8983
(-1.431)
/ 2.5
5.018666
5.110493
(1.830)
5.022996
(0.0863)
5.013442
(0.0654) / 4.5
10.75744
10.91598
(1.474)
10.81786
(0.5620)
10.69369
(-0.1041) / 6.5
22.88050
23.11866
(1.041)
23.12708
(1.077)
22.56313
(-1.387) / 7.5
34.77854
34.50074
(-0.7988)
35.18349
(1.164)
34.16100
(-1.777) / 8.5
54.27587
53.54411
(-1.348)
54.88119
(1.115)
53.11289
(-2.143) / 9.5
86.39378
85.45432
(-1.087)
87.23756
(0.9767)
84.22842
(-2.506)
/ 2.5
3.522213
3.587971
(1.867)
3.526090
(0.1101)
3.515788
(-0.1824) / 4.5
8.417498
8.532263
(1.364)
8.456268
(0.4606)
8.354629
(-0.7469) / 6.5
20.19859
20.33751
(0.6878)
20.33058
(0.6535)
19.89943
(-1.481) / 7.5
32.07222
31.82379
(-0.7746)
32.27620
(0.6360)
31.48677
(-1.825) / 8.5
51.59392
51.07383
(-1.008)
51.88638
(0.5668)
50.47709
(-2.165) / 9.5
83.75558
83.15104
(-0.7218)
84.15240
(0.4738)
81.64865
(-2.516)
/ 2.5
2.919916
2.957456
(1.286)
2.922571
(0.0909)
2.913175
(-0.2309) / 4.5
7.514970
7.602253
(1.161)
7.537647
(0.3018)
7.453848
(-0.8133) / 6.5
19.18124
19.14200
(-0.2046)
19.25206
(0.3692)
18.89273
(-1.504) / 7.5
31.04015
30.79369
(-0.7940)
31.14684
(0.3437)
30.47110
(-1.833) / 8.5
50.56026
50.25430
(-0.6051)
50.71068
(0.2975)
49.46522
(-2.166) / 9.5
82.72618
82.44262
(-0.3428)
82.92810
(0.2441)
80.64551
(-2.515)
/ 2.5
2.721359
2.750148
(1.058)
2.723338
(0.0727)
2.714556
(-0.2500) / 4.5
7.223767
7.288217
(0.8922)
7.239719
(0.2208)
7.163495
(-0.8344) / 6.5
18.85388
18.82199
(-0.1691)
18.90221
(0.2563)
18.56938
(-1.509) / 7.5
30.70658
30.55267
(-0.5012)
30.77877
(0.2351)
30.14343
(-1.834) / 8.5
50.22423
50.02311
(-0.4044)
50.32545
(0.2015)
49.13682
(-2.165) / 9.5
82.38959
82.22952
(-0.1943)
82.52499
(0.1643)
80.31797
(-2.514)
/ 2.5
2.622622
2.646009
(0.8917)
2.624194
(0.0599)
2.615799
(-0.2616) / 4.5
7.080249
7.131334
(0.7215)
7.092542
(0.1736)
7.02046
(-0.8444) / 6.5
18.69253
18.66670
(-0.1382)
18.72920
(0.1962)
18.41013
(-1.511) / 7.5
30.54182
30.42421
(-0.3851)
30.59636
(0.1786)
29.98171
(-1.834) / 8.5
50.05784
49.91080
(-0.2937)
50.13411
(0.1524)
48.97431
(-2.165) / 9.5
82.22253
82.11965
(-0.1251)
82.32438
(0.1239)
80.15549
(-2.514)
/ 2.5
2.563576
2.583279
(0.7598)
2.564878
(0.0508)
2.556745
(-0.2665) / 4.5
6.994847
7.037159
(0.7686)
7.004844
(0.1429)
6.935371
(-0.8503) / 6.5
18.59649
18.57502
(-0.1155)
18.62603
(0.1588)
18.31538
(-1.512) / 7.5
30.44362
30.34882
(-0.3124)
30.48745
(0.1440)
29.88536
(-1.834) / 8.5
49.95854
49.84368
(-0.2299)
50.01972
(0.1225)
48.87736
(-2.164) / 9.5
82.12270
82.05078
(-0.0876)
82.20431
(0.0994)
80.05841
(-2.514)
represents the ‘exact’ numerical results from the present paper, the results calculated with the approximate analytical expression Eq. (38) in Ref. [33], whereas the results calculated with the present Eq. (22)inscr, and the present Eq. (25)circum. The figures between brackets are percent relative errors calculated with a formulae of .
