Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport

<div>(a) The profile of the free chloride concentration obtained from the experimental data for <svg height="11.7391pt" id="M169" style="vertical-align:-3.40332pt" version="1.1" viewbox="-0.0498162 -8.33578 123.606 11.7391" width="123.606pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M478 400C478 445 461 451 447 451C425 451 399 442 369 425C316 395 241 339 172 252H170L191 340C198 371 203 395 203 412C203 439 194 451 178 451C147 451 81 411 24 351L43 324C68 349 101 371 111 371C117 371 122 363 115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.201,3.001)"><path d="M487 458L455 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(b) The profile of the free chloride concentration in the interval <svg height="11.4129pt" id="M170" style="vertical-align:-3.40334pt" version="1.1" viewbox="-0.0498162 -8.00956 33.1442 11.4129" width="33.1442pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M478 400C478 445 461 451 447 451C425 451 399 442 369 425C316 395 241 339 172 252H170L191 340C198 371 203 395 203 412C203 439 194 451 178 451C147 451 81 411 24 351L43 324C68 349 101 371 111 371C117 371 122 363 115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.202,0)"><path d="M552 72V131L122 319L552 507V566L59 344V293L552 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115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,32.752,3.001)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,37.698,0)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" 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Advances in Mathematical Physics

fig3

Figure 3

Figure 3: Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport 