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Easy movement of oxidized Galinstan in microfluidic channels is a promising way for the wide application of the non-toxic liquid metal. In this paper, two different surface modification techniques (physical and chemical) are reported, which dramatically improve the non-wetting characteristics of oxidized Galinstan in the microfluidic channel. In the physical technique, normal paper textures are transferred to the inner wall of polydimethylsiloxane (PDMS) channels and four types of nanoparticles are then coated on the surface of the wall for further improvement of the non-wetting characteristics. Highest advancing angle of 167° and receding angle of 151° are achieved on the paper-textured PDMS with titanium oxide (TiO2) nanoparticles. In the chemical technique, three types of inorganic acids are employed to generate dual-scale structures on the PDMS surface. The inner wall surface treated with sulfuric acid (H2SO4) shows the highest contact angle of 167° and a low hysteresis of ~14° in the dynamic measurement. Creating, transporting, separating and merging of oxidized Galinstan droplets are successfully demonstrated in the fabricated PDMS microfluidic channels. After optimization of these modification techniques, the potential application of tunable capacitors and electronic filters is realized by using liquid metal-based microfluidic devices.

Abstract: A chordal graph is the intersection graph of a family of subtrees of a host tree. In this paper we generalize this. A graph has an -representation if there exists a host tree T of maximum degree at most h, and a family of subtrees of T, all of maximum degree at most s, such that if and only if . For given , and t, there exist infinitely many forbidden induced subgraphs for the class of -graphs. On the other hand, for fixed , every graph is an -graph provided that we take t large enough. Under certain conditions representations of larger graphs can be obtained from those of smaller ones by amalgamation procedures. Other representability and non-representability results are presented as well. [Copyright &y& Elsevier]

The main topic of this paper is the investigation of generalized amalgamation properties for simple theories. That is, we are trying to answer the question of when a simple theory has the property of n-dimensional amalgamation, where two-dimensional amalgamation is the Independence Theorem for simple theories. We develop the notions of strong n-simplicity and n-simplicity for 1≤n≤ω, where both “1-simple” and “strongly 1-simple” are the same as “simple”. For strong n-simplicity, we present examples of simple unstable theories in each subclass and prove a characteristic property of strong n-simplicity in terms of strong n-dividing, a strengthening of the dependence relation called dividing in simple theories. We prove a strong three-dimensional amalgamation property for strongly 2-simple theories, and, under an additional assumption, a strong (n+1)-dimensional amalgamation property for strongly n-simple theories. In the last section of the paper we comment on why strong n-simplicity is called strong. [Copyright &y& Elsevier]