Table SII The same as in Table SI but for a 2:1 type electrolyte solution
/ 2.5
280.2335
280.2689
(0.0126)
280.2155
(-0.0064)
280.2540
(0.0073) / 4.5
504.4615
504.5628
(0.0201)
504.4197
(-0.0083)
504.4932
(0.0063) / 6.5
729.7032
729.2069
(-0.0680)
729.0238
(-0.0931)
729.0490
(-0.0897) / 7.5
842.5406
841.9569
(-0.0693)
841.8781
(-0.0786)
841.7578
(-0.0929) / 8.5
956.2659
955.4902
(-0.0811)
955.8002
(-0.0486)
955.2857
(-0.1025) / 9.5
1071.231
1070.835
(-0.0370)
1072.277
(0.0977)
1070.736
(-0.0462)
/ 2.5
127.4367
127.4862
(0.0388)
127.4234
(-0.0104)
127.4583
(0.0169) / 4.5
229.5085
229.6423
(0.0583)
229.4904
(-0.0079)
229.5278
(0.0085) / 6.5
332.8793
332.5518
(-0.0984)
332.4483
(-0.1295)
332.3056
(-0.1723) / 7.5
384.8286
384.9392
(0.0287)
385.1184
(0.0753)
384.6339
(-0.0506) / 8.5
439.7893
439.0376
(-0.1709)
440.0590
(0.0613)
438.7283
(-0.2412) / 9.5
498.6162
497.0682
(-0.3105)
500.3180
(0.3413)
496.9100
(-0.3422)
/ 2.5
30.19584
30.26553
(0.2308)
30.19394
(-0.0063)
30.20732
(0.0382) / 4.5
54.94092
55.09020
(0.2717)
54.98822
(0.0861)
54.90754
(0.0607) / 6.5
82.85807
82.77346
(-0.1021)
83.02933
(0.2067)
82.34480
(-0.6194) / 7.5
100.0750
100.0416
(-0.0334)
101.0379
(0.9622)
99.44022
(-0.6343) / 8.5
123.7737
123.3902
(-0.3098)
125.7025
(1.558)
122.2713
(-1.214) / 9.5
159.2841
159.1505
(-0.0839)
163.2747
(2.505)
156.5424
(-1.721)
/ 2.5
5.315309
5.352685
(0.7032)
5.322143
(0.1286)
5.310662
(-0.0872) / 4.5
11.70974
11.82681
(0.9998)
11.77782
(0.5814)
11.63229
(-0.6614) / 6.5
25.63909
25.60229
(-0.1435)
25.87856
(0.9340)
25.25031
(-1.516) / 7.5
39.35809
38.70995
(-1.647)
39.77607
(1.062)
38.64663
(-1.808) / 8.5
61.89523
60.89114
(-1.622)
62.50388
(0.9833)
60.55032
(-2.173) / 9.5
98.99869
97.99876
(-1.010)
99.84713
(0.8570)
96.50424
(-2.520)
/ 2.5
3.841270
3.866537
(0.6578)
3.846840
(0.1450)
3.835030
(-0.1623) / 4.5
9.415649
9.524377
(1.155)
9.457022
(0.4394)
9.340858
(-0.7944) / 6.5
23.00280
23.05296
(0.2181)
23.12889
(0.5482)
22.64740
(-1.545) / 7.5
36.70928
36.33018
(-1.033)
36.91044
(0.5480)
36.02870
(-1.854) / 8.5
59.25142
58.68982
(-0.9478)
59.54284
(0.4918)
57.96172
(-2.177) / 9.5
96.39079
95.89499
(-0.5144)
96.78750
(0.4112)
93.96129
(-2.520)
/ 2.5
3.249335
3.263346
(0.4312)
3.252559
(0.0992)
3.242529
(-0.2093) / 4.5
8.528104
8.598743
(0.8283)
8.551709
(0.2768)
8.455873
(-0.8470) / 6.5
21.99581
21.85784
(-0.6273)
22.06202
(0.3010)
21.65610
(-1.544) / 7.5
35.68652
35.42182
(-0.7417)
35.79059
(0.2916)
35.02611
(-1.851) / 8.5
58.22541
57.97296
(-0.4336)
58.37440
(0.2559)
56.96019
