{"id":1210,"date":"2024-09-04T19:57:10","date_gmt":"2024-09-04T17:57:10","guid":{"rendered":"https:\/\/test.kint.cz\/?p=1210"},"modified":"2025-06-04T18:32:39","modified_gmt":"2025-06-04T16:32:39","slug":"reologie","status":"publish","type":"post","link":"https:\/\/www.kint.cz\/es\/reologie\/","title":{"rendered":"Reologie"},"content":{"rendered":"\t\t
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Tento \u010dl\u00e1nek navazuje na \u010dl\u00e1nky\u00a0o termodynamice\u00a0<\/a>(\u010dl\u00e1nek 2<\/a>) a v kr\u00e1tkosti uv\u00e1d\u00ed problematiku reologie, co\u017e je zjednodu\u0161en\u011b nauka o toku materi\u00e1lu. V n\u00e1sleduj\u00edc\u00edch odstavc\u00edch se dozv\u00edte nap\u0159\u00edklad jak vznikaj\u00ed vodn\u00ed v\u00edry anebo jak se m\u011b\u0159\u00ed viskozita l\u00e1tek a podobn\u011b.<\/p>

N\u00e1sleduj\u00edc\u00ed odstavce poskytuj\u00ed souhrn a uveden\u00ed do problematiky na z\u00e1klad\u011b re\u0161er\u0161e z n\u00e1sleduj\u00edc\u00edch zdroj\u016f:<\/p>

PRAGOLAB. Semin\u00e1\u0159 reologie. Praha: Pragolab 2015. Dostupn\u00e9 z:\u00a0http:\/\/www.pragolab.cz\/files\/download\/Seminar_reologie_2015.pdf<\/a><\/p>

PRU\u0160KA, J.\u00a0Reologie, MH 8. P\u0159edn\u00e1\u0161ka.<\/em>\u00a0Praha: FS \u010cVUT 2008. Dostupn\u00e9 z:\u00a0http:\/\/departments.fsv.cvut.cz\/k135\/data\/wp-upload\/2008\/05\/reologie.pdf<\/a><\/p>

HOLUBOV\u00c1, Renata.\u00a0Z\u00e1klady reologie a reometrie kapalin<\/em>. Olomouc: Univerzita Palack\u00e9ho v Olomouci,2014. ISBN 978-80-244-4178-8<\/p>

Reologie je nauka o deformaci a toku materi\u00e1lu; o pohybu vazk\u00fdch (newtonov\u00fdch) kapalin a p\u0159etv\u00e1\u0159en\u00ed hmot. Tyto hmoty nejsou dokonale pru\u017en\u00e9 (Hookova hmota), ani zcela tv\u00e1rn\u00e9 (St. Venantova kapalina) \u010di vl\u00e1\u010dn\u00e9, ale u kter\u00fdch se vyskytuj\u00ed r\u016fzn\u00e9 kombinace t\u011bchto vlastnost\u00ed. Reologie se d\u011bl\u00ed na makroreologii a mikroreologii.<\/p>

Makroreologie\u00a0<\/em><\/strong>\u2013 zkoum\u00e1 p\u0159etv\u00e1rn\u00e9 vlastnosti hmoty z celkov\u00e9ho pohledu.<\/p>

Mikroreologie\u00a0<\/em><\/strong>-studuje p\u0159etv\u00e1rn\u00e9 vlastnosti jednotliv\u00fdch \u010d\u00e1st\u00ed hmoty.<\/p>

Reologie se zab\u00fdv\u00e1:<\/p>

\u2013\u00a0\u00a0 souvislostmi mezi r\u016fzn\u00fdmi druhy deformace hmoty a zkoum\u00e1 p\u0159\u00ed\u010diny a projevy deformac\u00ed,<\/p>

\u2013\u00a0\u00a0 vztahy mezi smykov\u00fdm nap\u011bt\u00edm a smykovou rychlost\u00ed,<\/p>

\u2013\u00a0\u00a0 hranicemi mezi kapalinou a pevnou l\u00e1tkou.<\/p>

Vlastnosti kapalin<\/h2>

Pro popis vlastnost\u00ed\u00a0ide\u00e1ln\u00edch kapalin<\/em><\/strong>\u00a0definujeme ide\u00e1ln\u00ed kapalinu jako kapalinu bez vnit\u0159n\u00edho t\u0159en\u00ed (nevisk\u00f3zn\u00ed), m\u00e1 nulovou objemovou rozta\u017enost i stla\u010ditelnost, nulovou rozpustnost plyn\u016f a nevypa\u0159uje se.<\/p>

