Abstract

Background: Bridging the gap between different phenomena, mechanisms and levels of description, different design methods can converge in a unitary way of formulation. This protocol consolidates the analogy and parallelism in the description of any unit operation of separation, as is the particular case of sedimentation. This holistic framework is compatible and complementary with other methodologies handled at length, and tries to contribute to the integration of some imaginative and useful - but marginal, heuristic or rustic- procedures for the design of settlers and thickeners, within well founded and unified methodology.

Objective: Classical models for hindered sedimentation allow solid flux in the direction of the gravity field to be formulated by analogy to changes obeying a potential, such as molecular transfer in the direction of the gradient and chemical transformation throughout the reaction coordinate. This article justifies the fundamentals of such a suggestive generalized analogy through the definition of the time of the sedimentation unit (TSU), the effective surface area of a sedimentation unit (ASU) and the number of sedimentation units (NSU), as elements of a sizing equation.

Methods: This article also introduces the generalization of the model ab initio: Analogy is a well known and efficient tool, not only in the interpretation of events with academic or coaching purposes, but also in the generalized modelling, prospective, innovation, analysis and synthesis of technological processes. Chemical Engineering protocols for the basic dimensioning of Unit Operations driven by potentials (momentum, heat and mass transfer chemical reaction) are founded in macroscopic balances of mass and energy.

Results: These balances, emphatically called “design equations”, result from the integration of mechanistic differential formulations at the microscopic level of description (“equations of variation”). In its turn, these equations include phenomenological terms that may be formulated in corpuscular terms in the field of Chemical Physics. The design equation correlates requirements in equipment (e.g. any practical forms of size and residence or elapsed time for an efficient interaction) to the objectives of the operation (e.g. variations in mass or energy contents of a confined or fluent system). This formulation allows the identification of different contributions: intrinsic terms (related to mechanistic kinetics of the phenomena) and circumstantial terms (related to conditions and variables of operation).

Conclusion: In fact, this model suggests that temporal or spatial dimensions of the equipment may be assumed to depend irrespectively on two design contributions: the entity of a representative “unit of operation (or process)” - illustrated by a descriptor of this dimension- and the “number of (these) units” needed to achieve the separating or transformative objectives of the operation.

Keywords: Unit operations, separation processes, design, particle technology, sedimentation, unified model.

Graphical Abstract