(-2.173) / 9.5
95.36729
95.26785
(-0.1043)
95.56848
(0.2110)
92.96592
(-2.518)
/ 2.5
3.054321
3.064810
(0.3434)
3.056664
(0.0767)
3.047352
(-0.2280) / 4.5
8.240900
8.295359
(0.6608)
8.257363
(0.1998)
8.169786
(-0.8630) / 6.5
21.67051
21.58273
(-0.4051)
21.71481
(0.2044)
21.33630
(-1.542) / 7.5
35.35475
35.15989
(-0.5512)
35.42457
(0.1975)
34.70132
(-1.848) / 8.5
57.89083
57.75955
(-0.2268)
57.99068
(0.1725)
56.63400
(-2.171) / 9.5
95.03181
95.04966
(0.0188)
95.16643
(0.1417)
92.64000
(-2.517)
/ 2.5
2.957356
2.965746
(0.2837)
2.959193
(0.0621)
2.950314
(-0.2380) / 4.5
8.099134
8.143309
(0.5454)
8.111765
(0.1560)
8.028636
(-0.8705) / 6.5
21.50991
21.44698
(-0.2926)
21.54287
(0.1523)
21.17850
(-1.541) / 7.5
35.19064
35.07432
(-0.3305)
35.24296
(0.1487)
34.54075
(-1.847) / 8.5
57.72495
57.64677
(-0.1354)
57.79991
(0.1299)
56.47237
(-2.170) / 9.5
94.86514
94.92248
(0.0604)
94.96622
(0.1066)
92.47816
(-2.516)
/ 2.5
2.899370
2.906363
(0.2412)
2.900880
(0.0521)
2.892286
(-0.2443) / 4.5
8.014694
8.051820
(0.4632)
8.024939
(0.1278)
7.944585
(-0.8748) / 6.5
21.41422
21.36564
(-0.2269)
21.44025
(0.1215)
21.08451
(-1.540) / 7.5
35.09274
35.00416
(-0.2524)
35.13445
(0.1189)
34.44499
(-1.846) / 8.5
57.62588
57.57519
(-0.0880)
57.68581
(0.1040)
56.37586
(-2.169) / 9.5
94.76549
94.83658
(0.0750)
94.84636
(0.0853)
92.38141
(-2.516)
Table SIII The same as in Table SI but for a 1:1 type electrolyte solution
/ 2.5
280.3014
280.2999
(-0.0005)
280.3046
(0.0011)
280.2983
(-0.0011) / 4.5
504.6835
504.6708
(-0.0025)
504.7078
(0.0048)
504.6626
(-0.0041) / 6.5
729.6443
729.5664
(-0.0107)
729.7732
(0.0177)
729.5445
(-0.0137) / 7.5
842.8477
842.6552
(-0.0228)
843.1500
(0.0359)
842.6431
(-0.0243) / 8.5
957.3948
956.9173
(-0.0499)
958.1304
(0.0768)
956.9742
(-0.0439) / 9.5
1075.073
1073.890
(-0.1100)
1076.922
(0.1720)
1074.182
(-0.0829)
/ 2.5
127.5485
127.5450
(-0.0027)
127.5535
(0.0039)
127.5433
(-0.0041) / 4.5
229.8816
229.8540
(-0.0120)
229.9225
(0.0178)
229.8438
(-0.0164) / 6.5
333.4437
333.2905
(-0.0459)
333.6820
(0.0715)
333.2533
(-0.0571) / 7.5
386.7663
386.4031
(-0.0939)
387.3445
(0.1495)
386.3700
(-0.1025) / 8.5
442.9340
442.0672
(-0.1957)
444.3587
(0.3217)
442.1115
(-0.1857) / 9.5
505.6078
503.5634
(-0.4043)
509.1160
(0.6939)
503.8701
(-0.3437)
/ 2.5
30.43912
30.42749
(-0.0382)
30.44947
(0.3400)
30.42946
(-0.0317) / 4.5
55.80100
55.72870
(-0.1296)
55.89632
(0.1708)
55.71448
(-0.1552) / 6.5
85.41306
85.18695
(-0.2647)
85.99021
(0.6757)
84.96244
(-0.5278) / 7.5
105.2414
104.9629
(-0.2646)
106.5391
