Membrane-based separation of phenol/water mixtures with concentrations of phenol between 3&#x2009;wt&#37; and 8&#x2009;wt&#37; in the feed has been performed with nonmodified as well as  cross-linked ethylene-methacrylic acid (E-MAA) copolymers with different amounts of methacrylic acid. As cross-linking agents, aluminium acetyl acetonate, which leads to ionically cross-linked membranes, and 2,3,5,6-tetramethyl-1,4-phenylene diamine and glycerine digycidether, leading to covalently cross-linked membranes, have been used. Generally, it was found that with increasing phenol content in the feed, the total flux is increasing whereas the enrichment factor is decreasing. Using nonmodified membranes with higher methacrylic acid monomer content in the polymer, lower fluxes and higher enrichment factors were observed. Investigation of different cross-linked membranes showed that with high phenol concentration in the feed, ionic cross-linking seems to be very promising. Furthermore, variation of feed temperature shows that ionically cross-linked membranes reached higher fluxes as well as higher enrichment factors at elevated temperatures. The temperature-dependent data were fitted based on an Arrhenius-type equation, and activation energies for the permeation of phenol and water through the membrane were calculated.

Alexander Mixa

Claudia Staudt

Membrane-Based Separation of Phenol/Water Mixtures Using Ionically and Covalently Cross-Linked Ethylene-Methacrylic Acid Copolymers

