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On the behavior of mud floe size distribution: model calibration and model behavior

机译：关于泥浆粒度分布的行为：模型校准和模型行为

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In this paper, we study a population balance equation (PBE) where flocs are distributed into classes according to their mass. Each class i contains i primary particles with mass m_p and size L_p. All differently sized flocs can aggregate, binary breakup into two equally sized flocs is used, and the floe's fractal dimension is d_0 = 2, independently of their size. The collision efficiency is kept constant, and the collision frequency derived by Saffman and Turner (J Fluid Mech 1:16-30, 1956) is used. For the breakup rate, the formulation by Winterwerp (J Hydraul Eng Res 36(3):309-326, 1998), which accounts for the porosity of flocs, is used. We show that the mean floc size computed with the PBE varies with the shear rate as the Kolmogorov microscale, as observed both in laboratory and in situ. Moreover, the equilibrium mean floc size varies linearly with a global parameter P which is proportional to the ratio between the rates of aggregation and breakup. The ratio between the parameters of aggregation and breakup can therefore be estimated analytically from the observed equilibrium floc size. The parameter for aggregation can be calibrated from the temporal evolution of the mean floc size. We calibrate the PBE model using mixing jar flocculation experiments, see Mietta et al. (J Colloid Interface Sci 336(1):134-141, 2009a, Ocean Dyn 59:751-763, 2009b) for details. We show that this model can reproduce the experimental data fairly accurately. The collision efficiency α and the ratio between parameters for aggregation and breakup α and E are shown to decrease linearly with increasing absolute value of the ξ-potential, both for mud and kaolinite suspensions. Suspensions at high pH and different dissolved salt type and concentration have been used. We show that the temporal evolution of the floc size distribution computed with this PBE is very similar to that computed with the PBE developed by Verney et al. (Cont Shelf Res, 2010) where classes are distributed following a geometrical series and mass conservation is statistically ensured. The same terms for aggregation and breakup are used in the two PBEs. Moreover, we argue, using both PBEs, that bimodal distributions become monomodal in a closed system with homogeneous sediment, even when a variable shear rate is applied.
机译：在本文中，我们研究了种群平衡方程（PBE），其中絮凝物根据其质量分布在各个类别中。每个类i包含i个质量为m_p和大小为L_p的初级粒子。所有大小不同的絮凝物都可以聚集，将二进制分解成两个大小相等的絮凝物，并且絮凝物的分形维数为d_0 = 2，与它们的大小无关。保持碰撞效率不变，并使用Saffman和Turner（J Fluid Mech 1：16-30，1956）得出的碰撞频率。对于分解率，使用了Winterwerp的配方（J Hydraul Eng Res 36（3）：309-326，1998），其说明了絮凝物的孔隙率。我们显示，用PBE计算的平均絮体尺寸随剪切速率的变化而变化，如在实验室和现场观察到的Kolmogorov微米级。此外，平衡平均絮凝物的大小随整体参数P线性变化，整体参数P与聚集率和分解率之比成比例。因此，可以从观察到的平衡絮状物尺寸分析性地估计聚集和分解参数之间的比率。聚集的参数可以根据平均絮状物尺寸的时间演变来校准。我们使用混合罐絮凝实验来校准PBE模型，请参见Mietta等。 （详细信息请参见J Colloid Interface Sci 336（1）：134-141，2009a，Ocean Dyn 59：751-763，2009b）。我们证明该模型可以相当准确地重现实验数据。对于泥浆和高岭石悬浮液，碰撞效率α以及聚集参数和分解参数α和E的比率均随ξ势绝对值的增加而线性降低。已经使用了在高pH值和不同溶解盐类型和浓度下的悬浮液。我们表明，用该PBE计算的絮凝物大小分布的时间演化与用Verney等人开发的PBE计算的絮凝非常相似。 （Cont Shelf Res，2010），其中按照几何级数分布类，并在统计上确保质量守恒。在两个PBE中使用相同的术语表示聚合和分解。此外，我们认为，使用两种PBE，即使采用可变的剪切速率，双峰分布在具有均质沉积物的封闭系统中也变为单峰。

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