(1.233)
104.3277
(-0.8684) / 8.5
133.2537
133.2373
(-0.0123)
135.9232
(2.003)
131.4785
(-1.332) / 9.5
176.9505
178.3664
(0.8002)
181.8406
(2.764)
173.6076
(-1.889)
/ 2.5
5.778353
5.778294
(0.0010)
5.789214
(0.1880)
5.766936
(-0.1976) / 4.5
13.30068
13.49961
(1.496)
13.37982
(0.5950)
13.19706
(-0.7793) / 6.5
30.23095
30.19613
(-0.1152)
30.50670
(0.9121)
29.77494
(-1.509) / 7.5
47.06113
46.22882
(-1.769)
47.49544
(0.9229)
46.19202
(-1.847) / 8.5
74.67354
73.63509
(-1.391)
75.30546
(0.8462)
73.04642
(-2.179) / 9.5
120.1456
119.4360
(-0.5906)
121.0118
(0.7209)
117.1136
(-2.524)
/ 2.5
4.341356
4.346362
(0.1153)
4.348388
(0.1620)
4.330367
(-0.2532) / 4.5
11.07615
11.29390
(1.966)
11.12131
(0.4077)
10.98002
(-0.8682) / 6.5
27.68135
27.96154
(-1.012)
27.82077
(0.5637)
27.25554
(-1.538) / 7.5
44.47363
44.28139
(-0.4323)
44.68446
(0.4741)
43.64853
(-1.855) / 8.5
72.08924
71.84975
(-0.3322)
72.38760
(0.4139)
70.51871
(-2.179) / 9.5
117.5826
117.6690
(0.0735)
117.9842
(0.3415)
114.6173
(-2.252)
/ 2.5
3.766468
3.774347
(0.2092)
3.770660
(0.1113)
3.755817
(-0.2828) / 4.5
10.21178
10.35104
(1.364)
10.23681
(0.2451)
10.12012
(-0.8977) / 6.5
26.69727
26.66994
(-0.1024)
26.77036
(0.2738)
26.28610
(-1.540) / 7.5
43.46890
43.41641
(-0.1208)
43.57758
(0.2500)
42.66392
(-1.852) / 8.5
71.07675
71.21904
(0.2002)
71.22882
(0.2140)
69.53113
(-2.175) / 9.5
116.5689
117.1220
(0.4745)
116.7721
(0.1743)
113.6323
(-2.519)
/ 2.5
3.577313
3.583904
(0.1842)
3.580289
(0.0832)
3.566809
(-0.2937) / 4.5
9.931051
10.04359
(1.133)
9.948334
(0.1740)
9.841111
(-0.9058) / 6.5
26.37761
26.40753
(0.1134)
26.42711
(0.1877)
25.97163
(-1.539) / 7.5
43.14133
43.18341
(0.0975)
43.21452
(0.1697)
42.34333
(-1.850) / 8.5
70.74519
70.97557
(0.3256)
70.84722
(0.1442)
69.20809
(-2.173) / 9.5
116.2355
116.8365
(0.5171)
116.3715
(0.1170)
113.3087
(-2.518)
/ 2.5
3.483296
3.488882
(0.1604)
3.485601
(0.0662)
3.4728873
(-0.2988) / 4.5
9.792219
9.885923
(0.9569)
9.805411
(0.1347)
9.703187
(-0.9094) / 6.5
26.21941
26.26579
(0.1769)
26.25683
(0.1427)
25.81608
(-1.538) / 7.5
42.97895
43.04897
(0.1629)
43.03412
(0.1283)
42.18449
(-1.849) / 8.5
70.58054
70.82064
(0.3402)
70.65730
(0.1087)
69.04774
(-2.172) / 9.5
116.0697
116.6357
(0.4876)
116.1719
(0.0881)
113.1478
(-2.517)
/ 2.5
3.427081
3.431908
(0.1408)
3.420962
(-0.1785)
3.416709
(-0.3027) / 4.5
9.709432
9.789526
(0.8249)
9.720099
(0.1099)
9.620961
(-0.9114) / 6.5
26.12502
26.17559
(0.1936)
26.15510
(0.1151)
25.72331
(-1.538) / 7.5
42.88198
42.95961
(0.0995)
42.92625
(0.1032)
42.08966
