Yeaw Chu Lee

Recent advances in computational fluid dynamics relevant to the modelling of pesticide flow on leaf surfaces

Increasing societal and governmental concern about the worldwide use of chemical pesticides is now providing strong drivers towards maximising the efficiency of pesticide utilisation and the development of alternative control techniques. There is growing recognition that the ultimate goal of achieving efficient and sustainable pesticide usage will require greater understanding of the fluid mechanical mechanisms governing the delivery to, and spreading of, pesticide droplets on target surfaces such as leaves. This has led to increasing use of computational fluid dynamics (CFD) as an important component of efficient process design with regard to pesticide delivery to the leaf surface. This perspective highlights recent advances in CFD methods for droplet spreading and film flows, which have the potential to provide accurate, predictive models for pesticide flow on leaf surfaces, and which can take account of each of the key influences of surface topography and chemistry, initial spray deposition conditions, evaporation and multiple droplet spreading interactions. The mathematical framework of these CFD methods is described briefly, and a series of new flow simulation results relevant to pesticide flows over foliage is provided. The potential benefits of employing CFD for practical process design are also discussed briefly.

Evaluation of crystallization kinetics of adipic acid in an oscillatory baffled crystallizer

For solution crystallization, nucleation can be characterized by the maximum sub-cooling (or metastable limit), which is known to vary with numerous process parameters. The relationship between the metastable limit and cooling rate is of particular interest, as it can be utilized to derive nucleation kinetic parameters. However, this relationship is open to interpretation. This work presents the application of three such interpretations (Nývlt, Kubota and a population balance based method) to a cooling crystallization of adipic acid in an oscillatory baffled crystallizer, a relatively new type of crystallizer with increased studies and applications in continuous plug flow operation. It also considers the role the device employed to detect nucleation events plays in the derived kinetic parameters. The result of this study shows that although all three interpretations can reasonably predict the maximum sub-cooling over a tested range of cooling rates, the linear assumptions in the Nývlt and Kubota interpretations give increased deviations from the experimental data, in particular for faster cooling rates. In contrast to the two aforementioned models, the population balance based method maintains a minimal deviation across the whole range of cooling rates used. In addition, although the population balance method does not consider the sensitivity of detection tools in its implementation, while the Kubota method does, the sensitivity of nucleation detection is reflected in the derived nucleation rate constants.

Thin film flow over flexible membranes containing surface texturing: Bio-inspired solutions

Abstract Gravity-driven continuous thin liquid film flow over a flexible membrane containing surface topography is modelled using lubrication theory. The associated coupled non-linear equation set, for the film thickness, pressure and membrane deflection, is solved using a state-of-the-art full approximation storage multi-grid algorithm with automatic mesh refinement and adaptive time-stepping, in order to maximize computational efficiency when fine-scale resolution is required while ensuring accurate mesh-independent solutions at the micro-scale. The robustness of the approach is demonstrated through the solution of a series of problems and comparisons drawn with the same flow on an equivalent completely rigid membrane. It is shown that the former differs considerably from the latter in that the film thickness affects the shape of the flexible membrane, the compliance of which in turn impinges on the profile of the resulting free-surface disturbance.

Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes

The comparative efficiency of time-splitting and multigrid schemes for the solution of lubrication models of three-dimensional (3D), thin film flow is demonstrated via detailed comparisons for benchmark gravity-driven continuous film and droplet spreading problems. Data are presented which show the effect of (1) problem formulation (either as a single fourth-order partial differential equation for the film thickness or two coupled second-order equations for film thickness and pressure) and (2) grid density on the choice of fixed time-step, CPU time per time-step and overall efficiency of each scheme. On the basis of these findings, recommendations are given as to the most efficient combination of problem formulation and numerical scheme for solving 3D thin film free surface flows over practical, engineering surfaces.

Multi-level adaptive solution of anisotropic porous media flow with strong discontinuous jumps in permeability

A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.

Parallel computing as a vehicle for engineering design of complex functional surfaces

Thin liquid film flow over surfaces containing complex multiply connected topography is modelled using lubrication theory. The resulting time dependent nonlinear coupled set of governing equations for film thickness and pressure is solved on different parallel computing platforms using a purpose written portable and scalable parallel multigrid algorithm in order to achieve the fine-scale resolution required to guarantee mesh independent solutions. The robustness of the approach is demonstrated via the solution of three problems: one to establish the convergence characteristics viz. the partitioning and message passing strategies adopted, taking flow over a well-defined trench topography as a benchmark against existing experimental and corresponding numerical predictions; two, flow through a sparsely distributed set of occlusions with computations performed on different parallel architectures; three, free-surface planarisation with respect to flow over complex topography - the first an engineered functional substrate, the second a naturally occurring surface.

Rheological effects on the levelling dynamics of thin fluid films

Purpose – The purpose of this paper is to investigate numerically the effect of rheology on the leveling of thin fluid films on horizontal solid substrates. Design/methodology/approach – A mathematical model based on the lubrication approximation which defines non-Newtonian rheology using a Power-law model is presented. The rheology is described by two parameters: the consistency factor and the flow behavior index. The resulting highly non-linear coupled set of equations is discretized using Finite-Difference and the resulting algebraic system is solved via an efficient Multigrid algorithm. Findings – Importantly, the non-dimensionalization process leads to a pair of Partial Differential Equations which depends on one parameter only, the flow behavior index. The authors show that the consistency factor only affects the time scale of the leveling process, hence stretching or contracting the time line. Results for the leveling of sinusoidal perturbations of the fluid film highlights important differences be...

Predicting Three-Dimensional Inertial Thin Film Flow over Micro-Scale Topography

Alternative lubrication and depth-averaged formulations of the unsteady Navier–Stokes equations are used to explore the problem of gravity-driven inertial thin film flow on substrates containing topography that is either fully submerged or protrudes through the film. The resulting discrete form of the equation sets are solved using a multigrid strategy incorporating automatic adaptive time-stepping, enabling accurate mesh independent solutions to be generated very efficiently. Two benchmark test problems are solved revealing the extent of the free surface disturbance that ensues, together with the effect of inertia on the same.

Adaptive Multigrid Solutions of Thin Film Flows over Topography

The behaviour of thin liquid films whether forced to spread or deposited as a distinct pattern on the surface of a substrate, is of enormous significance to many manufacturing and biological processes. The topic of the present study is the flow of continuous thin liquid films over surfaces containing topographical features. In the electronics sector (displays, printed circuits, micro-devices, sensors etc), for example, the industrial goal is often to minimise free surface deviations from planarity either for aesthetic reasons or to ensure predictable product properties [1].

The efficient and accurate solution of porous media flow problems with strongly discontinuous coefficients

Governing equations featuring strongly discontinuous coefficients arise in many physical and engineering applications. A case in point concerns flow in porous media which in a general sense, is anisotropic and heterogeneous in nature, and the use of simple homogeneous isotropic assumptions is inadequate [1, 2]. Indeed, accurate numerical solutions can only be achieved if the discretisation employed encompasses its surrounding neighbouring cells to take account of the full hydraulic conductivity tensors [3]. The sharp discontinuous characteristics observed in these tensorial coefficients require careful attention.