Kapaliny se d\u00e1le dle (Holubov\u00e1 R.) d\u011bl\u00ed na:<\/p>

\u2013\u00a0\u00a0 newtonsk\u00e9 (nap\u0159. voda), u nich\u017e je viskozita p\u0159i dan\u00e9 teplot\u011b a tlaku fyzik\u00e1ln\u00ed konstantou,<\/em><\/p>

\u2013\u00a0\u00a0 a ne-newtonsk\u00e9 (nap\u0159. emulze, sm\u011bsi pevn\u00fdch l\u00e1tek s kapalinami, nat\u011bra\u010dsk\u00e9 barvy), jejich\u017e viskozita nen\u00ed fyzik\u00e1ln\u00ed konstantou.<\/em><\/p>

Proud\u011bn\u00ed re\u00e1ln\u00e9 kapaliny<\/strong>\u00a0je:<\/em><\/p>

Lamin\u00e1rn\u00ed<\/strong>\u00a0\u2013\u00a0<\/em>\u010d\u00e1stice se pohybuj\u00ed ve vrstv\u00e1ch, kter\u00e9 jsou vz\u00e1jemn\u011b rovnob\u011b\u017en\u00e9, p\u0159i\u010dem\u017e nedoch\u00e1z\u00ed k p\u0159emis\u0165ov\u00e1n\u00ed \u010d\u00e1stic kolmo ke sm\u011bru pohybu;<\/p>

Turbulentn\u00ed\u00a0<\/strong>\u2013 \u010d<\/em>\u00e1stice maj\u00ed krom\u011b postupn\u00e9 rychlosti tak\u00e9 turbulentn\u00ed (fluktua\u010dn\u00ed) rychlost, pomoc\u00ed kter\u00e9 se p\u0159emis\u0165uj\u00ed po pr\u016f\u0159ezu.<\/p>

D\u00e1le se v oblasti vlastnosti kapalin definuj\u00ed n\u00e1sleduj\u00edc\u00ed vztahy pro nap\u011bt\u00ed.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em><\/p>

Norm\u00e1lov\u00e9 nap\u011bt\u00ed<\/strong><\/em>\u00a0(tlak) p \u2013 je d\u00e1no jako pod\u00edl norm\u00e1lov\u00e9 element\u00e1rn\u00ed s\u00edly a velikosti dan\u00e9 plochy:<\/p>

p = dFn\u00a0<\/sub>\/ dS,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (1)<\/p>

kde dS je element\u00e1rn\u00ed plocha uvnit\u0159 kapaliny, dFn\u00a0<\/sub>norm\u00e1lov\u00e1 slo\u017eka (p\u016fsob\u00edc\u00ed kolno na uva\u017eovanou plochu) element\u00e1rn\u00ed s\u00edly dF.<\/p>

V kapalin\u011b nelze vyvolat tahov\u00e9 nap\u011bt\u00ed, a proto tlak m\u011b\u0159\u00edme jako kladn\u00fd. M\u011b\u0159\u00edme-li tlak od nulov\u00e9 hodnoty, hovo\u0159\u00edme o tzv. absolutn\u00edm tlaku. N\u011bkdy je v\u00fdhodn\u00e9 m\u011b\u0159it tlak od jist\u00e9ho referen\u010dn\u00edho tlaku (v\u011bt\u0161inou atmosf\u00e9rick\u00fd tlak). Tlakov\u00e9 diference nad resp. pod t\u00edmto tlakem naz\u00fdv\u00e1me p\u0159etlak resp. podtlak.<\/p>

Te\u010dn\u00e9 (smykov\u00e9) nap\u011bt\u00ed<\/em><\/strong>\u00a0\u03c4 \u2013 je d\u00e1no jako pod\u00edl te\u010dn\u00e9 element\u00e1rn\u00ed s\u00edly a velikosti dan\u00e9 plochy:<\/p>

\u03c4 = dFt\u00a0<\/sub>\/ dS,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (2)<\/p>

kde dFt\u00a0\u00a0<\/sub>je te\u010dn\u00e1 slo\u017eka (vyvol\u00e1v\u00e1 v kapalin\u011b posun \u010d\u00e1stic) element\u00e1rn\u00ed s\u00edly dF p\u016fsob\u00edc\u00ed na element\u00e1rn\u00ed plochu dS.<\/p>

Pro element\u00e1rn\u00ed hranol o v\u00fd\u0161ce dy, jeho\u017e spodn\u00ed st\u011bna se pohybuje rychlost\u00ed v a horn\u00ed st\u011bna rychlost\u00ed v + dv dle [11] plat\u00ed:<\/p>

