surface-tension-calculator/lib/scripts/juszas_equation.dart

// ========== Juza's equation for 1/H ==========
import 'dart:math';

double HJuza(double _S_diamRatio, double _K) {
  // LowerS, UpperS, Ke, Kex, Kep, K3, K2, K1, K0

  // 0.82 - 0.999
  List<List<double>> Coefficient8 = [
    [
      0.82,
      0.83,
      1791452.8,
      533.85850,
      170.55837,
      -81676.15812,
      202187.89690,
      -166836.27680,
      45888.22973,
    ],
    [
      0.83,
      0.84,
      189.07578,
      272.52455,
      72.730022,
      -19963.60152,
      50019.79936,
      -41775.38186,
      11629.85610,
    ],
    [
      0.84,
      0.85,
      7.1549709,
      165.45945,
      35.285687,
      -6944.66848,
      17609.43832,
      -14883.84379,
      4193.34232,
    ],
    [
      0.85,
      0.87,
      1.1496269,
      95.066407,
      12.600013,
      -2158.91585,
      5571.60176,
      -4792.82331,
      1374.26272,
    ],
    [
      0.87,
      0.895,
      0.47873040,
      50.357240,
      0.089787883,
      -567.76534,
      1503.51828,
      -1327.11835,
      390.45562,
    ],
    [
      0.895,
      0.93,
      0.35255000,
      25.498893,
      -5.4176608,
      -165.99710,
      454.58851,
      -414.93772,
      126.23908,
    ],
    [
      0.93,
      0.97,
      0.32002037,
      6.8474560,
      -8.0901766,
      -102.84970,
      293.25377,
      -278.69176,
      88.27639,
    ],
    [
      0.97,
      0.99,
      0.30845061,
      -32.343947,
      -10.455428,
      -475.69091,
      1398.86173,
      -1371.17931,
      448.00538,
    ],
    [
      0.99,
      0.999,
      0.30110729,
      -333.50440,
      -15.711260,
      -11334.69334,
      33822.93507,
      -33642.61426,
      11154.37157,
    ],
  ];

  // 0.635 - 0.997
  List<List<double>> Coefficient9 = [
    [
      0.635,
      0.645,
      58249804,
      119.64583,
      89.483167,
      -28072.11478,
      53918.28040,
      -34519.94034,
      7366.77050,
    ],
    [
      0.645,
      0.66,
      5100.2910,
      70.920100,
      46.811007,
      -9051.10879,
      17726.62108,
      -15572.21470,
      2518.10214,
    ],
    [
      0.66,
      0.685,
      19.518159,
      38.509198,
      19.951285,
      -2338.00251,
      4719.64936,
      -3175.58038,
      712.17229,
    ],
    [
      0.685,
      0.72,
      1.3823760,
      20.055606,
      5.9746092,
      -522.67397,
      1102.26575,
      -774.75596,
      181.49582,
    ],
    [
      0.72,
      0.77,
      0.49074291,
      10.484929,
      -0.31885445,
      -111.99730,
      250.54286,
      -186.78287,
      46.40581,
    ],
    [
      0.77,
      0.84,
      0.34607161,
      5.4063548,
      -2.9788620,
      -24.21100,
      58.53312,
      -47.15244,
      12.65668,
    ],
    [
      0.84,
      0.93,
      0.31342828,
      2.1140055,
      -4.1151543,
      -9.16969,
      24.37544,
      -21.58758,
      6.36954,
    ],
    [
      0.93,
      0.98,
      0.30397966,
      -3.6334200,
      -4.9395699,
      -29.80626,
      85.43510,
      -81.61766,
      25.98669,
    ],
    [
      0.98,
      0.997,
      0.30007321,
      -34.095653,
      -6.1531194,
      -434.11439,
      1287.65238,
      -1273.10762,
      419.56923,
    ],
  ];

  // 0.17 - 0.983
  List<List<double>> Coefficient10 = [
    [
      0.17,
      0.30,
      0.31081678,
      -0.086278355,
      -2.7023254,
      -13.95071,
      10.30398,
      -2.49619,
      0.19805,
    ],
    [
      0.30,
      0.45,
      0.30636442,
      -0.094871613,
      -2.7246428,
      0.38766,
      -0.44128,
      0.16613,
      -0.02068,
    ],
    [
      0.45,
      0.68,
      0.31156188,
      -0.063734909,
      -2.6789763,
      0.41537,
      -0.71168,
      0.40321,
      -0.07551,
    ],
    [
      0.68,
      0.90,
      0.31195754,
      -0.092720991,
      -2.6863859,
      -0.44813,
      1.06637,
      -0.84260,
      0.22106,
    ],
    [
      0.90,
      0.983,
      0.30712046,
      -1.5619311,
      -2.9809169,
      -5.74538,
      16.23781,
      -15.29128,
      4.79808,
    ],
  ];

