Controlling pattern formation in single hole lifted Hele-Shaw cells*

A Hele-Shaw cell consists of a liquid sandwiched between two parallel plates at a fixed separation distance. When one plate is lifted from the other, a pressure differential is created, forcing ambient air into the liquid. As the liquid recedes, a Saffman-Taylor instability develops at the liquid-air interface. This leads to the evolution of long fingers, leaving a branched liquid pattern behind [1]. Control over the branching pattern can be achieved by strategically introducing asymmetry in one of the plates and controlling air entry points, for example, through the addition of holes [2]. By controlling the path of air in the Hele-Shaw cell, the pattern formed can be controlled.

In this work, we investigate methods of control over pattern formation in single hole lifted Hele-Shaw cells. Addition of an air hole introduces a second liquid-air interface which initiates air fingers from the centre to the outer liquid-air interface. The two air fingers create a ring of liquid at a radial distance between the outer liquid-air interface and the central hole. Control over this ring formation provides the fundamental understanding for repeatable, scalable and tailorable structures. Here, we investigate how the height, width, inner and outer radii of the ring is affected by different hole sizes, separation distances, lift speeds and spread radii.

By understanding the conditions under which these patterns form, we can build up a catalogue of formation environments, providing a strategy for precise control over pattern formation in lifted Hele-Shaw cells. These strategies hold significant potential for biomimicry of multiscale structures, providing the fundamental requirements for more efficient transport networks.

 

References

[1] P. Saffman and F. Sir G. Taylor, The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid, 20, (1958).

[2] T. u. Islam and P. S. Gandhi, Viscous fingering in multiport hele shaw cell for controlled shaping of fluids, Scientific Reports, 7, 9, (2017).