\u03c4 = \u03b7 dv\/dy,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (3)<\/p>

Dynamick\u00e1\u00a0viskozita\u00a0<\/em><\/strong>kapalin je obecn\u011b z\u00e1visl\u00e1 na teplot\u011b (s rostouc\u00ed teplotou kles\u00e1) a na tlaku (z\u00e1vislost je zanedbateln\u00e1). Projevuje se jako odpor proti pohybu \u010d\u00e1stic kapaliny. Podle z\u00e1vislosti dynamick\u00e9 viskozity na te\u010dn\u00e9m nap\u011bt\u00ed rozli\u0161ujeme kapaliny na newtonovsk\u00e9 (nez\u00e1visl\u00e9 \u2013 rovnice (2)) a ne-newtonovsk\u00e9 (z\u00e1visl\u00e9 \u2013 rovnice 3).<\/p>

Z\u00e1vislost viskozity na teplot\u011b lze vyj\u00e1d\u0159it pomoc\u00ed vztahu:<\/p>

\u03b7(T) = k * eb\/(T+\u0398)<\/sup>,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (4)<\/p>

kde konstanta k m\u00e1 rozm\u011br viskozity (Pa \u00b7 s), b a \u0398 jsou konstanty charakteristick\u00e9 pro danou tekutinu, jejich jednotka je kelvin.<\/em><\/p>

Z\u00e1vislost viskozity na tlaku vyjad\u0159uje vztah:<\/p>

\u03b7(p) = \u03b70<\/sub>\u00a0* e\u03b1p<\/sup>,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 (5)<\/p>

\u03b1 je koeficient z\u00e1visl\u00fd na teplot\u011b.<\/p>

Krom\u011b dynamick\u00e9 viskozity zav\u00e1d\u00edme tak\u00e9 veli\u010dinu\u00a0kinematick\u00e1 viskozita<\/strong><\/em>, kter\u00e1 je definov\u00e1na vztahem:<\/p>

\u03bd = \u03b7 \/ \u03c1,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (6)<\/p>

kde\u00a0 \u03c1 je hustota kapaliny.<\/p>

Pr\u016ftok kapaliny kapil\u00e1rou \u2013<\/em><\/strong>\u00a0charakteristick\u00fdmi veli\u010dinami pro popis pr\u016ftoku jsou: tlakov\u00fd rozd\u00edl \u0394p, d\u00e1lka kapil\u00e1ry l a jej\u00ed polom\u011br r. Ve stacion\u00e1rn\u00edm p\u0159\u00edpad\u011b mus\u00ed b\u00fdt tlakov\u00e9 s\u00edla Fp<\/sub>\u00a0rovna s\u00edle t\u0159ec\u00ed FR<\/sub>. U pr\u016ftoku kapil\u00e1rou se jedn\u00e1 o parabolick\u00e9 rozlo\u017een\u00ed rychlost\u00ed, tzn. \u017ee rychlost v(r) prostorov\u011b tvo\u0159\u00ed rota\u010dn\u00ed paraboloid. Vztahy pro rychlostn\u00ed profil i mno\u017estv\u00ed kapaliny, kter\u00e1 prote\u010de za jednotku \u010dasu t, jsou uveden\u00e9 v pr\u00e1ce.<\/p>

Navierova-Stokesova rovnice \u2013\u00a0<\/em><\/strong>p\u0159edstavuje pohybovou rovnici re\u00e1ln\u00e9 proud\u00edc\u00ed kapaliny. Na re\u00e1lnou kapalinu p\u016fsob\u00ed gravita\u010dn\u00ed s\u00edla, tlakov\u00e1 s\u00edla a t\u0159ec\u00ed s\u00edla. Celkovou s\u00edlu lze vyj\u00e1d\u0159it jako sou\u010det v\u0161ech p\u016fsob\u00edc\u00edch sil. C\u00edlem \u0159e\u0161en\u00ed je naj\u00edt rozlo\u017een\u00ed rychlost\u00ed a tlak\u016f. Je proto t\u0159eba zn\u00e1t jednak vn\u011bj\u0161\u00ed zrychlen\u00ed, d\u00e1le hustotu kapaliny a vn\u011bj\u0161\u00ed podm\u00ednky. Jednotliv\u00e9 \u010dleny Navierova-Stokesova rovnice p\u0159edstavuj\u00ed:<\/p>

\u2013\u00a0\u00a0 vn\u011bj\u0161\u00ed zrychlen\u00ed, kter\u00e9 je d\u016fsledkem p\u016fsoben\u00ed t\u00edhov\u00e9 s\u00edly,<\/em><\/p>

