% Representation of experimental data for the publication entitled: % "Insulating Travelling-Wave Electrophoresis" % Dataset corresponding to Figure 5 in the text. clear;clc;close all % General Parameters (SI units) sigma = [1.5 3 6]*10^(-3); epsilon = 80*8.85e-12; V_1 = 10; Vth = 25e-3; a = 10e-6; E_1 = V_1/1e-3; D = 2e-9; Eth = Vth/a; E0 = E_1/Eth; eta = 1e-3; u0 = epsilon*a*E_1^2/eta; omega0=D/a^2; R = 1e-5; % Colours defined for the plots colorR = [212 56 37]/255; colorO = [239 135 51]/255; colorY = [248 206 70]/255; colorG = [70 156 118]/255; colorB = [56 117 176]/255; %% Experimental measurements from PIV pxum = 1.66; fps = 16.67; x=1:30; circumference = 2*pi*x*75/30; rp_exp = x*75/30; % px rp_exp = rp_exp/pxum; % um fp_exp = [13 17 21 28 36 46]; % Hz % 1.7mS/m c_13_1 = [ NaN NaN NaN NaN NaN NaN... 55.7328 82.1288 108.1328 136.7982 161.7157 192.5982 226.0549... 270.9005 316.1597 349.6657 372.9548 380.2145 385.0823 369.7442... 347.4442 324.0577 292.2735 266.3806 246.9016 236.6650 229.8576... 223.7105 217.1397 NaN]; % px^2/fr v_13_1 =c_13_1./circumference; % px/fr c_17_1 = [ NaN NaN NaN NaN NaN NaN... 46.7318 75.4744 105.1968 135.0144 163.5574 189.2616 211.6781... 222.0691 221.8913 220.1391 217.1953 208.9407 199.0663 192.2640... 184.7047 173.9517 160.3800 146.7473 133.5661 120.0088 106.6085... 95.3773 NaN NaN]; v_17_1 =c_17_1./circumference; c_21_1 = [ NaN NaN NaN NaN NaN NaN... NaN 66.9126 92.0635 116.9306 135.0233 148.4937 161.9871... 173.7403 181.6977 183.1349 187.2674 188.6314 182.9895 173.4806... 159.4983 143.3461 133.3136 121.6780 113.8396 104.5600 94.5287... 88.2508 81.3745 NaN]; v_21_1 =c_21_1./circumference; c_28_1 = [ NaN NaN NaN NaN NaN NaN... 24.6538 42.8310 65.2884 88.2906 107.6233 120.0729 127.9941... 136.3905 143.9407 148.1213 148.9410 144.2062 135.6827 125.8144... 113.1574 101.6231 94.0466 88.6490 83.8646 76.6943 71.9993... 66.2441 NaN NaN]; v_28_1 =c_28_1./circumference; c_36_1 = [ NaN NaN NaN NaN NaN NaN... NaN 29.7251 49.7586 64.9580 79.9438 97.1044 111.8788... 123.4349 133.7907 139.7377 138.1592 130.6750 121.3075 113.5967... 106.8515 98.8248 94.4317 89.8773 NaN NaN NaN... 51.3187 NaN NaN]; v_36_1 =c_36_1./circumference; c_46_1 = [ NaN NaN NaN NaN NaN NaN... 21.5728 32.0253 46.8276 57.4681 65.5417 73.2394 80.1622... 84.4618 84.4039 81.1378 78.1544 74.1681 72.1020 72.4821... 71.9848 66.6850 63.8430 61.8910 57.1863 52.1088 45.9140... 41.6369 NaN NaN]; v_46_1 =c_46_1./circumference; c_60_1 = [ NaN NaN NaN NaN NaN NaN... NaN 25.7446 38.1565 53.3012 64.5386 70.2261 73.8238... 75.1614 74.2901 73.2186 70.8184 67.1127 64.3744 61.2575... 