(-1.848) / 8.5
70.48211
70.71196
(0.3261)
70.54364
(0.0873)
68.95191
(-2.171) / 9.5
115.9704
116.4880
(0.4463)
116.0523
(0.0706)
113.0515
(-2.517)
Table SIV Dimensionless electrical potential distribution for a spherical colloidal particle immersed in a 3:1 type electrolyte solution
，/ 0.01
2.247839
2.247831
(-0.0004)
2.247872
(0.0015)
2.247808
(-0.0014) / 0.02
1.113168
1.113123
(-0.0040)
1.113350
(0.0163)
1.112997
(-0.0154) / 0.03
0.7349956
0.7349397
(-0.0076)
0.7352292
(0.0318)
0.5457053
(-0.0296) / 0.04
0.5459467
0.5458862
(-0.0111)
0.5462059
(0.0475)
0.5456132
(-0.0442) / 0.05
0.4325480
0.4324853
(-0.0145)
0.4328227
(0.0635)
0.4322921
(-0.0592) / 0.06
0.3569753
0.3569118
(-0.0178)
0.3572601
(0.0798)
0.3567092
(-0.0746)
，
/ 0.01
4.046134
4.046110
(-0.0006)
4.046218
(0.0021)
4.046082
(-0.0013) / 0.02
2.003977
2.003852
(-0.0062)
2.004463
(0.0243)
2.003686
(-0.0145) / 0.03
1.323396
1.323241
(-0.0117)
1.324025
(0.0475)
1.323022
(-0.0283) / 0.04
0.9831769
0.9830093
(-0.0171)
0.9838805
(0.0716)
0.9827570
(-0.0427) / 0.05
0.7790982
0.7789243
(-0.0223)
0.7798473
(0.0961)
0.7786496
(-0.0576) / 0.06
0.6430892
0.6429123
(-0.0275)
0.6438693
(0.1213)
0.6426214
(-0.0728)
，
/ 0.03
1.651066
1.650960
(-0.0064)
1.651256
(0.0115)
1.650840
(-0.0137) / 0.05
0.9721471
0.9719642
(-0.0188)
0.9724960
(0.0359)
0.9717384
(-0.0421) / 0.07
0.6813695
0.6811591
(-0.0308)
0.6817885
(0.0615)
0.6808815
(-0.0717) / 0.09
0.5199703
0.5197490
(-0.0426)
0.5204292
(0.0883)
0.5194377
(-0.1025) / 0.11
0.4173821
0.4171573
(-0.0539)
0.4178664
(0.1160)
0.4168194
(-0.1349) / 0.13
0.3464638
0.3462394
(-0.0647)
0.3469648
(0.1446)
0.3458776
(-0.1692)
，
/ 0.03
2.972085
2.971782
(-0.0102)
2.972503
(0.0141)
2.971809
(-0.0093) / 0.05
1.750587
1.750077
(-0.0291)
1.751411
(0.0471)
1.750067
(-0.0298) / 0.07
1.227521
1.226940
(-0.0473)
1.228540
(0.0830)
1.226881
(-0.0522) / 0.09
0.9371956
0.9365847
(-0.0652)
0.9383339
(0.1215)
0.9364741
(-0.0770) / 0.11
0.7526475
0.7520258
(-0.0826)
0.7538647
(0.1617)
0.7518711
(-0.1032) / 0.13
0.6250545
0.6244317
(-0.0996)
0.6263289
(0.2039)
0.6242397
(-0.1304)
，
/ 0.1
2.229868
2.229482
(-0.0173)
2.229948
(0.0036)
2.229738
(-0.0058) / 0.3
0.6205031
0.6185039
(-0.3222)
0.6213221
(0.1320)
0.6195119
(-0.1596) / 0.5
0.3090705
0.3072940
(-0.5748)
0.3100919
(0.3305)
0.3077874
(-0.4149) / 0.7
0.1824760
0.1810644
(-0.7736)
0.1835484
(0.5877)
0.1808877
(-0.8699) / 0.9
0.1169733
0.1158910
(-0.9253)
0.1179915
(0.8705)
0.1152731
(-1.453) / 1.1
0.0787273
0.0779087
(-1.040)
0.0779764
(-0.9538)
0.0772181
