The constitutive equation and flow dynamics of bubbly magmas
The constitutive equation and flow dynamics of bubbly magmas
复制标题
DOI：
10.1029/2002gl015697
复制
发表时间：
2002-12-20
影响因子：
5.2
通讯作者：
Wilson, SDR
中科院分区：
文献类型：
--
作者：
Llewellin, EW;Mader, HM;Wilson, SDR
一个广义的本构方程的气泡液体，成功地再现了预期的粘度响应稳定的流动与不同的毛细管数Ca（气泡变形的措施）和不稳定的流动与不同的动态毛细管数Cd（流动的稳定性的措施）先前在单独的研究。本构方程是根据可观察的材料和流动参数给出的，并且至少在Ca类似于O（1000）和Cd类似于O（10）时是有效的。给出了稳态、简单剪切流（Ca变量）和小总应变振荡流（Cd变量）的解析解。研究了圆形管道中稳定流动的特殊情况--类似于火山管道中的岩浆流动。通过管道的速度分布被发现是抛物线或活塞流取决于一个无量纲数，管道毛细管数Cc。活塞流预测为Ccapproximate到4，这是在火山喷发条件的中间范围。
A generalized constitutive equation for bubbly liquids is presented which successfully reproduces the expected viscosity response for both steady flows with varying capillary number Ca (a measure of the bubble deformation) and unsteady flows with varying dynamic capillary number Cd (a measure of the steadiness of the flow) previously given in separate studies. The constitutive equation is given in terms of observable material and flow parameters and is valid at least up to Casimilar toO(1000) and Cdsimilar toO(10). Analytical solutions are presented for steady, simple-shearing flow (Ca variable) and oscillatory flow with small total-strains (Cd variable). The special case of steady flow in a circular pipe-analogous to magma flow in a volcanic conduit-is investigated. Velocity profiles across the conduit are found to be parabolic or plug-flow depending on a dimensionless number, the conduit capillary number Cc. Plug flow is predicted for Ccapproximate to4 which is in the mid-range for volcanic-eruption conditions.