% Representation of the experimental dataset for % "Wall Repulsion of Charged Colloidal Particles during Electrophoresis in % Microfluidic Channels" close all;clear;clc %% Slip velocity measurements as a function of frequency % 2 micron particles carboxylate; 1.7mS/m KCl conductivity % Frequencies used in this case f_2um = [50 90 167 292 527]; % 50Hz U0_50= [349.33649 407.67317 485.84007 431.00703 334.55345 405.13197... 395.59938 648.34251... 327.06033 225.82288 312.47774 362.66635 677.20505 372.36427 563.59241... 545.31517 359.04816 644.52837 336.53721 375.07497 469.04308 879.98965... 347.27517 512.96702 279.37545 321.07442 327.29480 726.95539]*1e-6; % m M_U0_50 = mean(U0_50); STD_U0_50 = std(U0_50); % 90Hz U0_90= [184.07742 148.83231 251.22052 241.22550 369.48325 307.20635... 307.13223 289.84857 141.61092 260.60546 209.50989 122.30284 196.70617... 252.95816 315.85563 365.74947 350.00487 74.04437 221.41470 327.01188... 202.36337 244.49305 230.39916 169.55278 332.83429 491.73370 309.66623... 317.42329]*1e-6; % m M_U0_90 = mean(U0_90); STD_U0_90 = std(U0_90); % 167Hz U0_167= [ 262.36060 73.36663 143.81121 158.42687 211.46106 221.58612... 189.11457 148.93043 133.72287 277.13429 178.33631]*1e-6; % m M_U0_167 = mean(U0_167); STD_U0_167 = std(U0_167); % 292Hz U0_292= [138.29481 181.38639 155.22833 172.50010 124.12263 161.64740... 76.35529]*1e-6; % m M_U0_292 = mean(U0_292); STD_U0_292 = std(U0_292); % 527Hz U0_527= [131.31686 91.33914 86.50738]*1e-6; % m M_U0_527 = mean(U0_527); STD_U0_527 = std(U0_527); U0_2um = [M_U0_50,M_U0_90,M_U0_167,M_U0_292,M_U0_527]; errU0_2um = [STD_U0_50,STD_U0_90,STD_U0_167,STD_U0_292,STD_U0_527]; % 3 micron particles carboxylate; 1.7mS/m KCl conductivity % Frequencies used in this case f_3um_1mSm = [167 292 527 1700 3000]; % 167Hz U0_167= [262.00653, 305.29099, 319.26687, 317.43353, 205.50513, 234.51935 ... 420.11423 170.15919 289.14377 265.17237 305.54558 398.25553 343.37439 ... 342.16947 207.12036 265.25451 342.24173]*1e-6; %m M_U0_167 = mean(U0_167); STD_U0_167 = std(U0_167); % 292Hz U0_292= [158, 197.87408, 137.38681, 189.01469, 137.43513, 203.56408,160.60123,... 170.81300,179.08539, 99.00018,205.88668,138.64840,181.88285,182.89,183.84270,... 148.36302,207.63641,147.67829,211.59531,174.50382,274.19922,160.07999,... 259.26205,77.29851]*1e-6; %m M_U0_292 = mean(U0_292); STD_U0_292 = std(U0_292); % 527 Hz U0_527= [99, 63, 147.69812,148.96679,110.49295,91.59467,171.31164,72.51698,... 103.88572,92.79771,139.46999,92.93605,143.7545,99.35827,116.81864,123.29044,... 97.71257,99.53143,135.96428,80.24131,107.88546,151.29214,73.02991,118.57834,... 176.43192,121.15181,118.59056,89.09187,78.09237,118.47169,166.45603]*1e-6; %m M_U0_527 = mean(U0_527); STD_U0_527 = std(U0_527); % 1.7kHz U0_1700= [21.00830,77.88052,102.49395,84.94266,75.74054,105.37700,115.88873,... 81.66619,122.96756,74.97226,75.53630,94.36877,88.88602,92.11911,109.52405,... 145.38195,129.77701,111.07995,51.58619,103.43681,88.74308,104.60295,... 