Показатель нелинейности

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Показатель нелинейности (индекс течения, показатель поведения жидкости) — степенной показатель в модели Оствальда де-Вилля. Данная модель описывает реологические свойства жидкости степенным уравнением, связывающим компоненты тензора напряжений и тензора скоростей деформаций.

Степенное уравнение имеет вид: $\tau _{i\,j}=2kA^{n-1}e_{i,j}$ , где $\tau _{i},j$ — компоненты девиатора тензора напряжений; $k$ — показатель консистенции; $A$ — второй инвариант тензора скоростей деформаций; $n$ — показатель нелинейности; $e_{i}j$ — компоненты тензора скоростей деформаций.

Показатель нелинейности является безразмерным параметром. Жидкости, движение которых описывается степенным уравнением, в зависимости от значения показателя нелинейности, можно разделить на три группы:

псевдопластические ( $n<1$ ) — эффективная вязкость уменьшается при увеличении скоростей сдвига и стремится к бесконечности при нулевых скоростях;
ньютоновские ( $n=1$ ) — тензор напряжений и тензор скоростей деформаций линейно зависимы;
дилатантные ( $n>1$ ) — эффективная вязкость увеличивается при увеличении скоростей сдвига.

Литература

Пономарева М.А., Филина М.П., Якутенок В.А. Моделирование течений нелинейновязкой жидкости со свободной поверхностью методом граничных элементов. — Известия высших учебных заведений, 2013.

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