  // 0.06 - 0.953
  List<List<double>> Coefficient11 = [
    [
      0.06,
      0.08,
      1.6030433,
      0.043380701,
      -0.15208454,
      -1341.32950,
      282.27311,
      -19.71010,
      0.45664,
    ],
    [
      0.08,
      0.13,
      0.85491410,
      -0.056761738,
      -0.65372414,
      -160.97221,
      50.59168,
      -5.23625,
      0.17842,
    ],
    [
      0.13,
      0.20,
      0.57401485,
      -0.15265815,
      -1.0443069,
      -42.79943,
      21.22139,
      -3.47357,
      0.18765,
    ],
    [
      0.20,
      0.30,
      0.41622542,
      -0.27871823,
      -1.4464670,
      -14.08741,
      10.58863,
      -2.63159,
      0.21621,
    ],
    [
      0.30,
      0.44,
      0.33587066,
      -0.42674255,
      -1.8022482,
      -3.22540,
      3.58964,
      -1.32194,
      0.16106,
    ],
    [
      0.44,
      0.75,
      0.31504207,
      -0.51197565,
      -1.9499037,
      0.07609,
      -0.13681,
      0.08090,
      -0.01572,
    ],
    [
      0.75,
      0.953,
      0.31658938,
      -0.49808609,
      -1.9290368,
      -0.24018,
      0.61450,
      -0.52258,
      0.14771,
    ],
  ];

  // 0.10 - 0.902
  List<List<double>> Coefficient12 = [
    [
      0.10,
      0.12,
      103.56308,
      1.2019976,
      4.4869062,
      -6625.95443,
      2292.46751,
      -264.28560,
      10.15218,
    ],
    [
      0.12,
      0.14,
      2.1585254,
      0.34129627,
      0.83653215,
      -742.15388,
      289.52312,
      -37.59979,
      1.62555,
    ],
    [
      0.14,
      0.19,
      0.65654048,
      0.031877859,
      -0.37693028,
      -66.92134,
      33.18430,
      -5.45788,
      0.29773,
    ],
    [
      0.19,
      0.27,
      0.45076908,
      -0.10378254,
      -0.82836350,
      -10.66154,
      7.36263,
      -1.68453,
      0.12768,
    ],
    [
      0.27,
      0.40,
      0.37085833,
      -0.21965481,
      -1.1287016,
      -2.87493,
      2.88810,
      -0.95966,
      0.10546,
    ],
    [
      0.40,
      0.55,
      0.33605594,
      -0.33317467,
      -1.3397591,
      -0.70394,
      1.00402,
      -0.47492,
      0.07450,
    ],
    [
      0.55,
      0.902,
      0.32790337,
      -0.39597877,
      -1.4180887,
      0.00490,
      -0.01070,
      0.00769,
      -0.00182,
    ],
  ];

  List<List<double>> Coeff = [];
  if (_K == 0.8) {
    Coeff = Coefficient8;
  }
  if (_K == 0.9) {
    Coeff = Coefficient9;
  }
  if (_K == 1.0) {
    Coeff = Coefficient10;
  }
  if (_K == 1.1) {
    Coeff = Coefficient11;
  }
  if (_K == 1.2) {
    Coeff = Coefficient12;
  }

  // Juza 1996/1997 Equation: 8
  for (var Entry_k in Coeff) {
    if (Entry_k[0] <= _S_diamRatio && _S_diamRatio <= Entry_k[1]) {
      double HInv =
          Entry_k[2] *
              pow(_S_diamRatio, (Entry_k[3] * log(_S_diamRatio) + Entry_k[4])) +
          Entry_k[5] * pow(_S_diamRatio, 3.0) +
          Entry_k[6] * pow(_S_diamRatio, 2.0) +
          Entry_k[7] * _S_diamRatio +
          Entry_k[8];
      return HInv;
    }
  }

  return 0;
}