122.57149,99.11064]*1e-6; %m M_U0_1700 = mean(U0_1700); STD_U0_1700 = std(U0_1700); % 3kHz U0_3000= [55.96952,53.61539,36.03259,65.89498,66.91511,60.16586,45.26259,... 89.63774,84.90840,30.61107,88.55048,56.55701]*1e-6; %m M_U0_3000 = mean(U0_3000); STD_U0_3000 = std(U0_3000); U0_3um_1mSm = [M_U0_167,M_U0_292,M_U0_527,M_U0_1700,M_U0_3000]; errU0_3um_1mSm = [STD_U0_167,STD_U0_292,STD_U0_527,STD_U0_1700,STD_U0_3000]; % 3 micron particles carboxylate; 6.1mS/m KCl conductivity % Frequencies used in this case f_3um_6mSm = [292 527 950 1700 3000]; % 292Hz U0_292= [82.87943 201.15698 200.29010 162.78050 74.12257 180.78844 156.04079... 172.62837 155.08051 185.13457 248.78728 122.27741 115.34002... 169.87182 151.23307 107.64429 133.47170 77.84851 202.02953... 101.30548 263.34334 263.03118 282.06796]*1e-6; %m M_U0_292 = mean(U0_292); STD_U0_292 = std(U0_292); % 405.38303 66.86557 % 527 Hz U0_527= [89.73476 125.67262 80.26238 97.80237 171.65052 74.90453 102.62054... 84.22372 68.42143 69.58164 72.26578 76.04611 126.32276... 80.25972 126.67878 76.25524 137.17255 83.98019]*1e-6; %m M_U0_527 = mean(U0_527); STD_U0_527 = std(U0_527); % 950Hz U0_950= [86.36843 54.80086 49.19913 42.90621 90.41856 54.19688 51.79581... 92.92946 46.79108 88.59952 85.76865 93.26571 82.71330 89.98863... 102.15295 79.58258 95.40528]*1e-6; %m M_U0_950 = mean(U0_950); STD_U0_950 = std(U0_950); % 1.7kHz U0_1700= [75.82699 65.70891 46.28854 62.37795 25.45878 62.81552 52.98366... 31.68199 46.34104 61.38784 55.03009 39.17195 47.77235 49.44359... 67.64728 50.12064 44.91125 61.83985 51.61868 48.08283 64.04330... 35.27590 73.22250 32.68255 47.87963]*1e-6; %m M_U0_1700 = mean(U0_1700); STD_U0_1700 = std(U0_1700); % 3kHz U0_3000= [28.33310 34.33920 46.41218 35.08882 41.40081 31.17777... 41.73921 34.14100 37.48416 49.73559 48.41859 44.90926... 35.07191 48.07850]*1e-6; %m M_U0_3000 = mean(U0_3000); STD_U0_3000 = std(U0_3000); U0_3um_6mSm = [M_U0_292,M_U0_527,M_U0_950,M_U0_1700,M_U0_3000]; errU0_3um_6mSm = [STD_U0_292,STD_U0_527,STD_U0_950,STD_U0_1700,STD_U0_3000]; % 3 micron particles carboxylate; 15.7mS/m KCl conductivity % Frequencies used in this case f_3um_15mSm = [292 527]; % 292Hz U0_292= [69.12112 53.09561 27.47570 41.97331 31.85817 32.56533 55.43035... 44.92299]*1e-6; %m M_U0_292 = mean(U0_292); STD_U0_292 = std(U0_292); % 527 Hz U0_527= [18.68710 27.20358 19.75232 27.60908 25.91743 39.64986 16.51558... 42.38937 24.19093]*1e-6; %m M_U0_527 = mean(U0_527); STD_U0_527 = std(U0_527); U0_3um_15mSm = [M_U0_292,M_U0_527]; errU0_3um_15mSm = [STD_U0_292,STD_U0_527]; % 3 micron particles Plain; 1.7mS/m KCl conductivity % Frequencies used in this case f_3ump_1mSm = [50 100 200 500]; % 50Hz U0_50= [224.07163 287.68364 244.17742 149.79121 246.77620 191.64864... 194.11744 189.49370 133.81734 270.24182 194.02180 150.77370 166.91771... 160.93097 204.72475 349.70156 158.03994 144.34689 185.57340 238.05374... 