Thermodynamic functions, including enthalpy (<svg style="vertical-align:-0.0pt;width:21.575001px;" id="M1" height="16.75" version="1.1" viewBox="0 0 21.575001 16.75" width="21.575001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g><g transform="matrix(.012,-0,0,-.012,14.975,8.538)"><path id="x1D703" d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123&#xA;t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" /></g></svg>) and entropy (<svg style="vertical-align:-0.23206pt;width:14.8375px;" id="M2" height="17.049999" version="1.1" viewBox="0 0 14.8375 17.049999" width="14.8375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x1D446" d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68&#xA;l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" /></g><g transform="matrix(.012,-0,0,-.012,8.225,8.537)"><use xlink:href="#x1D703" /></g></svg>) for 76 polychlorophenazines (PCPZs) in the gas state at 298.15 K 
  and 101.325 kPa, have been calculated using the B3LYP/6-31<svg style="vertical-align:-0.20473pt;width:19.887501px;" id="M3" height="14" version="1.1" viewBox="0 0 19.887501 14" width="19.887501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,13.688)"><path id="x47" d="M692 302v-28q-45 -6 -54.5 -17t-9.5 -55v-86q0 -62 7 -95q-7 -2 -32 -7.5l-37 -8l-35.5 -7.5t-40.5 -7t-38.5 -4t-40.5 -2q-165 0 -266 93t-101 243q0 84 32 151t86 108t121.5 63t142.5 22q29 0 62.5 -4t52 -7.5t47.5 -10.5t31 -7l15 -156l-28 -6q-17 87 -66.5 121.5&#xA;t-128.5 34.5q-117 0 -191 -80.5t-74 -216.5q0 -56 17 -110t49.5 -100.5t87.5 -74.5t124 -28q53 0 87 17q17 9 24.5 23t7.5 43v85q0 54 -15.5 67.5t-89.5 18.5v28h254z" /></g><g transform="matrix(.012,-0,0,-.012,12.213,5.525)"><path id="x2217" d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5&#xA;q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" /></g></svg> level with Gaussian 03 program, and considered on solvation affects. Total free energy in water (<svg style="vertical-align:-3.3907pt;width:21.525px;" id="M4" height="15.6875" version="1.1" viewBox="0 0 21.525 15.6875" width="21.525" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path id="x1D43A" d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242&#xA;q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" /></g><g transform="matrix(.012,-0,0,-.012,12.375,15.475)"><path id="x1D464" d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152&#xA;q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" /></g></svg>) was calculated with the same program. Based on these data, the 
isodesmic reactions were designed to calculate the standard formation heat 
(<svg style="vertical-align:-5.76988pt;width:40.737499px;" id="M5" height="23.9375" version="1.1" viewBox="0 0 40.737499 23.9375" width="40.737499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x394" d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" /></g><g transform="matrix(.012,-0,0,-.012,10.963,20.775)"><path id="x1D453" d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19&#xA;q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" /></g><g transform="matrix(.017,-0,0,-.017,19.225,16.7)"><use xlink:href="#x1D43B" /></g><g transform="matrix(.012,-0,0,-.012,34.125,8.538)"><use xlink:href="#x1D703" /></g></svg>) and standard free energy of formation in water <svg style="vertical-align:-5.76988pt;width:52.450001px;" id="M6" height="23.9375" version="1.1" viewBox="0 0 52.450001 23.9375" width="52.450001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,5.944,16.7)"><use xlink:href="#x394" /></g><g transform="matrix(.012,-0,0,-.012,16.838,20.775)"><use xlink:href="#x1D453" /></g><g transform="matrix(.017,-0,0,-.017,25.1,16.7)"><use xlink:href="#x1D43A" /></g><g transform="matrix(.012,-0,0,-.012,37.412,8.538)"><use xlink:href="#x1D703" /></g><g transform="matrix(.012,-0,0,-.012,37.412,20.775)"><use xlink:href="#x1D464" /></g><g transform="matrix(.017,-0,0,-.017,46.5,16.7)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g></svg>. The dependences of these thermodynamic parameters on the numbers and positions of chlorine substitution (<svg style="vertical-align:-3.41936pt;width:35.862499px;" id="M7" height="15.4375" version="1.1" viewBox="0 0 35.862499 15.4375" width="35.862499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D441" d="M857 650l-6 -28q-44 -4 -61.5 -16.5t-29.5 -48.5q-11 -32 -37 -166l-78 -399h-29l-351 537h-4l-56 -276q-24 -120 -24 -164q0 -35 17.5 -46t75.5 -15l-6 -28h-245l7 28q41 2 62 14t31 44q10 30 41 171l53 245q8 44 6.5 60.5t-14.5 33.5q-10 15 -27 19.5t-64 6.5l6 28h153&#xA;l350 -516h5l48 257q25 131 25 171q0 34 -17.5 45t-77.5 15l7 28h240z" /></g><g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><path