本文仿照Sommerfeld（2001）提出用來界定稀薄流與濃稠流的參數τp/τc，另外提出一個用來界定使用軟球模式或者硬球模式的參數τr/τc，利用自行建立之軟球模式以及硬球模式，並搭配決定論法，於靜止流場中，加入週期力場以驅動顆粒的碰撞，分別模擬顆粒數為64，顆粒直徑為0.005m、0.0075m以及0.012m的顆粒運動情形，並收集比較兩模式下之平均速度、平均擾動速度以及瞬時擾動速度之PDF分布，當兩模式之結果開始出現變化時，其 值即可做為區分使用軟球模式與硬球模式的參考值。
當τr/τc為0.052時，軟球與硬球模式之結果在整體平均速度或者是取樣空間中的擾動速度值幾乎是沒有差別，而當τr/τc為0.127時，軟球與硬球模式所得出之整體平均速度以及平均擾動速度已經出現些微的差別，當τr/τc為0.455時，整體平均速度及擾動速度的差別增大，而取樣空間中的瞬時擾動速度分布更是出現了明顯的差異。另外也發現當流場接近濃稠流時，硬球模式的模擬結果會出現嚴重的顆粒重疊現象，造成τc值本身的不準確，因此除了以τr/τc做為區分使用硬球或軟球模式的參考值外，也可以加入體積比（void fraction）作為輔助的參考值，則可發現體積比小於0.8時，兩模式間會出現差異，而當體積比接近0.5時，硬球模式已經不適用。

According to Summerfeld（2001）, the dilute flow and dense flow can be estimated by the ratio of particle relaxation time and mean free time between collisions τp/τc, likewise, a ratio of particle recovery time and mean free time between collisions τr/τc is assumed to be an index which might be able to distinguish the suitable numerical method between hard-sphere model and soft-sphere model. Inter-particle collision motion of 64 particles with diameters of 0.005m, 0.0075m and 0.012m in a two phase flow with steady flow field and artificial periodic force field is studied numerically by hard-sphere model and soft-sphere model with deterministic method. By comparing the average velocity, root mean square of fluctuating velocity, and PDF distribution of fluctuating velocity between two models, we can find a proper value of τr/τc as an index of using hard-sphere model or soft-sphere model.
It is found that when τr/τc equals to 0.052, there is almost no difference in average velocity, r.m.s. of fluctuation velocity, and the PDF distribution of fluctuating velocity between two models; as τr/τc equals 0.127, there is a slight difference in the average velocity and r.m.s. of fluctuating velocity; when τr/τc reaches 0.455, the difference in PDF distribution of fluctuation velocity between two models becomes extremely large. It is also shown that, as the flow comes to dense flow, a serious particle overlapping problem came up in the particle motion modeled by hard-sphere model, which may cause the inaccuracy of the value of τc, thus another value such as void fraction might be an auxiliary index of using hard-sphere model or soft-sphere model beside the value of τr/τc. It is found that when void fraction is less than 0.8, the result between two model has a slight difference, and the hard sphere model is not suitable as the value of void fraction reaches 0.5.

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