150.46283 166.85206 170.61987 153.69701 200.22792 145.04819 208.31277... 260.81165 203.88858 236.60426 184.72271 256.57028 171.95970 158.08569... 271.24565 222.40230 230.29680 199.85134]*1e-6; % m M_U0_50 = mean(U0_50); STD_U0_50 = std(U0_50); % 100Hz U0_100= [107.30982 96.11367 132.79508 156.90203 149.56921 124.25748 138.95971... 98.49707 138.07719 110.21234 61.56658 125.95760 151.34169 150.09383... 109.98102 103.23477 101.54792 169.47151 155.04466 100.20027 163.46638... 181.22379 118.01352 121.59104 102.86852 148.73526 114.90594 116.68046]*1e-6; % m M_U0_100 = mean(U0_100); STD_U0_100 = std(U0_100); % 200Hz U0_200= [151.25698 88.93221 128.06932 108.72828 97.66795 120.67721 111.66275... 77.37301 115.93702 78.17927 130.23261 74.11105 94.75062 132.29215... 74.47927]*1e-6; % m M_U0_200 = mean(U0_200); STD_U0_200 = std(U0_200); % 500Hz U0_500= [73.92616 44.57198 36.49826 43.24353 41.35579 65.64086 117.22864... 104.66057 65.26262 41.63866 81.28385 71.70411 69.60932 50.70511... 66.07398]*1e-6; % m M_U0_500 = mean(U0_500); STD_U0_500 = std(U0_500); U0_3ump_1mSm = [M_U0_50,M_U0_100,M_U0_200,M_U0_500]; errU0_3ump_1mSm = [STD_U0_50,STD_U0_100,STD_U0_200,STD_U0_500]; %% Representation of Figure 1(c) figure('Name','Figure 1(c)') hold on box on ylabel('\fontname{Times New Roman} U_0 (\mum/s)') xlabel('\fontname{Times New Roman} f (Hz)') set(gca,'YScale','log','XScale','log') ax=gca; ax.FontName = 'Times New Roman'; ax.FontSize = 20; ax.LineWidth=1; colorR = [212 56 37]/255; colorG = [70 156 118]/255; colorB = [56 117 176]/255; colorO = [239 135 51]/255; colorY = [248 206 70]/255; % 2um c2um=errorbar(f_2um,U0_2um*1e6,errU0_2um*1e6,'-sk','MarkerFaceColor',colorG,... 'Color',colorG,'MarkerSize',10,'LineWidth',1.5); % 3um 1.7mS/m c3um1=errorbar(f_3um_1mSm,U0_3um_1mSm*1e6,errU0_3um_1mSm*1e6,'-^k','MarkerFaceColor',colorR,... 'Color',colorR,'MarkerSize',10,'LineWidth',1.5); % 3um 6.1mS/m c3um6=errorbar(f_3um_6mSm,U0_3um_6mSm*1e6,errU0_3um_6mSm*1e6,'->k','MarkerFaceColor',colorO,... 'Color',colorO,'MarkerSize',10,'LineWidth',1.5); % 3um 15.7mS/m c3um15=errorbar(f_3um_15mSm,U0_3um_15mSm*1e6,errU0_3um_15mSm*1e6,'-^k','MarkerFaceColor',colorY,... 'Color',colorY,'MarkerSize',10,'LineWidth',1.5); % 3um plain 1.7mS/m c3ump1=errorbar(f_3ump_1mSm,U0_3ump_1mSm*1e6,errU0_3ump_1mSm*1e6,'-^k','MarkerFaceColor','k',... 'MarkerSize',10,'LineWidth',1.5); legend([c2um c3um1 c3um6 c3um15 c3ump1],'2 um Carboxylate(\sigma=1.7 mS/m)',... '3 um Carboxylate (\sigma=1.7 mS/m)',... '3 um Carboxylate (\sigma=6.1 mS/m)','3 um Carboxylate (\sigma=15.7 mS/m)',... '3 um Plain (\sigma=1.7 mS/m)',... 'Location','Best') %% Wall Repulsion measurements as a function of frequency % Frequencies used f = [50 90 167 292 527 950 1700 3000 5500 10000]; % Hz % For the Plain 3 um particles, different frequencies were used f_P = [50 100 200 500 5e3 1e4]; % Hz % Data for fixed conductivity at 1.7 mS/m % 1um Carboxylate yd_1um = [10.0602409 10.30120482 8.3734939 8.6144578 9.819277108... 