57.9865 54.3124 50.9545 48.8119 45.8285 43.6989 35.9091... 31.3670 NaN NaN]; v_60_1 =c_60_1./circumference; % 3.0mS/m c_13_3 = [ NaN NaN NaN NaN NaN NaN... 88.4829 124.7820 145.6562 164.0535 176.5984 191.6790 212.5621... 247.0618 285.2704 311.9448 329.9438 337.8986 338.6292 334.4151... 325.0016 316.4255 309.0068 305.4618 290.5266 273.0103 254.2842... 237.1812 NaN NaN]; v_13_3 =c_13_3./circumference; c_17_3 = [ NaN NaN NaN NaN NaN NaN... NaN 155.0192 195.3148 220.7019 239.9675 254.1918 261.8219... 261.4517 254.6844 243.8277 236.9746 229.8423 214.6460 199.0473... 183.2103 169.2464 156.0233 147.0796 139.2486 127.4098 119.4144... 114.1851 NaN NaN]; v_17_3 =c_17_3./circumference; c_21_3 = [ NaN NaN NaN NaN NaN NaN... NaN 104.1596 135.5458 161.7381 180.9811 191.2881 192.1704... 189.7471 189.7928 189.9229 187.4625 178.8577 168.6074 158.3234... 148.7344 141.2575 128.6707 116.3554 107.7145 103.2376 95.4446... 90.0554 NaN NaN]; v_21_3 =c_21_3./circumference; c_28_3 = [ NaN NaN NaN NaN NaN NaN... NaN 66.6904 84.9192 95.9624 102.7737 107.1876 108.0110... 108.3020 104.6597 96.1072 87.7040 81.6400 75.6214 67.0457... 56.5503 51.7564 42.2574 33.1226 25.0401 19.7342 12.4565... 8.0223 7.4117 NaN]; v_28_3 =c_28_3./circumference; c_36_3 = [ NaN NaN NaN NaN NaN NaN... NaN 73.8166 96.6530 118.6481 133.5869 140.2262 142.3186... 141.2906 136.2597 128.6455 127.1671 127.2143 120.4758 112.0228... 106.7524 100.1572 91.3954 82.2273 71.8400 63.5185 56.7375... NaN NaN NaN]; v_36_3 =c_36_3./circumference; c_46_3 = [ NaN NaN NaN NaN NaN NaN... NaN 52.5328 66.8066 75.6127 83.6565 88.2324 88.0075... 86.9008 86.5582 85.2776 83.2067 80.0098 77.2032 73.8150... 69.9765 64.9081 62.0601 55.7546 50.0862 46.0404 41.3259... 37.2183 37.6991 NaN]; v_46_3 =c_46_3./circumference; % 6mS/m c_13_6 = [ NaN NaN NaN NaN NaN NaN... NaN 113.9492 152.4944 184.7239 205.6802 222.5384 237.2576... 249.7188 256.6391 251.8777 235.9813 221.6319 203.1915 188.3704... 171.7073 153.3472 137.8011 125.4943 114.1173 104.0493 94.6731... 90.8929 NaN NaN]; v_13_6 =c_13_6./circumference; c_17_6 = [ NaN NaN NaN NaN NaN NaN... NaN NaN 162.6191 187.8248 204.0590 215.6086 219.0174... 215.0694 210.1779 202.5394 192.9068 182.6549 171.6102 161.0599... 150.1559 138.8750 127.9291 117.4405 107.9473 99.1740 90.4040... 82.6934 74.8113 NaN]; v_17_6 =c_17_6./circumference; c_21_6 = [NaN NaN NaN NaN NaN NaN NaN... 96.2802 120.5397 129.4357 134.7874 137.9504 135.5245 130.3754... 127.2987 125.8548 119.7955 108.1520 97.6717 89.8536 83.6342... 77.8131 73.0040 67.0554 57.0142 47.8872 42.5130 37.2564... 