本研究以離散元素法(Discrete Element Method, DEM)數值運算模擬陶
瓷粉體在溶液中的分散與沉降行為。此方法將每顆陶瓷粉體視為單獨的
元素，並將陶瓷粉體間在溶液中所受到的不同交互作用力如凡德瓦吸引
力、電雙層排斥力、浮力、重力、摩擦力等納入計算中，利用數值運算
模擬其在有限空間與時間下的膠凝分散行為與沉降微觀結構。陶瓷粉體
在分散與加壓沉降過程中，膠凝穩定狀態與製程參數對陶瓷粉體堆積結
構具有即時與主導性的影響，而此影響皆可由數值運算模擬與分析得到
驗證。具高界達電位(Zeta Potential, ζ)的陶瓷粉體懸浮液，其分散穩定
性較為良好，而具低界達電位懸浮液中的陶瓷粉體則會形成凝團。在加
壓沉降實驗中，具較高界達電位且分散穩定性良好的懸浮液會形成較緻
密堆積結構；當沉降速率加快，形成的粉體堆積缺陷就越多，導致較低
的堆積密度。

The colloidal dispersion and sedimentation behaviors of ceramic powder
suspensions have been assessed by numerical simulation using discrete
element method (DEM). Forces of particle-particle including van der Waal’s
attractive and double-layer repulsive forces, and particle-medium including
buoyancy, gravitation and friction forces are included in the simulation. The
results show that the ceramic powder suspension with a high zeta potential
exhibits a better colloidal dispersion, in relative to agglomeration for the
suspension with a low zeta potential. For colloidal filtration, a higher powder
packing density is resulted for the sediments formed from the suspension with
a higher zeta potential than those with a low zeta potential, consistent with
those observed experimentally.

摘要 II
Abstract III
誌謝 IV
目錄 VI
圖目錄 VIII
第一章 前言 1
1.1離散元素分析法(Discrete Element Method, DEM) 2
1.1.1 DEM模型建立 3
1.2 粒子間交互作用力 6
1.2.1 靜電排斥力 6
1.2.2 凡得瓦吸引力 7
1.3 粒子與流體間交互作用力 7
1.3.1重力 7
1.3.2浮力 7
1.3.3拖曳力 8
1.3.4旋轉阻力 8
1.3.5流體動力升力 8
1.3.6布朗運動 8
1.4 粒子在溶液中之所有作用力 9
第二章 實驗方法 10
2.1 DEM-CFD模型 10
2.2 模擬系統 11
第三章 結果與討論 12
3.1 陶瓷粉末間交互作用能量與作用力 12
3.2 2D模擬結果 13
3.3 3D模擬結果 16
第四章 結論 18
參考文獻 19

[1] P. A. Cundall and O. D. L. Strack, ‘‘A Discrete Numerical Model for Granular Assemblies’’, Geotechnique 29, 47–65, (1979).

[2] Y. Tsuji, T. Tanaka and T. Ishida, ‘‘Lagrangian Numerical Simulation of Plug Flow of Cohesionless Particle in a Horizontal Pipe’’, Powder Technol. 71, 239-250 (1992).

[3] D. J. Shaw, Introduction to Colloid and Surface Chemistry, 4th ed; Butterworth-Heinemann, London (1992).

[4] P. C. Hiemenz, Principles of Colloid and Surface Chemistry, 3rd ed; Marcel Dekker, New York (1997).

[5] R. J. Hunter, Foundations of Colloid Science, Vol. I; p. 182. Clarendon, Oxford, UK (1992).

[6] G. G. Stokes, ‘‘On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids”, Trans. Cambridge Philos. Soc. VIII, 287-319, (1845).

[7] C.W. Hong and P. Greil, ‘‘DEM Simulation of Particle-Packing Dynamics Packing in Colloidal Forming Processes during Colloidal Forming Processes’’; pp. 349–53 in Ceramic Trans., Am. Ceram. Soc., Columbs, OH, USA (1995).

[8] S. Dey, S. Z. Ali and E. Padhi, ‘‘Hydrodynamic Lift on Sediment Particles at Entrainment: Present Status and Its Prospect’’, J. Hydraul. Eng., 146(6), 03120001 (2020).

[9] C.W. Hong, ‘‘New Concept for Simulating Particle Packing in Colloidal Forming Processes”, J. Am. Ceram. Soc. 80, 2517–24, (1997).

[10] C.W. Hong, ‘‘Discrete Element Modeling of Colloidal Packing Dynamics during Centrifugal Casting’’, J. Ceram Soc. 104, 793-795, (1996).

[11] J. Gustafsson, E. Nordenswan, and J. B. Rosenholm, ‘‘Consolidation Behavior in Sedimentation of TiO2 Suspensions in the Presence of Electrolytes”, J. Colloid and Interface Sci. 258, 235–243, (2003).

[12] M. Kosmulski, S. D. Vidal, J. Gustafsson, and J.B. Rosenholm, ‘‘Charge Interactions in Semi-concentrated Titania Suspensions at very High Ionic Strengths ”, J. Colloid and Interface Sci. 157, 245–259, (1999).

[13] M. Kosmulski, J. Gustafsson, and J. B. Rosenholm, ‘‘Correlation between the Zeta Potential and Rheological Properties of Anatase Dispersions”, J. Colloid and Interface Sci. 209, 200–206, (1999).

[14] Z. Peng, E. Doroodchi , G. Evans, ‘‘DEM simulation of aggregation of suspended nanoparticles’’, Powder Technology 204, 91-102, (2010).