(-1.916)
，
/ 0.1
4.011105
4.009810
(-0.0323)
4.010680
(-0.0106)
4.011254
(0.0037) / 0.3
1.118968
1.113465
(-0.4918)
1.119650
(0.0609)
1.119000
(0.0031) / 0.5
0.5610525
0.5561576
(-0.8724)
0.5627176
(0.2968)
0.5604193
(-0.1125) / 0.7
0.3331793
0.3291932
(-1.196)
0.3353378
(0.6478)
0.3321235
(-0.3162) / 0.9
0.2145604
0.2114296
(-1.459)
0.2168630
(1.073)
0.2130457
(-0.7048) / 1.1
0.1449122
0.1424978
(-1.666)
0.1472416
(1.607)
0.1430496
(-1.284)
，
/ 1.0
2.060510
2.060780
(0.0131)
2.059276
(-0.0599)
2.060948
(0.0216) / 1.5
0.8964832
0.9014663
(0.5558)
0.8955561
(-0.1034)
0.8971844
(0.0816) / 2.0
0.4322536
0.4367674
(1.044)
0.4327847
(0.1229)
0.4324758
(0.0620) / 2.5
0.2175898
0.2201950
(1.197)
0.2188478
(0.5782)
0.2163898
(-0.5239) / 3.0
0.1123422
0.1136879
(1.198)
0.1136759
(1.187)
0.1099504
(-2.060) / 3.5
0.0591010
0.0597899
(1.166)
0.0603177
(2.059)
0.0571614
(-3.106)
，
/ 1.0
3.609054
3.588902
(-0.5584)
3.593630
(-0.4274)
3.614237
(0.1440) / 1.5
1.531676
1.515418
(-1.061)
1.515928
(-1.028)
1.542612
(0.7178) / 2.0
0.7498868
0.7456811
(-0.5069)
0.7423697
(-1.002)
0.7566389
(0.9128) / 2.5
0.3843374
0.3834851
(-0.2218)
0.3823118
(-0.5270)
0.3877977
(0.9332) / 3.0
0.2011093
0.2007613
(-0.1730)
0.2016860
(-0.2868)
0.2015227
(0.2871) / 3.5
0.1067007
0.1064708
(-0.2155)
0.1084941
(1.681)
0.1051928
(-1.213)
，
/ 1.5
2.622693
2.581401
(-1.574)
2.599169
(-0.8969)
2.633701
(0.4211) / 2.0
1.278026
1.255408
(-1.770)
1.261912
(-1.261)
1.290144
(0.9550) / 2.5
0.6663770
0.6574153
(-1.345)
0.6585891
(-1.169)
0.6734930
(1.088) / 3.0
0.3549095
0.3508797
(-1.135)
0.3526114
(-0.6475)
0.3586787
(1.114) / 3.5
0.1907590
0.1885728
(-1.146)
0.1910848
(0.1708)
0.1912899
(0.4064) / 4.0
0.1032598
0.1019977
(-1.222)
0.1049208
(1.609)
0.1018488
(-1.052)
，
/ 2.0
2.042201
1.992640
(-2.427)
2.017690
(-1.200)
2.055799
(0.6689) / 2.5
1.069462
1.043806
(-2.399)
1.054315
(-1.416)
1.081298
(1.118) / 3.0
0.5789346
0.5670351
(-2.055)
0.5716900
(-1.251)
0.5859405
(1.242) / 3.5
0.3159689
0.3097949
(-1.954)
0.3138726
(-0.6635)
0.3195933
(1.227) / 4.0
0.1729353
0.1694421
(-2.020)
0.1732678
(0.1922)
0.1732418
(0.3725) / 4.5
0.0949636
0.0929517
(-2.119)
0.0966214
(1.746)
0.0935665
(-0.9913)
represents the ‘exact’ numerical results from the present paper, the results calculated with the approximate analytical expression Eq. (70) in Ref. [33], whereas the results calculated with the present Eq. (19)inscr, and the present Eq. (19)circum. The figures between brackets are percent relative errors calculated with a formulae of .