36.3763 NaN]; v_21_6 =c_21_6./circumference; c_28_6 = [ NaN NaN NaN NaN NaN NaN... NaN 71.6516 89.2452 99.1459 101.2147 101.9525 103.0044... 100.1589 98.0570 95.3706 87.4261 80.0163 72.0606 66.2658... 59.4688 54.4824 50.7522 47.1349 44.5248 41.1688 36.1375... 30.3781 29.1113 NaN]; v_28_6 =c_28_6./circumference; c_36_6 = [ NaN NaN NaN NaN NaN NaN... NaN 60.0723 68.2756 69.4831 67.9771 65.1803 62.6307... 60.4221 59.8463 58.6495 55.6281 52.3041 48.8400 43.5724... 40.3357 35.9799 30.7977 25.5306 20.8348 16.6499 13.0749... 8.2313 NaN NaN]; v_36_6 =c_36_6./circumference; c_46_6 = [ NaN NaN NaN NaN NaN NaN... NaN 55.4252 57.5583 57.6325 56.3719 54.1191 52.4685... 50.3153 46.7844 44.0346 42.7636 41.7333 39.3983 36.4676... 34.2401 32.6580 28.6704 23.9055 19.8076 18.5731 13.9467... 13.0754 NaN NaN]; v_46_6 =c_46_6./circumference; % Creation of a single matrix containing all experimental information % in the form M=M(f,sigma,r) Mexp = zeros(6,3,30); Mexp(1,1,:) = v_13_1; Mexp(1,2,:)=v_13_3; Mexp(1,3,:)=v_13_6; Mexp(2,1,:) = v_17_1; Mexp(2,2,:)=v_17_3; Mexp(2,3,:)=v_17_6; Mexp(3,1,:) = v_21_1; Mexp(3,2,:)=v_21_3; Mexp(3,3,:)=v_21_6; Mexp(4,1,:) = v_28_1; Mexp(4,2,:)=v_28_3; Mexp(4,3,:)=v_28_6; Mexp(5,1,:) = v_36_1; Mexp(5,2,:)=v_36_3; Mexp(5,3,:)=v_36_6; Mexp(6,1,:) = v_46_1; Mexp(6,2,:)=v_46_3; Mexp(6,3,:)=v_46_6; % px/fr M_EXP = Mexp/pxum*fps; % um/s %% Figure 2a % Distance sweep for a fixed frequency of f = 17 Hz % Experimental values vE_f17Hz_1mSm = squeeze(M_EXP(2,1,10:end)); vE_f17Hz_3mSm = squeeze(M_EXP(2,2,10:end)); vE_f17Hz_6mSm = squeeze(M_EXP(2,3,10:end)); oE_f17Hz_1mSm = vE_f17Hz_1mSm'./rp_exp(10:end); oE_f17Hz_3mSm = vE_f17Hz_3mSm'./rp_exp(10:end); oE_f17Hz_6mSm = vE_f17Hz_6mSm'./rp_exp(10:end); % HFA predictions omega = 2*pi*17; zeta = [79.44 74.605 64.934]*1e-3; mu = epsilon*zeta(1)/eta; mutilde = mu*E_1./omega/R; r0 = linspace(1.5,4.5); omega_HFA = zeros(size(omega)); for ii = 1:length(r0) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde^2/r0(ii)^6); end oHFA_f17Hz_1mSm = omega_HFA; mu = epsilon*zeta(2)/eta; mutilde = mu*E_1./omega/R; omega_HFA = zeros(size(omega)); for ii = 1:length(r0) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde^2/r0(ii)^6); end oHFA_f17Hz_3mSm = omega_HFA; mu = epsilon*zeta(3)/eta; mutilde = mu*E_1./omega/R; omega_HFA = zeros(size(omega)); for ii = 1:length(r0) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde^2/r0(ii)^6); end oHFA_f17Hz_6mSm = omega_HFA; % PLOTS figure hold on box on ax=gca; ax.FontSize = 20; ax.FontName = 'Times New Roman'; ax.LineWidth = 1; set(gca, 'XScale','log', 'YScale','log') xlabel('\fontname{Times New Roman} \fontsize{24} r_0 (\mum)') ylabel('\fontname{Times New Roman} \fontsize{24} \omega_p (rad/s)') title('f = 17 Hz') h1=plot(rp_exp(10:end),oE_f17Hz_1mSm,'ok','MarkerSize',8,'MarkerFaceColor',colorR,... 