id="x50" d="M46 650h247q112 0 169 -41q64 -49 64 -141q0 -91 -56.5 -143t-138.5 -62q-23 -3 -45 -1l-74 19v-157q0 -63 15.5 -77t83.5 -19v-28h-271v28q60 5 74 20t14 77v400q0 65 -12.5 79t-69.5 18v28zM212 559v-245q31 -12 73 -12q59 0 102 38t43 124q0 77 -42.5 115.5&#xA;t-108.5 38.5q-44 0 -56 -12q-11 -8 -11 -47z" /></g><g transform="matrix(.012,-0,0,-.012,21.624,15.187)"><path id="x43" d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207&#xA;q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" /></g><g transform="matrix(.012,-0,0,-.012,29.537,15.187)"><path id="x53" d="M409 504l-29 -5q-16 60 -44.5 96t-86.5 36q-54 0 -82.5 -32t-28.5 -77q0 -51 30.5 -82.5t96.5 -65.5l35.5 -18t33 -19.5t33.5 -23.5l27 -25.5t24.5 -32t13.5 -36.5t6 -45q0 -80 -62 -134.5t-160 -54.5q-47 0 -98 15q-22 7 -50 21q-8 23 -27 155l30 7q7 -27 18 -52&#xA;t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" /></g></svg>) were discussed. It is suggested that  <svg style="vertical-align:-5.76988pt;width:67.824997px;" id="M8" height="23.9375" version="1.1" viewBox="0 0 67.824997 23.9375" width="67.824997" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x1D446" /></g><g transform="matrix(.012,-0,0,-.012,8.225,8.538)"><use xlink:href="#x1D703" /></g><g transform="matrix(.017,-0,0,-.017,14.775,16.7)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,27.133,16.7)"><use xlink:href="#x394" /></g><g transform="matrix(.012,-0,0,-.012,38.038,20.775)"><use xlink:href="#x1D453" /></g><g transform="matrix(.017,-0,0,-.017,46.3,16.7)"><use xlink:href="#x1D43B" /></g><g transform="matrix(.012,-0,0,-.012,61.212,8.538)"><use xlink:href="#x1D703" /></g></svg>, and <svg style="vertical-align:-5.76988pt;width:40.6875px;" id="M9" height="23.9375" version="1.1" viewBox="0 0 40.6875 23.9375" width="40.6875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x394" /></g><g transform="matrix(.012,-0,0,-.012,10.963,20.775)"><use xlink:href="#x1D453" /></g><g transform="matrix(.017,-0,0,-.017,19.225,16.7)"><use xlink:href="#x1D43A" /></g><g transform="matrix(.012,-0,0,-.012,31.525,8.538)"><use xlink:href="#x1D703" /></g><g transform="matrix(.012,-0,0,-.012,31.525,20.775)"><use xlink:href="#x1D464" /></g></svg> of PCPZs varied greatly with <svg style="vertical-align:-3.41936pt;width:35.862499px;" id="M10" height="15.4375" version="1.1" viewBox="0 0 35.862499 15.4375" width="35.862499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D441" /></g><g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><use xlink:href="#x50" /></g><g transform="matrix(.012,-0,0,-.012,21.624,15.187)"><use xlink:href="#x43" /></g><g transform="matrix(.012,-0,0,-.012,29.537,15.187)"><use xlink:href="#x53" /></g></svg>. Moreover, the values of molar heat capacity at constant pressure (<svg style="vertical-align:-5.73167pt;width:31.887501px;" id="M11" height="18.6" version="1.1" viewBox="0 0 31.887501 18.6" width="31.887501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5&#xA;t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g><g transform="matrix(.012,-0,0,-.012,19.106,15.475)"><use xlink:href="#x2C" /></g><g transform="matrix(.012,-0,0,-.012,21.819,15.475)"><path id="x1D45A" d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6&#xA;q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" /></g></svg>) from 200 to 1800 K for PCPZ congeners were calculated using a statistical thermodynamics calculation program based on Gaussian output files, and the temperature-dependence relation of <svg style="vertical-align:-5.73167pt;width:31.887501px;" id="M12" height="18.6" version="1.1" viewBox="0 0 31.887501 18.6" width="31.887501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D436" /></g><g transform="matrix(.012,-0,0,-.012,12.05,15.475)"><use xlink:href="#x1D45D" /></g><g transform="matrix(.012,-0,0,-.012,19.106,15.475)"><use xlink:href="#x2C" /></g><g transform="matrix(.012,-0,0,-.012,21.819,15.475)"><use xlink:href="#x1D45A" /></g></svg> was obtained using the least-squares method. In addition, according to the relative magnitude of their <svg style="vertical-align:-5.76988pt;width:40.6875px;" id="M13" height="23.9375" version="1.1" viewBox="0 0 40.6875 23.9375" width="40.6875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x394" /></g><g transform="matrix(.012,-0,0,-.012,10.963,20.775)"><use xlink:href="#x1D453" /></g><g transform="matrix(.017,-0,0,-.017,19.225,16.7)"><use xlink:href="#x1D43A" /></g><g transform="matrix(.012,-0,0,-.012,31.525,8.538)"><use xlink:href="#x1D703" /></g><g transform="matrix(.012,-0,0,-.012,31.525,20.775)"><use xlink:href="#x1D464" /></g></svg>, the relative stability order of PCPZ congeners was theoretically proposed.