9.819277108 9.337349398 8.13253012 6.686746988 5.963855422]*1e-6; % m % 2um Carboxylate yd_2um = [16.02564103 14.74358974 13.46153846 11.53846154 11.53846154... 11.53846154 9.615384615 8.974358974 7.692307692 7.051282051]*1e-6; % m % 3um Carboxylate yd_3um = [20.99358974 19.23076923 18.91025641 17.62820513 16.98717949... 15.38461538 15.06410256 13.78205128 11.21794872 9.615384615]*1e-6; % m % 3um Plain yd_3um_P = [15.36144578 14.75903614 13.55421687 12.34939759... 7.831325301 7.831325301]; % m % Theoretical DEP repulsion estimation a = 0.5*[1 2 3 3]*1e-6; % m (particle radius) y_DEP1um = separation(a(1))*1e6; y_DEP2um = separation(a(2))*1e6; y_DEP3um = separation(a(3))*1e6; y_DEP3Pum = separation(a(4))*1e6; % Data for fixed particle size at 3 um in diameter % Frequencies are the same yd_1mSm = [20.99358974 19.23076923 18.91025641 17.62820513 16.98717949... 15.38461538 15.06410256 13.78205128 11.21794872 9.615384615]*1e-6; % m yd_6mSm = [14.42307692 13.46153846 13.46153846 12.82051282 12.17948718... 11.21794872 10.25641026 9.294871795 8.974358974 7.692307692]*1e-6; % m yd_15mSm = [14.42307692 13.46153846 12.82051282 11.85897436 10.8974359... 8.653846154 8.333333333 7.692307692 7.692307692 7.371794872]*1e-6; % m %% Representation of Figure 4(a) figure('Name', 'Figure 4(a)') hold on box on ylabel('\fontname{Times New Roman} Wall separation (um)'); xlabel('\fontname{Times New Roman} f (Hz)') set(gca,'XScale','log') ax=gca; ax.LineWidth=1; ax.FontName = 'Times New Roman'; ax.FontSize = 20; colorR = [212 56 37]/255; colorG = [70 156 118]/255; colorB = [56 117 176]/255; errorbar(f,yd_1um*1e6,1/4.15*ones(1,length(yd_1um)),... 'ok','MarkerFaceColor',colorB,'MarkerSize',10,'Color',colorB); errorbar(f,yd_2um*1e6,1/1.66*ones(1,length(yd_2um)),... 'sk','MarkerFaceColor',colorG,'MarkerSize',10,'Color',colorG); errorbar(f,yd_3um*1e6,1/3.12*ones(1,length(yd_3um)),... '^k','MarkerFaceColor',colorR,'MarkerSize',10,'Color',colorR); errorbar(f_P,yd_3um_P,1/3.12*ones(1,length(yd_3um_P)),... '^k','MarkerFaceColor','k','MarkerSize',10); plot(f,y_DEP1um*ones(size(f)),'--k','LineWidth',1) plot(f,y_DEP2um*ones(size(f)),'--k','LineWidth',1) plot(f,y_DEP3um*ones(size(f)),'--k','LineWidth',1) plot(f,y_DEP3Pum*ones(size(f)),'--k','LineWidth',1) lgd=legend('1 um Carboxylate','2 um Carboxylate','3 um Carboxylate',... '3 um Plain','DEP Repulsion'); lgd.FontSize = 20; %% Supporting function function [y] = separation(a) % Computes DEP separation for maximum nDEP (fCM=-0.5) Deltap = 100; % Pa eta = 1e-3; % m^2/s L = 1e-2; % m Channel total length W = 50e-6; % m Channel Width U = Deltap*W^2/16/eta/L; % m/s Maximum Poiseuille velocity epsilon = 80*8.85e-12; E0 = 8e4; % V/m fCM = -0.5; factor = epsilon*a^5*L*(fCM*E0)^2/(U*W^5*eta); syms f(x) f(x)= factor-32/21*(7*x^6-6*x^7); x0=((3/32)*factor)^(1/6); % Estimation sol=fzero(f,x0);% Non-dimensional estimation hreal=50e-6*sol; % Separation in microns y=hreal; end