{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:57:45Z","timestamp":1791392265977,"version":"4.3.3"},"reference-count":55,"publisher":"National Academy of Sciences","issue":"41","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"MOST | National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12272050"],"award-info":[{"award-number":["12272050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"MOST | National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U23B6009"],"award-info":[{"award-number":["U23B6009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"MOE | Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2025CX01001"],"award-info":[{"award-number":["2025CX01001"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:p>\n                    Capillary breakup of fluid threads underlies lab-on-a-chip diagnostics, drug encapsulation, and oil trapping in underground rock. Rectangular channels are the practical norm, yet no unified geometric criterion explains how their shape controls the onset and geometry of breakup. Combining direct numerical simulations, stop-flow analysis, and static equilibrium analysis, we show that breakup is triggered when the family of equilibrium neck shapes terminates. The associated critical continuous-phase volume depends only on the channel aspect ratio\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>W<\/mml:mi>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mi>H<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , and the critical neck geometry transitions between two distinct collapse modes at a threshold\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>W<\/mml:mi>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mi>H<\/mml:mi>\n                          <mml:mo>\u2248<\/mml:mo>\n                          <mml:mn>2.0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . Below this threshold, the neck detaches from the top and bottom walls before pinch-off, with a slow three-dimensional necking stage intervening between the two events. Above it, detachment and pinch-off coincide. This geometry-derived critical volume serves as the mechanism-based input to a semiempirical thread-length model, validated for both primary thread breakup and secondary thread breakup across\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>W<\/mml:mi>\n                          <mml:mo stretchy=\"false\">\/<\/mml:mo>\n                          <mml:mi>H<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    from 1.0 to 3.0. Turning this principle into a design rule, we design a curved junction that matches the critical neck profile and directly reduces the critical volume, enabling on-chip production of densely packed emulsions beyond the close-packing limit of monodisperse spheres. By linking confined thread breakup in rectangular microchannels to a single dimensionless ratio, these results provide geometry-based design rules for droplet microfluidics, enhanced oil recovery, and precision emulsion manufacturing.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2617004123","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:35:51Z","timestamp":1791390951000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Geometric criterion for capillary thread breakup in rectangular microchannels"],"prefix":"10.1073","volume":"123","author":[{"given":"Luyao","family":"He","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01skt4w74","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Aerospace Engineering, Beijing Institute of Technology","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5530-2637","authenticated-orcid":false,"given":"Xiaodong","family":"Chen","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01skt4w74","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Aerospace Engineering, Beijing Institute of Technology","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1021\/ac202028g"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0910781107"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.drudis.2007.10.003"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1369-7021(08)70053-1"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1039\/C6LC00809G"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.2118\/2504-PA"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fuel.2020.118232"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.3390\/eng4040163"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2310584120"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s1-10.1.4"},{"key":"e_1_3_4_11_2","unstructured":"J. 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