Hong-Xia Yu

Hui Liu

Zun-Yao Wang

Lian-Sheng Wang

DFT Calculation on 76 Polychlorophenazines: Their Thermodynamic Function and Implication of Cl Substituted Position

Plant polyphenol, including vanillin, is often used as the intermediate materials of the medicines and vanilla flavoring. In agriculture generally vanillin is produced from vanilla plant and in industry from lignin of disposed wood pulp. We have recently developed a method for the production of plant polyphenol with the excrement as a natural resource of lignin, of the herbivorous animals, by using the subcritical water. The method for using the subcritical water is superior to that of the supercritical water because in the latter complete decomposition occurs. We have successfully produced the vanillin, protocatechuic acid, vanillic acid, and syringic acid in products. Our method is simpler and more efficient not only because it requires the shorter treatment time but also because it releases less amount of carbon dioxide into the atmosphere.

Mayu Yamamoto

Yasuhiro Futamura

Kouki Fujioka

Kenji Yamamoto

Novel Production Method for Plant Polyphenol from Livestock Excrement Using Subcritical Water Reaction

Scaling analyses based on subsurface layer instability were performed to explore the role of three independent (surface tension, gravity, and viscosity) influences on the mechanism of pulsating flame spread under normal and microgravity conditions. These three influences form two independent pi-numbers: the Marangoni (Ma) number and Grashof (Gr) number, which include the characteristic length scale ratio (depth of subsurface circulation)/(horizontal length of preheated liquid surface). The Prandtl (Pr) number was introduced to compensate for the different thermal diffusivity and kinematic viscosity of different liquids. Also a nondimensional flame spread rate, <svg style="vertical-align:-3.27605pt;width:42.537498px;" id="M1" height="16.15" version="1.1" viewBox="0 0 42.537498 16.15" width="42.537498" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path id="x1D449" d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" /></g><g transform="matrix(.017,-0,0,-.017,12.676,12.012)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,19.679,12.012)"><use xlink:href="#x1D449" /></g><g transform="matrix(.012,-0,0,-.012,32.287,16.087)"><path id="x1D437" d="M780 372q0 -191 -178 -297q-128 -75 -335 -75h-250l7 27q61 7 77 22t28 76l77 398q11 62 0 76.5t-77 22.5l6 28h292q164 0 258.5 -67.5t94.5 -210.5zM678 375q0 119 -73 180.5t-201 61.5q-62 0 -82 -13q-17 -7 -25 -53l-80 -427q-8 -47 -4 -62t26 -20q24 -6 80 -6&#xA;q166 0 262.5 95t96.5 244z" /></g></svg> (= <svg style="vertical-align:-2.22495pt;width:42.174999px;" id="M2" height="15" version="1.1" viewBox="0 0 42.174999 15" width="42.174999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D449" /></g><g transform="matrix(.017,-0,0,-.017,12.676,12.162)"><path id="x1D6FF" d="M494 514l-10 -15q-56 76 -106.5 117t-110.5 41q-45 0 -45 -30q0 -28 109 -152q59 -68 86 -118.5t27 -107.5q0 -62 -29.5 -119.5t-86.5 -96.5q-64 -45 -138 -45q-76 0 -121.5 53t-45.5 136q0 74 40.5 135t98.5 95q43 26 87 42q-40 59 -57.5 92t-17.5 62q0 46 39 77.5&#xA;t90 31.5q54 0 97.5 -35.5t65 -78.5t28.5 -84zM359 234q0 84 -90 191q-47 -17 -74 -47q-81 -89 -81 -200q0 -71 32.5 -109.5t72.5 -38.5q47 0 80 33t46.5 77.5t13.5 93.5z" /></g><g transform="matrix(.017,-0,0,-.017,21.464,12.162)"><use xlink:href="#x2F" /></g><g transform="matrix(.017,-0,0,-.017,28.467,12.162)"><use xlink:href="#x1D437" /></g></svg>, where <svg style="vertical-align:-0.1638pt;width:8.9125004px;" id="M3" height="12.4375" version="1.1" viewBox="0 0 8.9125004 12.4375" width="8.9125004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D6FF" /></g></svg> is the quenching distance and <svg style="vertical-align:-0.0pt;width:13.775px;" id="M4" height="11.175" version="1.1" viewBox="0 0 13.775 11.175" width="13.775" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D437" /></g></svg> is the diffusivity of fuel vapor) was introduced. Using these nondimensional parameters, the flame spread mechanism was divided into two separate regimes: for the shallow liquid pool the nondimensional flame spread rate was correlated with <svg style="vertical-align:-2.3205pt;width:128px;" id="M5" height="22" version="1.1" viewBox="0 0 128 22" width="128" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,19.05)"><path id="x7B" d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117&#xA;q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" /></g><g transform="matrix(.017,-0,0,-.017,5.961,19.05)"><path id="x47" d="M692 302v-28q-45 -6 -54.5 -17t-9.5 -55v-86q0 -62 7 -95q-7 -2 -32 -7.5l-37 -8l-35.5 -7.5t-40.5 -7t-38.5 -4t-40.5 -2q-165 0 -266 93t-101 243q0 84 32 151t86 108t121.5 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Kozue Takahashi

Akihiko Ito

Yuji Kudo

Tadashi Konishi

Kozo Saito

Scaling Analysis on Pulsating Flame Spread over Liquids

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<p><em>International Journal of Chemical Engineering</em> publishes research focused on technologies for the production, processing, transportation and use of chemicals on an industrial scale.</p>


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<p>Chief Editor, Evangelos Tsotsas, holds the Chair of Thermal Process Engineering at Otto von Guericke University Magdeburg (Germany) since 1994. The main focus of his work is on drying, and on particle formulation processes related to drying, such as spray fluidized bed agglomeration.</p>


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International Journal of Chemical Engineering | Hindawi

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International Journal of Chemical Engineering publishes research focused on technologies for the production, processing, transportation and use of chemicals on an industrial scale.

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International Journal of Chemical Engineering

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International Journal of Chemical Engineering