Table SV The same as in Table SIV but for a 2:1 type electrolyte solution
，/ 0.01
2.247792
2.247789
(-0.0001)
2.247807
(0.0007)
2.247773
(-0.0008) / 0.02
1.112924
1.112910
(-0.0013)
1.113013
(0.0080)
1.112822
(-0.0092) / 0.03
0.7347016
0.7346846
(-0.0023)
0.7348169
(0.0157)
0.7345713
(-0.0178) / 0.04
0.5456372
0.5456187
(-0.0034)
0.5457656
(0.0235)
0.5454924
(-0.0266) / 0.05
0.4322356
0.4322164
(-0.0044)
0.4323720
(0.0316)
0.4320821
(-0.0356) / 0.06
0.3566656
0.3566462
(-0.0054)
0.3568074
(0.0397)
0.3565063
(-0.0447)
，
/ 0.01
4.045997
4.045988
(-0.0002)
4.046030
(0.0008)
4.045968
(-0.0007) / 0.02
2.003298
2.003255
(-0.0021)
2.003515
(0.0108)
2.003135
(-0.0082) / 0.03
1.322583
1.322530
(-0.0040)
1.322872
(0.0219)
1.322369
(-0.0162) / 0.04
0.9823187
0.9822618
(-0.0058)
0.9826485
(0.0336)
0.9820726
(-0.0251) / 0.05
0.7782281
0.7781693
(-0.0076)
0.7785832
(0.0456)
0.7779600
(-0.0345) / 0.06
0.6422224
0.6421628
(-0.0093)
0.6425953
(0.0581)
0.6419390
(-0.0442)
，
/ 0.03
1.650534
1.650497
(-0.0022)
1.650622
(0.0053)
1.650389
(-0.0088) / 0.05
0.9712640
0.9711998
(-0.0066)
0.9714281
(0.0169)
0.9710008
(-0.0272) / 0.07
0.6803893
0.6803158
(-0.0108)
0.6805894
(0.0294)
0.6800735
(-0.0465) / 0.09
0.5189708
0.5188938
(-0.0148)
0.5191922
(0.0427)
0.5186251
(-0.0668) / 0.11
0.4163947
0.4163167
(-0.0187)
0.4166298
(0.0565)
0.4160297
(-0.0878) / 0.13
0.3455024
0.3454248
(-0.0225)
0.3457469
(0.0708)
0.3451239
(-0.1098)
，
/ 0.03
2.970595
2.970474
(-0.0041)
2.970704
(0.0037)
2.970459
(-0.0046) / 0.05
1.748182
1.747981
(-0.0115)
1.748472
(0.0166)
1.747904
(-0.0159) / 0.07
1.224864
1.224637
(-0.0185)
1.225260
(0.0323)
1.224506
(-0.0293) / 0.09
0.9344794
0.9342433
(-0.0253)
0.9349479
(0.0501)
0.9340495
(-0.0460) / 0.11
0.7499512
0.7497127
(-0.0318)
0.7504693
(0.0691)
0.7494671
(-0.0646) / 0.13
0.6224148
0.6221776
(-0.0381)
0.6229711
(0.0894)
0.6218913
(-0.0841)
，
/ 0.1
2.228410
2.228236
(-0.0078)
2.228404
(-0.0003)
2.228306
(-0.0047) / 0.3
0.6137814
0.6129444
(-0.1364)
0.6140788
(0.0485)
0.6129382
(-0.1378) / 0.5
0.3036110
0.3028989
(-0.2345)
0.3040527
(0.1455)
0.3025564
(-0.3485) / 0.7
0.1783954
0.1778441
(-0.3090)
0.1788854
(0.2747)
0.1772396
(-0.6496) / 0.9
0.1139728
0.1135570
(-0.3648)
0.1144469
(0.4160)
0.1128770
(-0.9632) / 1.1
0.0765236
0.0762124
(-0.4067)
0.0769724
