论文标题
活跃悬浮液的捕获粒子微流变学
Trapped-particle microrheology of active suspensions
论文作者
论文摘要
在微流变学中，通过嵌入式胶体探针颗粒的自由运动或强制运动推断出局部的流变特性，例如复杂流体的粘弹性。为胶体悬浮液的强制探针微流变而开发的理论机制，这些胶体悬浮液集中于恒定（CF）或恒定速度（CV）探针，而在实验中，探针的力和运动学都不是固定的。更重要的是，由于热力学不确定性关系，CF或CV的限制在有意义的量化探针波动方面引入了困难。众所周知，对于被困在谐波电位井中的布朗粒子，陷阱力和粒子位置的标准偏差的产物为$ d k_bt $ in $ d $ dumensions，其中$ k_bt $是热能。结果，如果不允许力（位置）波动，则位置（力）波动将变得无限。为了允许进行波动的测量，在这项工作中，我们考虑了一个微流变模型，其中嵌入式探针被移动的谐波电势拖动，以使其位置和陷阱力都可以波动。从$ n $硬活动的布朗尼颗粒的动力学的完整Smoluchowski方程开始，我们得出了一个Smoluchowski方程，描述了探针的动力学，因为它通过忽略稀释极限中颗粒之间的流体动力相互作用而与一个浴粒子相互作用。由此，我们确定探针位置的均值和方差（即波动），以对概率分布。然后，我们在弱陷阱和强陷阱的范围内表征系统的行为。通过采取适当的限制，我们表明我们的广义模型可以简化为经过良好研究的CF或CV微流变模型。
In microrheology, the local rheological properties such as viscoelasticity of a complex fluid are inferred from the free or forced motion of embedded colloidal probe particles. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes while in experiments neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It is known that for a Brownian particle trapped in a harmonic potential well, the product of the standard deviations of the trap force and the particle position is $d k_BT$ in $d$ dimensions with $k_BT$ being the thermal energy. As a result, if the force (position) is not allowed to fluctuate, the position (force) fluctuation becomes infinite. To allow the measurement of fluctuations, in this work we consider a microrheology model in which the embedded probe is dragged along by a moving harmonic potential so that both its position and the trap force are allowed to fluctuate. Starting from the full Smoluchowski equation governing the dynamics of $N$ hard active Brownian particles, we derive a pair Smoluchowski equation describing the dynamics of the probe as it interacts with one bath particle by neglecting hydrodynamic interactions among particles in the dilute limit. From this, we determine the mean and the variance (i.e., fluctuation) of the probe position in terms of the pair probability distribution. We then characterize the behavior of the system in the limits of both weak and strong trap. By taking appropriate limits, we show that our generalized model can be reduced to the well-studied CF or CV microrheology models.
