Modelling and simulation of micro-well formation

Figures & data

Figure 1. Atomic force microscope (AFM) image of a micro-well produced with the ‘sessile drop method’ (note the different scale on the z-axis).

Figure 2. Video sequence of a toluene drop evaporation on polystyrene (∼2.5 s, drop diameter ∼300 μm).

Figure 3. Physical and chemical processes in the evaporating drop.

Figure 4. Nomenclature of the variables.

Figure 5. Pinning effect transporting liquid with the solute into the outer region of the drop.

Figure 6. Calculation of the amount of material that precipitates.

Figure 7. Measured (left) and averaged (right) profile of a micro-well (‘sessile drop method’).

Figure 8. Integral function (left) and function (6) for the zero at 44 μm (right).

Figure 9. Coordinate system used for the simulation.

Figure 10. Height difference (left) and resulting flow rate (right).

Figure 11. Increased concentration in the outer part of the drop (with time as parameter).

Table 1. Physical parameters.

Meaning	Value
Parameters of the drop:
Radius of the drop
Maximum contact angle
Diffusion constant of polystyrene in toluene
Desorption constant
(Concentrations are calculated in volume per cent)	R = 44 μm
ϑ = 0.0675 rad
D solv = 2.7 × 10^– 7 cm^2 s^– 1
D esorp = 0.013 cm s^– 1
Parameter of the solvent:
Density of toluene	ρ = 0.86 g cm^– 3 (from [8])
Parameters of the gas phase:
Saturation concentration for toluene
Diffusion constant	C sat = 0.00016 g cm^– 3
D = 0.0806 cm^2 s^– 1, both values from [8]
Parameter of the substrate:
Density of polystyrene	ρ = 1 g cm^– 3

Figure 12. Measured data (left) and simulated (right) data (parameter C _max).

Figure 13. Variation of the parameters D _esorp (left) and V _flow (right).

Erbil , HY and Avci , Y . 2002 . Simultaneous determination of toluene diffusion coefficient in air from thin tube evaporation and sessile drop evaporation on a solid surface . Langmuir , 18 : 5113 – 5119

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