Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit. In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier-Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet-air interface. Laplace stresses and thermal Marangoni stresses are accounted for. The particle concentration is tracked by solving a continuum advection-diffusion equation. Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles. Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microsphere evaporating on respectively glass and polydimethylsiloxane substrates. Measured evaporation times, deposit shape and sizes, and flow fields are in very good agreement with the numerical results. Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump

Thermal and economical optimization for a finned-tube, air-cooled condenser design of a roof-top bus air-conditioning system

The current paper presents a methodology of a design optimization technique that can be useful in assessing the best configuration of a finned-tube condenser, using a thermal and economical optimization approach. The assessment has been carried out on an air-cooled finned-tube condenser of a vapour compression cycle for a roof-top bus air-conditioning system at a specified cooling capacity. The methodology has been conducted by studying the effect of some operational and geometrical design parameters for the condenser on the entire cycle exergy destruction or irreversibility, air-conditioning system coefficient of performance (COP), and total annual cost. The heat exchangers for the bus air-conditioning system are featured by a very compact frontal area due to the stringent space limitations and structure standard for the system installation. Therefore, the current study also takes in its account the effect of the varying design parameters on the condenser frontal area. The irreversibility due to heat transfer across the stream-to-stream temperature-difference and due to frictional pressure-drops is calculated as a function of the design parameters. A cost function is introduced, defined as the sum of two contributions, the investment expense of the condenser material and the system compressor, and the operational expense of air-conditioning system, which is usually driven by an auxiliary engine or coupled with the main bus engine. The optimal trade-off between investment and operating cost is therefore investigated. A numerical example is discussed, in which, a comparison between the commercial condenser design and optimal design configuration has been presented in terms of the system COP and condenser material cost. The results show that a significant improvement can be obtained for the optimal condenser design compared to that of the commercial finned-tube condenser, which is designed based on the conventional values of the design parameters