EXPERIMENTS ON A GRAVITY-FREE DISPERSION OF LARGE SOLID SPHERES IN A NEWTONIAN FLUID UNDER SHEAR
EXPERIMENTS ON A GRAVITY-FREE DISPERSION OF LARGE SOLID SPHERES IN A NEWTONIAN FLUID UNDER SHEAR
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DOI：
10.1098/rspa.1954.0186
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发表时间：
1954-01-01
影响因子：
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通讯作者：
BAGNOLD, RA
中科院分区：
文献类型：
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作者：
BAGNOLD, RA
直径D = 0.13cm的固体球形颗粒分散体在两个同心圆筒之间的环形空间中在不同粘度的牛顿流体（水和甘油-水-醇混合物）中被剪切。颗粒的密度σ与流体的密度ρ相平衡，给出了径向加速度不产生微分力的条件。颗粒的体积浓度C在62 - 13%之间变化。一个实质性的径向分散压力被认为是施加在晶粒之间。这被测量为具有可变形周边的内部固定鼓中的静压的增加。还测量了内桶上的扭矩。分散压力P与颗粒产生的剪切应力λ成正比。线性颗粒浓度λ被定义为颗粒直径/平均自由分散距离的比值，并且与C 0相关，其中C 0是最大可能静态体积浓度。对于λ< 12的所有值（C= 57%左右），作为无量纲群T σD2/λη2和P σD2/λη2的应力T和P都与无量纲剪应变群λ 12 σD2（dU/dy）1 η具有单值经验关系。其中dU/dy是颗粒彼此之间的剪切速率，η是流体粘度。这个关系式给出了dU/dy的大小，即取决于是颗粒惯性还是流体粘度占主导地位。当T为总剪应力时，在粘性情况下，得到了另一个半经验关系F =（1 +λ）（1+½λ）ηdU/dy。在惯性区，T/P比恒定在约0.3，在粘性区，T/P比恒定在约0.75。这些结果适用于一些迄今无法解释的自然现象。
Dispersions of solid spherical grains of diameterD= 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentrationCof the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressurePwas found to be proportional to a shear stressλattributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related toCbywhereC0is the maximum possible static volume concentration. Both the stressesTandP, as dimensionless groupsTσD2/λη2, andPσD2/λη2, were found to bear single-valued empirical relations to a dimensionless shear strain group λ½σD2(dU/dy)lη for all the values of λ< 12(C= 57% approx.) where dU/dyis the rate of shearing of the grains over one another, and η the fluid viscosity. This relation givesandaccording as dU/dyis large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relationF= (1+λ)(1+½λ)ηdU/dywas found for the viscous case, whenTis the whole shear stress. The ratioT/Pwas constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.