'LineWidth',1.25,'Color',colorR); h2=plot(rp_exp(10:end),oE_f17Hz_3mSm,'sk','MarkerSize',8,'MarkerFaceColor',colorG,... 'LineWidth',1.25,'Color',colorG); h3=plot(rp_exp(10:end),oE_f17Hz_6mSm,'^k','MarkerSize',8,'MarkerFaceColor',colorB,... 'LineWidth',1.25,'Color',colorB); plot(r0*10,oHFA_f17Hz_1mSm.*omega,'color',colorR,'LineWidth',2) plot(r0*10,oHFA_f17Hz_3mSm.*omega,'color',colorG,'LineWidth',2) plot(r0*10,oHFA_f17Hz_6mSm.*omega,'color',colorB,'LineWidth',2) legend([h1,h2,h3],'\sigma = 1.5 mS/m','\sigma = 3 mS/m','\sigma = 6 mS/m') axis([15,42,0.04,1]) %% Figure 2b % Frequency sweep for a fixed radius of r = 2R % Experimental values vE_r2a_1mSm = M_EXP(:,1,13); vE_r2a_3mSm = M_EXP(:,2,13); vE_r2a_6mSm = M_EXP(:,3,13); omeg = 2*pi*fp_exp; oE_r2a_1mSm = vE_r2a_1mSm'/rp_exp(13); oE_r2a_3mSm = vE_r2a_3mSm'/rp_exp(13); oE_r2a_6mSm = vE_r2a_6mSm'/rp_exp(13); % HFA predictions omega = linspace(min(omeg),max(omeg)); zeta = [79.44 74.605 64.934]*1e-3; mu = epsilon*zeta(1)/eta; mutilde = mu*E_1./omega/R; omega_HFA = zeros(size(omega)); for ii = 1:length(omega) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde(ii)^2/2^6); end oHFA_r2a_1mSm = omega_HFA; mu = epsilon*zeta(2)/eta; mutilde = mu*E_1./omega/R; omega_HFA = zeros(size(omega)); for ii = 1:length(omega) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde(ii)^2/2^6); end oHFA_r2a_3mSm = omega_HFA; mu = epsilon*zeta(3)/eta; mutilde = mu*E_1./omega/R; omega_HFA = zeros(size(omega)); for ii = 1:length(omega) omega_HFA(ii) = 0.5-sqrt(0.25-2*mutilde(ii)^2/2^6); end oHFA_r2a_6mSm = omega_HFA; % PLOTS figure hold on box on ax=gca; ax.FontSize = 20; ax.FontName = 'Times New Roman'; ax.LineWidth = 1; set(gca, 'XScale','log', 'YScale','log') xlabel('\fontname{Times New Roman} \fontsize{24} \omega_{field} (rad/s)') ylabel('\fontname{Times New Roman} \fontsize{24} \omega_p (rad/s)') title('r = 2R') h1=plot(omeg,oE_r2a_1mSm,'ok','MarkerSize',8,'MarkerFaceColor',colorR,... 'LineWidth',1.25,'Color',colorR); h2=plot(omeg,oE_r2a_3mSm,'sk','MarkerSize',8,'MarkerFaceColor',colorG,... 'LineWidth',1.25,'Color',colorG); h3=plot(omeg,oE_r2a_6mSm,'^k','MarkerSize',8,'MarkerFaceColor',colorB,... 'LineWidth',1.25,'Color',colorB); plot(omega,oHFA_r2a_1mSm.*omega,'color',colorR,'LineWidth',2) plot(omega,oHFA_r2a_3mSm.*omega,'color',colorG,'LineWidth',2) plot(omega,oHFA_r2a_6mSm.*omega,'color',colorB,'LineWidth',2) legend([h1,h2,h3],'\sigma = 1.5 mS/m','\sigma = 3 mS/m','\sigma = 6 mS/m')