\u2013\u00a0\u00a0 zrychlen\u00ed od plo\u0161n\u00e9 (tlakov\u00e9) s\u00edly,<\/em><\/p>

\u2013\u00a0\u00a0 zrychlen\u00ed pot\u0159ebn\u00e9 k p\u0159ekon\u00e1n\u00ed visk\u00f3zn\u00edho t\u0159en\u00ed kapalin,<\/em><\/p>

\u2013\u00a0\u00a0 zrychlen\u00ed vlivem viskozity u stla\u010diteln\u00fdch kapalin,<\/em><\/p>

\u2013\u00a0\u00a0 konvektivn\u00ed zrychlen\u00ed od setrva\u010dn\u00e9 s\u00edly,<\/em><\/p>

\u2013\u00a0\u00a0 lok\u00e1ln\u00ed zrychlen\u00ed od setrva\u010dn\u00e9 s\u00edly.<\/em><\/p>

U nestla\u010diteln\u00e9 kapaliny odpad\u00e1 d\u00edky rovnici kontinuity \u010dtvrt\u00fd \u010dlen rovnice (zrychlen\u00ed vlivem viskozity), v nevisk\u00f3zn\u00ed kapalin\u011b p\u0159ech\u00e1z\u00ed rovnice v Eulerovu rovnici hydrodynamiky. Pomoc\u00ed Navierovy-Stokesovy rovnice lze popsat klasickou hydrodynamiku. Na rozd\u00edl od Eulerovy rovnice obsahuje \u010dlen, kter\u00fd vyjad\u0159uje vnit\u0159n\u00ed t\u0159en\u00ed v tekutin\u011b.<\/p>

Navierova-Stokesova rovnice p\u0159edstavuje neline\u00e1rn\u00ed diferenci\u00e1ln\u00ed rovnici. Jej\u00edm \u0159e\u0161en\u00edm dostaneme rozd\u011blen\u00ed rychlost\u00ed v tekutin\u011b v z\u00e1vislosti na m\u00edst\u011b a \u010dase. Matematika nezn\u00e1 postup analytick\u00e9ho \u0159e\u0161en\u00ed t\u00e9to rovnice, \u0159e\u0161it lze pouze speci\u00e1ln\u00ed p\u0159\u00edpady.<\/p>

Lamin\u00e1rn\u00ed proud\u011bn\u00ed kolem kuli\u010dky\u00a0<\/em><\/strong>\u2013<\/em>\u00a0visk\u00f3zn\u00ed kapaliny p\u016fsob\u00ed silou na ka\u017ed\u00fd p\u0159edm\u011bt, kter\u00fd se v kapalin\u011b pohybuje. Lze vy\u0161et\u0159it nap\u0159\u00edklad, jak popsat p\u00e1d p\u0159edm\u011btu ve visk\u00f3zn\u00ed kapalin\u011b. Vlivem t\u00edhov\u00e9 s\u00edly Fg<\/sub>\u00a0je p\u0159edm\u011bt urychlov\u00e1n a jeho po\u010d\u00e1te\u010dn\u00ed rychlost v0<\/sub>\u00a0= 0 se kontinu\u00e1ln\u011b zv\u011bt\u0161uje. Jev trv\u00e1 tak dlouho, a\u017e p\u0159edm\u011bt p\u0159ejde v pohyb rovnom\u011brn\u00fd s konstantn\u00ed rychlost\u00ed poklesu v , tzn. zrychlen\u00ed je nulov\u00e9. Pot\u00e9 existuje rovnov\u00e1ha mezi dol\u016f sm\u011b\u0159uj\u00edc\u00ed t\u00edhovou silou a vzh\u016fru sm\u011b\u0159uj\u00edc\u00edmi silami \u2013 vztlakovou silou a silou t\u0159en\u00ed: Fg<\/sub>=Fvz\u00a0<\/sub>+ FT<\/sub>.<\/p>

Na z\u00e1klad\u011b experiment\u016f s kuli\u010dkami r\u016fzn\u00fdch velikost\u00ed a s pou\u017eit\u00edm r\u016fzn\u00fdch kapalin zjist\u00edme, \u017ee t\u0159ec\u00ed s\u00edla z\u00e1vis\u00ed na koeficientu \u03b7, kone\u010dn\u00e9 rychlosti v a polom\u011bru kuli\u010dky r, tj.\u00a0Stokes\u016fv z\u00e1kon<\/strong>:<\/p>

FT<\/sub>\u00a0= -6\u03c0\u03b7rv.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (7)<\/p>