(0.5865)
0.0756130
(-1.191)
，
/ 0.1
4.006714
4.006040
(-0.0168)
4.005922
(-0.0198)
4.007002
(0.0072) / 0.3
1.101323
1.098748
(-0.2338)
1.100540
(-0.0711)
1.101990
(0.0603) / 0.5
0.5464603
0.5443228
(-0.3912)
0.5466025
(0.0260)
0.5461190
(-0.0631) / 0.7
0.3220036
0.3203428
(-0.5158)
0.3226352
(0.1961)
0.3211724
(-0.2595) / 0.9
0.2061791
0.2049157
(-0.6128)
0.2070183
(0.4070)
0.2050552
(-0.5471) / 1.1
0.1386648
0.1377117
(-0.6873)
0.1396095
(0.6813)
0.1374285
(-0.8937)
，
/ 1.0
2.037730
2.037824
(0.0461)
2.036078
(-0.0811)
2.038106
(0.0185) / 1.5
0.8488084
0.8523199
(0.4137)
0.8470566
(-0.2064)
0.8489414
(0.0163) / 2.0
0.3969610
0.4009605
(1.008)
0.3965231
(-0.1103)
0.3960760
(-0.2211) / 2.5
0.1959479
0.1987557
(1.433)
0.1961987
(0.1280)
0.1942510
(-0.8599) / 3.0
0.1000042
0.1016843
(1.680)
0.1004349
(0.4307)
0.0982506
(-1.730) / 3.5
0.0522673
0.0532160
(1.815)
0.0527428
(0.9097)
0.0510788
(-2.203)
，
/ 1.0
3.546806
3.526228
(-0.5802)
3.529177
(-0.4970)
3.553113
(0.1779) / 1.5
1.425303
1.403749
(-1.512)
1.408018
(-1.213)
1.438786
(0.9467) / 2.0
0.6701338
0.6629727
(-1.069)
0.6614543
(-1.295)
0.6773250
(1.075) / 2.5
0.3334569
0.3319105
(-0.4637)
0.3299569
(-1.050)
0.3360892
(0.7936) / 3.0
0.1711608
0.1711050
(-0.0326)
0.1700952
(-0.6226)
0.1712439
(0.0609) / 3.5
0.0897693
0.0899705
(-0.2241)
0.0899250
(0.1734)
0.0890472
(-0.7647)
，
/ 1.5
2.510767
2.466211
(-1.775)
2.485267
(-1.016)
2.523824
(0.5203) / 2.0
1.164958
1.138419
(-2.278)
1.148008
(-1.455)
1.179277
(1.230) / 2.5
0.5841477
0.5736886
(-1.790)
0.5755721
(-1.468)
0.5912058
(1.211) / 3.0
0.3023409
0.2986568
(-1.219)
0.2987349
(-1.192)
0.3050183
(0.8919) / 3.5
0.1594871
0.1581862
(-0.8157)
0.1582953
(-0.7473)
0.1596202
(0.1017) / 4.0
0.0853564
0.0848671
(-0.5732)
0.0854244
(0.0797)
0.0847203
(-0.6893)
，
/ 2.0
1.911990
1.859231
(-2.759)
1.886185
(-1.350)
1.927749
(0.8247) / 2.5
0.9561356
0.9283230
(-2.909)
0.9406925
(-1.615)
0.9694744
(1.397) / 3.0
0.4986955
0.4868445
(-2.376)
0.4908925
(-1.565)
0.5051104
(1.290) / 3.5
0.2649498
0.2600682
(-1.842)
0.2616168
(-1.258)
0.2673056
(0.8982) / 4.0
0.1424885
0.1403843
(-1.477)
0.1414002
(-0.7638)
0.1424955
(0.0316) / 4.5
0.0774139
0.0764412
(-1.256)
0.0775046
(0.1172)
0.0768251
(-0.6820)
Table SVI The same as in Table SIV but for a 1:1 type electrolyte solution