Unified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration-consolidation equations modified to consider power-law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi-solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.

中文翻译：

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连续固液过滤预测和恒压表达式的统一模型

提出了统一的非线性模型，用于预测连续固液过滤和恒压下的表达。该模型基于 Darcy-Terzaghi 过滤固结方程，修改后考虑了特定滤饼阻力的幂律压力依赖性，并将达西定律转换为线性形式。该模型考虑了过滤得到的可压缩滤饼的非均匀结构，并有以下表达式。对不同的中高压缩滤饼（HK高岭土、CaCO ₃，二氧化硅，活性污泥）基于模型的解析和数值解。结果表明，固-液表达的行为取决于压缩材料的初始结构。过滤形成的初始结构不均匀的滤饼的固结率U与结构初始均匀的半固体物料的固结率U不同。针对结构不均匀的滤饼，分析和比较了确定固结系数的不同方法。