{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T05:16:22Z","timestamp":1788498982438,"version":"build-2803163510"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["2329761 and 2315376"],"award-info":[{"award-number":["2329761 and 2315376"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"award":["2329761 and 2315376"],"award-info":[{"award-number":["2329761 and 2315376"]}],"id":[{"id":"https:\/\/ror.org\/021nxhr62","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Microfluidic Hall-effect biosensors detect superparamagnetic bead labels as they flow past a thin-film Hall element in a microchannel. Designing one couples bead magnetization, stray-field distribution, Hall transport, and channel flow across 14 parameters that finite-element solvers explore only at minutes to hours per configuration. We present a coupled analytical\u2013numerical framework for this signal chain: Clausius\u2013Mossotti bead magnetization with a volume fraction correction, a point-dipole stray field, a volume-averaged Hall voltage, Poiseuille transport, and a Johnson\u2013Nyquist and Hooge 1\/f noise model, evaluated across 12 sensor presets compiled from the literature, spanning graphene, III\u2013V semiconductors, Si CMOS, bismuth, and topological insulators; any other platform can be defined from user-supplied transport parameters. Benchmarked against a companion COMSOL Multiphysics 6.0 study, the framework reproduces the Hall voltage to within 4.8% at a favorable bead-to-sensor area ratio and deviates by 22% and 15% at off-optimum geometries, consistent with the point-dipole near-field limit at h\/rb=1. Three design rules follow: a signal-to-noise ridge at sensor widths comparable to the bead diameter (w*\u2248db; area ratios 0.4\u20131.0 at constant voltage, 0.5\u20132.6 at constant current), matching reported single-bead geometries; a material choice that must be made under an explicit electrical drive constraint; and a sampling-limited flow-velocity window. Predicted signals agree at the order-of-magnitude level with published InAs and Si CMOS experiments. We release the model as a freely accessible, no-install browser implementation with a built-in 2D axisymmetric magnetostatic finite-element (FEM) solver that maps where the dipole approximation degrades.<\/jats:p>","DOI":"10.3390\/mi17091042","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T01:05:26Z","timestamp":1788224726000},"page":"1042","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["\u03bcFlow: A Computational Platform for Microfluidic Hall-Effect Magnetic Bead Detection with Parametric Design Optimization"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-0721","authenticated-orcid":false,"given":"Harshitha","family":"Govindaraju","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Rutgers, The State University of New Jersey, 94 Brett Road, Piscataway, NJ 08854, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1562-855X","authenticated-orcid":false,"given":"Umer","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Rutgers, The State University of New Jersey, 94 Brett Road, Piscataway, NJ 08854, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1063\/1.1759380","article-title":"Planar Hall effect sensor for magnetic micro- and nanobead detection","volume":"84","author":"Ejsing","year":"2004","journal-title":"Appl. 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