V\u00edry \u2013\u00a0<\/em><\/strong>charakteristick\u00fd znak pro turbulence je vznik v\u00edr\u016f. P\u0159edstavme si v\u00e1lec obt\u00e9kan\u00fd tekutinou. Od ur\u010dit\u00e9 rychlosti proud\u011bn\u00ed v G se za\u010dnou za v\u00e1lcem v oblasti tzv. mrtv\u00e9 vody, tvo\u0159it stacion\u00e1rn\u00ed v\u00edry s opa\u010dn\u00fdm sm\u011brem rotace. V\u00edr<\/em>\u00a0lze rozd\u011blit do dvou oblast\u00ed \u2013 j\u00e1dro a oblast cirkulace. Vysv\u011btlen\u00ed vzniku v\u00edr\u016f provedeme pomoc\u00ed v\u00e1lce, kter\u00fd je vlo\u017een do tekutiny, kter\u00e1 se pohybuje zleva doprava a \u201enar\u00e1\u017e\u00ed\u201c na t\u011bleso \u2013 viz obr\u00e1zek.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Fyzika \u2013 Reologie: Mechanismus vzniku V\u00edr\u016f viz (HOLUBOV\u00c1, R.)<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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V bod\u011b S1<\/sub>\u00a0(m\u00edsto n\u00e1razu) je rychlost minim\u00e1ln\u00ed, tzn. \u017ee podle Bernoulliho rovnice je statick\u00fd tlak v tomto m\u00edst\u011b maxim\u00e1ln\u00ed. Vytvo\u0159\u00ed se tlakov\u00fd sp\u00e1d mezi body S\u00a01<\/sub>\u00a0a K na vrcholu t\u011blesa. Na vrcholu t\u011blesa v bod\u011b K je statick\u00fd tlak minim\u00e1ln\u00ed a rychlost maxim\u00e1ln\u00ed, zmen\u0161en\u00e1 jen o vliv t\u0159en\u00ed\u00a0 (v < vmax<\/sub>\u00a0). Nyn\u00ed mus\u00ed tekutina p\u0159ekonat existuj\u00edc\u00ed n\u00e1r\u016fst tlaku na zadn\u00ed stran\u011b v\u00e1lce, tj. mezi bodem K a bodem S\u00a02<\/sub>. Proto\u017ee je v < v\u00a0max<\/sub>\u00a0, nesta\u010d\u00ed kinetick\u00e1 energie k tomu, aby bylo dosa\u017eeno bodu S\u00a02<\/sub>. Proud\u011bn\u00ed m\u00e1 v bod\u011b obratu W rychlost nulovou, proto\u017ee v\u0161ak p\u016fsob\u00ed tlakov\u00e1 s\u00edla od bodu S\u00a02<\/sub>\u00a0sm\u011brem k bodu K, jsou zbrzd\u011bn\u00e9 \u010d\u00e1ste\u010dky tekutiny tla\u010deny proti sm\u011bru proud\u011bn\u00ed vn\u011bj\u0161\u00ed vrstvy. Doch\u00e1z\u00ed ke sto\u010den\u00ed elementu tekutiny v okol\u00ed bodu W, \u010d\u00edm\u017e vznikne v\u00edr. Tak\u00e9 na spodn\u00ed stran\u011b v\u00e1lce se rozv\u00edj\u00ed v\u00edr, ale s opa\u010dn\u00fdm sm\u011brem rotace. Oba v\u00edry se odpout\u00e1vaj\u00ed od v\u00e1lce a jsou nahrazov\u00e1ny nov\u00fdmi. Vznik\u00e1 tzv.\u00a0K\u00e1rm\u00e1nova v\u00edrov\u00e1 cesta<\/strong>.<\/em><\/p>

Zm\u011bny tlaku a rychlosti p\u0159ed a za obt\u00e9kan\u00fdm t\u011blesem lze odhadnout pomoc\u00ed Bernoulliho rovnice.<\/p>

Na z\u00e1klad\u011b t\u011bchto \u00favah lze stanovit odporovou tlakovou s\u00edlu, kter\u00e1 p\u016fsob\u00ed na obt\u00e9kan\u00e9 t\u011bleso.<\/p>

