粉体工学会誌
Online ISSN : 1883-7239
Print ISSN : 0386-6157
粒子間に付着力が働く場合の粉体力学の基礎方程式
長尾 高明
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ジャーナル フリー

23 巻 (1986) 4 号 p. 240-249

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The fundamental equations of the dynamics of granular materials has been considered for adhesive forces due to liquid surface tension which act between grains and for the other kinds of adhesive forces which act between grains. The following conclusions have been deduced:
1) The force distribution around grains is ellipsoidal with the principal values PJ=T+3σJ/(2rΛ), where J (=I, II, III) denotes one of the directions of the principal stress axes, T the adhesive force between grains due to liquid surface tension, (σJ) the principal stress, r the mean radius of grains, and Λ the number of contacts within unit volume. The stressstrain equations are given by substituting this PJ for that in the known equations.
2) The adhesive force between grains T which is due to the liquid surface tension is given as follows:
T0=2πrs (cosφ-√α/2)
α=(C1ρa/2πλρ1)1/2
T=T0 [1-w/(α′γ)], α′=α(cosφ-√α/2)/(cosφ-√α/8)
where w denotes the displacement between the adjacent two grains, which must be small, and s denotes liquid surface tension, C1 the weight ratio of liquid to the total granular mixture, ρa the apparent density, ρ1 the liquid density and λ is equal to r3 Λ.
3) The Mohr failure envelope is given by
I σIII)/(σIIII+2σT)=sinΘ
where σI and σIII denote the maximum and the minimum principal stress (positive in compression), respectively, and σT is given by (2/3)γΛΤ.
4) When an adhesive force the strength of which is ft per unit area acts between grains in a tangential direction, the condition of slip is given by the following expression:
[1/2∑JK(PJ-PK)2cos2ηJcos2ηK]1/2>2πrftbm(∑JPJcos2ηJ)1/m
where J or K (=I, II, III) denotes the principal stress direction, and ηJ denotes the angle between the J-direction and the normal at the point where the force acts on the grain surface.

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