论文标题
稀释聚合物溶液中球的稀释悬浮液的稳态延伸流变学
Steady state extensional rheology of a dilute suspension of spheres in a dilute polymer solution
论文作者
论文摘要
我们研究了稀聚合物溶液中球形颗粒的稀释悬浮液的稳态延展性流变学。对于无颗粒的聚合物流体，除了溶剂粘度之外，由于聚合物所引起的延伸粘度，$μ^\ text {poly} $，还有助于总非限制扩展粘度$ 1+μ^\ text {poly} $。当将小体积分数（$ ϕ $）添加到聚合物流体中时，爱因斯坦粘度为2.5 $ ϕ $和两个其他应力贡献会改变应力：相互作用应力和粒子诱导的聚合物应力（PIPS）。在较低的Deborah数字（延长率和聚合物放松时间的产物），$ de \ lysSIM0.5 $和大$ de $的负数下，净相互作用应力为阳性。相对于不受干扰的流，单轴延伸流中的球体存在会产生越来越小的局部拉伸区域。在线圈拉伸过渡的下方（$ de <0.5 $）下方，远离颗粒的聚合物处于盘绕状态，并且在粒子周围的大拉伸区域拉伸时，呈拉伸聚合物的唤醒形成。这会导致正相互压力（表面）和PIP（拉伸唤醒）。除了线圈拉伸过渡之外，聚合物远离粒子的聚合物是高度伸展的，但是它们在到达粒子表面附近的低伸缩区域时靠近盘绕状态。因此，阴性ppip来自倒塌聚合物区域。当$ de \ gtrsim0.6 $时，相互作用压力和pips的扩展粘度的变化分别为$ ϕμ^\ text {poly} $和大约-1.85 $ ϕμ^\ text {poly} $。在大$ de $上，聚合物的扩展粘度，$μ^\ text {poly} $，很大。因此，添加粒子会降低悬架的延伸粘度（$（2.5-0.85μ^\ text {poly}）ϕ <0 $）。
We investigate the steady-state extensional rheology of a dilute suspension of spherical particles in a dilute polymer solution. For a particle-free polymeric fluid, in addition to the solvent viscosity, the extensional viscosity due to the polymers, $μ^\text{poly}$, contributes to the total non-dimensionalized extensional viscosity $1+μ^\text{poly}$. When a small volume fraction, $ϕ$, of spheres is added to a polymeric fluid, the stress is altered by the Einstein viscosity of 2.5$ϕ$ and two additional stress contributions: the interaction stresslet and the particle-induced polymer stress (PIPS). The net interaction stress is positive at lower Deborah numbers (product of extension rate and polymer relaxation time), $De\lesssim0.5$, and negative at large $De$. Relative to undisturbed flow, the presence of spheres in uniaxial extensional flow creates larger and smaller local stretching regions. Below the coil-stretch transition ($De<0.5$), the polymers far from the particles are in a coiled state, and a wake of stretched polymers forms downstream of the particle as they are stretched by the large stretching regions around the particle. This leads to a positive interaction stresslet (surface) and the PIPS (stretched wake). Beyond the coil-stretch transition, polymers far from the particle are highly stretched, but they collapse closer to the coiled state as they arrive at the low-stretching regions near the particle surface. Therefore, a negative PIPS results from the regions of collapsed polymers. When $De\gtrsim0.6$, the changes in extensional viscosity from the interaction stresslet and the PIPS are $ϕμ^\text{poly}$ and approximately -1.85$ϕμ^\text{poly}$, respectively. At large $De$, the polymer extensional viscosity, $μ^\text{poly}$, is large. Therefore, adding particles reduces the extensional viscosity of the suspension ($(2.5-0.85μ^\text{poly})ϕ<0$).