Uvnit\u0159 v\u00edru existuje oblast kolem j\u00e1dra, kde se tekutina ot\u00e1\u010d\u00ed jako pevn\u00e9 t\u011bleso, tj. s konstantn\u00ed \u00fahlovou rychlost\u00ed \u03c9. Obvodov\u00e1 rychlost rotace v = \u03c9xr roste line\u00e1rn\u011b se vzd\u00e1lenost\u00ed r od centra. Krom\u011b toho v\u0161echny \u010d\u00e1ste\u010dky maj\u00ed vlastn\u00ed rotaci. Jestli\u017ee se \u010d\u00e1stice oto\u010d\u00ed jednou kolem j\u00e1dra, sou\u010dasn\u011b se oto\u010d\u00ed i jednou kolem vlastn\u00ed osy. Pro oblast mimo j\u00e1dro (pro r > rk<\/sub>\u00a0) rychlost rotace \u010d\u00e1ste\u010dek se vzr\u016fstaj\u00edc\u00ed vzd\u00e1lenost\u00ed kles\u00e1. Rotace je jen kolem j\u00e1dra a nikoli kolem vlastn\u00ed osy\u2026oblast cirkulace<\/em>\u00a0[11].<\/em><\/p>

Lamin\u00e1rn\u00ed\u00a0<\/strong>proud\u011bn\u00ed p\u0159ech\u00e1z\u00ed v\u00a0turbulentn\u00ed<\/strong>\u00a0p\u0159i p\u0159ekro\u010den\u00ed tzv. kritick\u00e9 hodnoty Reynoldsova \u010d\u00edsla. To z\u00e1vis\u00ed na viskozit\u011b, rychlosti proud\u011bn\u00ed tekutiny a geometrii proud\u011bn\u00ed. P\u0159echod lamin\u00e1rn\u00edho proud\u011bn\u00ed v turbulentn\u00ed z\u00e1vis\u00ed d\u00e1le tak\u00e9\u00a0<\/em>(nap\u0159. v potrub\u00ed)\u00a0na geometrick\u00e9m tvaru pr\u016fto\u010dn\u00fdch \u010d\u00e1st\u00ed, zaoblen\u00ed hran na po\u010d\u00e1te\u010dn\u00edm \u00faseku potrub\u00ed, drsnosti st\u011bn potrub\u00ed, stupni turbulence p\u0159it\u00e9kaj\u00edc\u00edho proudu apod.\u00a0<\/em>P\u0159i proud\u011bn\u00ed re\u00e1ln\u00e9 kapaliny existuje p\u0159echodov\u00e1 oblast, kdy se m\u016f\u017ee podle konkr\u00e9tn\u00edch podm\u00ednek vyskytovat lamin\u00e1rn\u00ed i turbulentn\u00ed proud\u011bn\u00ed.<\/p>

Hagen\u016fv-Poiseuille\u016fv z\u00e1kon<\/em><\/strong>\u00a0\u2013 ur\u010den\u00ed st\u0159edn\u00ed rychlosti proud\u011bn\u00ed kapaliny z objemov\u00e9ho pr\u016ftoku, viz (HOLUBOV\u00c1, R.).<\/p>

Newtonovsk\u00e9 kapaliny<\/em><\/h3>

Viskozita newtonovsk\u00e9 kapaliny z\u00e1vis\u00ed jen na teplot\u011b, je spln\u011bna p\u0159\u00edm\u00e1 \u00fam\u011brnost mezi smykov\u00fdm nap\u011bt\u00edm a gradientem rychlosti (Newton\u016fv z\u00e1kon viskozity) (nap\u0159. voda, ml\u00e9ko, roztok cukru, miner\u00e1ln\u00ed oleje).\u00a0V p\u0159\u00edpad\u011b ide\u00e1ln\u011b visk\u00f3zn\u00edho materi\u00e1lu plat\u00ed pro te\u010dn\u00e9 nap\u011bt\u00ed klasick\u00fd Newtov\u016fv z\u00e1ko<\/em>n, viz vztah (3).<\/p>

Ne-Newtonovsk\u00e9 kapaliny<\/em><\/h3>

\u010c<\/em><\/strong>asov\u011b z\u00e1visl\u00e9<\/strong>:<\/em><\/p>

\u2013\u00a0\u00a0 thixotropn\u00ed (s \u010dasem \u0159idnou, viskozita s \u010dasem kles\u00e1) \u2013 pou\u017e\u00edvaj\u00ed se v chemii, potravin\u00e1\u0159stv\u00ed (jogurt),<\/em><\/p>

\u2013\u00a0\u00a0 rheopetick\u00e9 (s \u010dasem houstnou, viskozita s \u010dasem roste) \u2013 nevyskytuj\u00ed se tak \u010dasto, p\u0159\u00edkladem je s\u00e1dra,<\/em><\/p>

