Numerical Simulation of Protein Stamping Process Driven by Capillary Force
Authors: Lin Shih-Chang , Tseng Fangang , Chieng Ching-Chang 
Published: June 2008

“Microstamping” is one of patterning techniques [1] developed to deliver thousands of samples in parallel onto a surface for use in biosensors and medical diagnostics and the inexpensive production of micropatterned arrays of active proteins is of interest. Successful print of these protein island arrays includes conformal contact between an inked patterned stamp and the surface of a substrate and the full control over the amount and distribution of protein solution transferred from the impregnated stamps. In most common design, stamper is made of a solid material and proper inking method is required. Martin et al [2] have created a microstamper constructed by forming the hydrogel in sequence within the narrow ends of machine-pulled capillary tubes. This paper studies the protein-filling (inking)/stamping/printing process by numerical computations for a proposed Array-Stamper Chip with embedded microchannels. (Fig. 1) The array chip consists of thousands of microchannels with their own stampers to deliver thousands of fixed size/shape liquid samples to a bottom chip by capillary force simultaneously. The transfer process and physics are analyzed by solving first principle equations, i.e. conservation laws of mass, momentum. Due to the symmetry design of the array chip, the analysis is performed for a representative stamp only (Fig. 1b). Stable and robust numerical approaches as volume-of-Fluid (VOF) method [3] for two phase homogenous flow model and the interface tracking technique in cooperation with Continuum Surface tension Force (CSF) Model [4] are employed to determine the shape of liquid/gas interface as well as the fluid flowing pattern. Figure 2 shows the entire protein transfer during stamping/printing process, the Stamper Chip is moved toward/touch/away bio reaction chip starting at a distance of 50 μm away. The process consists of (a) The liquid fluid forms a meniscus and tends to reach out at the tip of the microchannel from the Stamping Chip (Fig. 2a), (b) The droplet meniscus is formed and the Stamper Chip starts to be moved toward the bottom chip (Fig. 2b), (c) The Stamper Chip is touched down and then is pulled up from the Bio-Reaction Chip, the liquid flows horizontally via the horizontal microchannels (Fig. 2c) and reaches the bottom chip, (d) part of the liquid is pushed upward and formed a small waist (Fig. 2d), (e) The Stamper Chip is moved further upwards with liquid slug of narrower waist (Fig. 2e), and (f) Stamper Chip is back to the original position with part of liquid broken at some point and left on the Bio-reaction Chip successfully. The controlling of the spot size left on bio-chip can be manipulated by physical properties of the filling protein, the inner/outer diameter of the microchannel, moving speed of the Stamper Chip, and the hydrophilic nature of the outer edge surface of the stamper. Two sets of physical properties are employed for computations (1) protein of low concentration with physical properties as water (2) 2mg/ml BSA concentration according to Fig. 3. Degree of hydrophilic nature with different liquid/gas/solid contact angle on stamper edge surface AB and the stamping speed do play significant role on the printing spot formation and size as shown in Table 1. Figure 4 shows that the size of printing size decreases with outer diameter of the microchannel. The detailed flowing process illustrate that the formations of the printing spot are resulted from forces interactions between the capillary flow formation process and stamper moving speed. In summary, numerical simulations not only give the suggestions for the array-stamper design with precise control of printing spot but also provide the physics and detailed information of the spot formation.