ABSTRACT
In this paper, we study the cyclicity of some degenerate slow-fast cycles with two canard mechanisms in planar slow-fast systems. One canard mechanism originates from a slow-fast Hopf point and the other from a point of self-intersection where the so-called entry-exit relation can be used. By studying the difference map, we show that the cyclicity of such slow-fast cycles is at most two (the associated slow divergence integral is nonzero or vanishes). As an example, we apply this result to the modified Holling-Tanner model.
ABSTRACT
Acoustic microfluidic chips, fabricated by combining lithium niobate (LiNbO3 ) with polydimethylsiloxane (PDMS), practically find applications in biomedicine. However, high-strength direct bonding of LiNbO3 substrate with PDMS microchannel remains a challenge due to the large mismatching of thermal expansion coefficient at the interface and the lack of bonding theory. This paper elaborately reveals the bonding mechanisms of PDMS and LiNbO3 , demonstrating an irreversible bonding method for PDMS-LiNbO3 heterostructures using oxygen plasma modification. An in-situ monitoring strategy by using resonant devices is proposed for oxygen plasma, including quartz crystal microbalance (QCM) covered with PDMS and surface acoustic wave (SAW) fabricated by LiNbO3 . When oxygen plasma exposure occurs, surfaces are cleaned, oxygen ions are implanted, and hydroxyl groups (-OH) are formed. Upon interfaces bonding, the interface will form niobium-oxygen-silicon covalent bonds to realize an irreversible connection. A champion bonding strength is obtained of 1.1 MPa, and the PDMS-LiNbO3 acoustic microfluidic chip excels in leakage tests, withstanding pressures exceeding 60 psi, outperforming many previously reported devices. This work addresses the gap in PDMS-LiNbO3 bonding theory and advances its practical application in the acoustic microfluidic field.