\u010casov\u011b nez\u00e1visl\u00e9<\/strong>\u00a0z\u00e1vis\u00ed na teplot\u011b:<\/em><\/p>

\u2013\u00a0\u00a0 pseudoplastick\u00e9 (\u0159idnouc\u00ed) \u2013 viskozita kles\u00e1 se zvy\u0161uj\u00edc\u00edm se smykov\u00fdm nap\u011bt\u00edm (\u0161amp\u00f3n, koncentr\u00e1ty d\u017eusu, ke\u010dup),<\/p>

\u2013\u00a0\u00a0 dilatantn\u00ed (houstnouc\u00ed) \u2013 viskozita roste se zvy\u0161uj\u00edc\u00edm se te\u010dn\u00fdm nap\u011bt\u00edm (mokr\u00fd p\u00edsek, koncentrovan\u00e9 suspenze \u0161krobu),<\/p>

\u2013\u00a0\u00a0 plastick\u00e9 \u2013 maj\u00ed mez poddajnosti (tvaroh, zubn\u00ed pasta).<\/p>

Metody m\u011b\u0159en\u00ed v reologii<\/h2>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a) absolutn\u00ed m\u011b\u0159en\u00ed \u2013 z\u00a0Poiseuilleova z\u00e1kona<\/a>, m\u011b\u0159\u00edme v\u0161echny ostatn\u00ed veli\u010diny,<\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b) relativn\u00ed m\u011b\u0159en\u00ed \u2013 srovn\u00e1n\u00ed s kapalinou, jej\u00ed\u017e dynamick\u00e1 viskozita je zn\u00e1ma
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u2013 Ostwald\u016fv viskozimetr, H\u00f6ppler\u016fv viskozimetr\u016f;<\/em><\/p>

K m\u011b\u0159en\u00ed viskozity se b\u011b\u017en\u011b pou\u017e\u00edvaj\u00ed pr\u016ftokov\u00e9, p\u00e1dov\u00e9 a rota\u010dn\u00ed viskozimetry, z nich\u017e v\u0161ak pouze posledn\u00ed typ a speci\u00e1ln\u00ed kapil\u00e1rn\u00ed viskozimetry umo\u017e\u0148uj\u00ed dostate\u010dn\u011b charakterizovat tokovou k\u0159ivku nenewtonsk\u00fdch kapalin. Podm\u00ednkou spr\u00e1vn\u00e9ho m\u011b\u0159en\u00ed je v\u017edy lamin\u00e1rnost proud\u011bn\u00ed v cel\u00e9m rozsahu m\u011b\u0159en\u00ed a dob\u0159e definovan\u00e1 geometrie toku (mo\u017enost ur\u010dov\u00e1n\u00ed D a \u03c4 ) v p\u0159\u00edpad\u011b nenewtonsk\u00fdch kapalin.<\/p>

M\u011b\u0159\u00edc\u00ed za\u0159\u00edzen\u00ed vyu\u017e\u00edvan\u00e9 v reologii:<\/h3>

\u2013\u00a0\u00a0\u00a0<\/em>z\u00e1kladn\u00ed p\u0159\u00edstroje,<\/p>

\u2013\u00a0\u00a0 kapil\u00e1rn\u00ed viskozimetry,<\/p>

\u2013\u00a0\u00a0 viskozimetry s padaj\u00edc\u00ed kuli\u010dkou,<\/p>

\u2013\u00a0\u00a0 rota\u010dn\u00ed viskozimetry,<\/p>

\u2013\u00a0\u00a0 rota\u010dn\u00ed reometry,<\/p>

\u2013\u00a0\u00a0 senzory \u2013 geometrie,<\/p>

\u2013\u00a0\u00a0 extenzn\u00ed reometry,<\/p>

\u2013\u00a0\u00a0 vytla\u010dovac\u00ed reometry.<\/p>

Princip<\/em><\/strong><\/td>Za\u0159\u00edzen\u00ed<\/em><\/strong><\/td>M\u011b\u0159en\u00e1 veli\u010dina<\/em><\/strong><\/td><\/tr>
\u00a0<\/td>\u00a0<\/td>\u00a0<\/td><\/tr>
Objemov\u00fd pr\u016ftok<\/td>fordova n\u00e1levka;
kapil\u00e1rn\u00ed viskozimetr<\/td>		\u010das;
\u010das (tlak, dislokace)<\/td><\/tr>
Padaj\u00edc\u00ed kuli\u010dka<\/td>h\u00f6ppler\u016fv viskozimetr<\/td>\u010das<\/td><\/tr>
Komprese<\/td>kompresn\u00ed viskozimetr<\/td>s\u00edla, dislokace<\/td><\/tr>
Rotace<\/td>rota\u010dn\u00ed viskozimetr, reometr<\/td>s\u00edla, dislokace<\/td><\/tr><\/tbody><\/table><\/figure>

