Microstructure of strongly sheared suspensions and its impact on rheology and diffusion
Microstructure of strongly sheared suspensions and its impact on rheology and diffusion
复制标题
DOI：
10.1017/s0022112097006320
复制
发表时间：
1997-10-10
影响因子：
3.7
通讯作者：
Morris, JF
中科院分区：
文献类型：
--
作者：
Brady, JF;Morris, JF
本文分析了布朗运动和硬球型粒子间力对强剪切悬浮液中粒子构型的影响。在极限Pe -->无穷的影响下的流体动力学相互作用单独的，成对分布函数的稀释悬浮液的球具有对称性，产生牛顿本构行为和零自扩散。在此，Pe =（gamma）over dot a（2）/2D是佩克莱数，（gamma）over dot是剪切速率，a是颗粒半径，D是孤立颗粒的扩散率。大Pe时的布朗扩散在接触处产生O（aPe（-1））的薄边界层，其中布朗扩散和平流的作用是平衡的，在接触值为O的边界层内，对分布函数是不对称的（Pe（0.78））;非牛顿效应，作为接触值和O（a（3）Pe（-1））层体积的乘积，随着Pe的增加而消失。然而，如果通过硬球力将粒子保持在最小间隔2 B，其中B > a，则也存在厚度为O（aPe（-1））的边界层，但是对于这种情况，对分布函数的不对称性为O（Pe），沿压缩轴沿着具有过量的颗粒。非对称对分布函数和薄边界层体积的乘积现在是O（1）（依赖于B/a），Pe -->无穷大，从而产生具有法向应力的非牛顿流变学，其标度为点上的η（γ），其中η是流体粘度。对于一般线性流动中没有流体动力学相互作用的稀悬浮液，由对相互作用产生的体积应力与eta（gamma）/点phi（B）（2）（a/B）成比例，其中phi（B）= 4/3 pi B（3）n是热力学体积分数。包括水动力相互作用，水动力法向应力差为O（eta（gamma）除以点phi（2））。O（phi（2））流体动力学对边界层粘度的贡献是剪切增稠。对称性破缺和边界层结构也产生了O（（gamma）over dot a（2）phi）的剪切诱导自扩散率，因为Pe ->无穷大。在较高浓度下，边界层结构是相同的，边界层外的成对分布函数从其稀释值变为浓度依赖函数g（infinity）（r;phi），它必须自洽地确定;函数g（infinity）（r;phi）在这里不确定。高浓度下的适当佩克莱数基于柱e =（gamma）上点a（2）/2D（0）（s）（phi）上的浓度依赖性短时自扩散率（P）。边界层的应力贡献比例为eta（gamma）/dot phi（2）g（infinity）（2;phi）D/D-0（s）（phi），其中g（infinity）（2;phi）是接触时的成对分布函数，并被认为在高浓度下占主导地位。由边界层结构引起的长时间自扩散率预计按（gamma）/a（2）phi g（infinity）（2;phi）的比例缩放。
The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe --> infinity under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe = (gamma) over dot a(2)/2D is the Peclet number with (gamma) over dot the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O(aPe(-1)) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe(0.78)) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O(a(3)Pe(-1)) layer volume, vanish as Pe(-0.22) as Pe --> infinity.If, however, particles are maintained at a minimum separation of 2b, with b > a, by a hard-sphere force there is also a boundary layer of thickness of O(aPe(-1)), but the asymmetry of the pair-distribution function for this situation is O(Pe), with an excess of particles along the compressional axes. The product of the asymmetric pair-distribution function and the thin boundary layer volume is now O(1) (with dependence on b/a) as Pe --> infinity, thus yielding non-Newtonian rheology with normal stresses scaling as eta(gamma) over dot, where eta is the fluid viscosity. For a dilute suspension without hydrodynamic interactions in a general linear flow, the bulk stress resulting from pair interactions is proportional to eta(gamma)over dot phi(b)(2)(a/b), where phi(b) = 4/3 pi b(3)n is the thermodynamic volume fraction. Including hydrodynamic interactions, the hydrodynamic normal stress differences are O(eta(gamma)over dot phi(2)). The O(phi(2)) hydrodynamic contribution to the viscosity due to the boundary layer is shear-thickening The broken symmetry and boundary-layer structure also yield a shear-induced self-diffusivity of O((gamma) over dot a(2) phi) as Pe --> infinity.At higher concentrations the boundary-layer structure is the same, with the pair-distribution function outside the boundary layer changed from its dilute value to a concentration-dependent function g(infinity)(r;phi), which must be determined self-consistently; the function g(infinity)(r;phi) is not determined here. The appropriate Peclet number at high concentration is based on the concentration-dependent short-time self-diffusivity (P) over bar e = (gamma)over dot a(2)/2D(0)(s)(phi). The stress contributions from the boundary layer scale as eta(gamma) over dot phi(2)g(infinity)(2;phi)D/D-0(s)(phi), where g(infinity)(2;phi) is the pair-distribution function at contact, and are argued to be dominant at high concentrations. The long-time self-diffusivity arising from the boundary-layer structure is predicted to scale as (gamma) over dot a(2) phi g(infinity)(2;phi).