Vyu\u017eit\u00ed reologie<\/em><\/h2>

V\u011bdn\u00ed obor naz\u00fdvan\u00fd reologie se zab\u00fdv\u00e1 studiem vnit\u0159n\u00ed reakce l\u00e1tek (pevn\u00fdch i tekut\u00fdch) na p\u016fsoben\u00ed vn\u011bj\u0161\u00edch sil resp. jejich deformovatelnost\u00ed a tokov\u00fdmi vlastnostmi. Souvislost mezi mikrostrukturou a reologick\u00fdmi vlastnostmi zkoum\u00e1 mikroreologie. Pro pot\u0159eby (ne jen) chemick\u00e9ho in\u017een\u00fdrstv\u00ed m\u00e1 v\u00fdznam zejm\u00e9na fenomenologick\u00e1 reologie (makroreologie) kapalin, kter\u00e1 na n\u011b pohl\u00ed\u017e\u00ed jako na kontinuum a formuluje z\u00e1konitosti visk\u00f3zn\u00edho toku .<\/p>

Matematick\u00fdm vyj\u00e1d\u0159en\u00edm tokov\u00fdch vlastnost\u00ed kapalin jsou reologick\u00e9 stavov\u00e9 rovnice, kter\u00e9 zpravidla vyjad\u0159uj\u00ed vztah mezi deforma\u010dn\u00edm smykov\u00fdm (te\u010dn\u00fdm, vazk\u00fdm) nap\u011bt\u00edm \u03c4 a deformac\u00ed kapaliny. Jejich grafickou podobou jsou tokov\u00e9 k\u0159ivky (HOLUBOV\u00c1, R).<\/em><\/p>

Reologick\u00e9 chov\u00e1n\u00ed tekut\u00fdch materi\u00e1l\u016f hraje d\u016fle\u017eitou roli v \u0159ad\u011b technologick\u00fdch operac\u00ed. Znalost z\u00e1kladn\u00edch reologick\u00fdch veli\u010din, viskozity, meze toku a modul\u016f pru\u017enosti je pot\u0159ebn\u00e1 nejen k charakterizov\u00e1n\u00ed surovin, pop\u0159. produkt\u016f, ale i k \u0159e\u0161en\u00ed mnoha technick\u00fdch \u00faloh a in\u017een\u00fdrsk\u00fdch v\u00fdpo\u010dt\u016f p\u0159i navrhov\u00e1n\u00ed, zdokonalov\u00e1n\u00ed a kontrole r\u016fzn\u00fdch v\u00fdrobn\u00edch a dopravn\u00edch za\u0159\u00edzen\u00ed (HOLUBOV\u00c1,\u00a0<\/em>R).\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em><\/p>

P\u0159edev\u0161\u00edm v oblastech technick\u00fdch \u00faloh a in\u017een\u00fdrsk\u00fdch v\u00fdpo\u010dt\u016f p\u0159i navrhov\u00e1n\u00ed a kontrole hraje reologie v\u00fdznamnou roli z hlediska bezpe\u010dnostn\u00edch obor\u016f, proto\u017ee je zde velk\u00fd prostor na chyby a zanedb\u00e1n\u00ed, kter\u00e9 mohou v\u00e9st k velk\u00fdm selh\u00e1n\u00edm a hav\u00e1ri\u00edm v \u0159e\u0161en\u00e9 oblasti.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Tento \u010dl\u00e1nek navazuje na \u010dl\u00e1nky\u00a0o termodynamice\u00a0(\u010dl\u00e1nek 2) a v kr\u00e1tkosti uv\u00e1d\u00ed problematiku reologie, co\u017e je zjednodu\u0161en\u011b nauka o toku materi\u00e1lu. […]<\/p>\n","protected":false},"author":1,"featured_media":1211,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[184],"tags":[95,105,133],"class_list":["post-1210","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fyzika-a-bezpecnost","tag-bezpecnost","tag-fyzika","tag-reologie"],"_links":{"self":[{"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/posts\/1210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/comments?post=1210"}],"version-history":[{"count":17,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/posts\/1210\/revisions"}],"predecessor-version":[{"id":3771,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/posts\/1210\/revisions\/3771"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/media\/1211"}],"wp:attachment":[{"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/media?parent=1210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/categories?post=1210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kint.cz\/es\/wp-json\/wp\/v2\/tags?post=1210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}