Living systems formed and evolved under constraints that govern their interactions with the inorganic world. These interactions are definable using basic physico-chemical principles. Here, we formulate a comprehensive set of ten governing abiotic constraints that define possible quantitative metabolomes. We apply these constraints to a metabolic network of Escherichia coli that represents 90% of its metabolome. We show that the quantitative metabolomes allowed by the abiotic constraints are consistent with metabolomic and isotope-labeling data. We find that: (i) abiotic constraints drive the evolution of high-affinity phosphate transporters; (ii) Charge-, hydrogen- and magnesium-related constraints underlie transcriptional regulatory responses to osmotic stress; and (iii) hydrogen-ion and charge imbalance underlie transcriptional regulatory responses to acid stress. Thus, quantifying the constraints that the inorganic world imposes on living systems provides insights into their key characteristics, helps understand the outcomes of evolutionary adaptation, and should be considered as a fundamental part of theoretical biology and for understanding the constraints on evolution.

The static stability of weightless liquid bridges with a free contact line with respect to axisymmetric and nonaxisymmetric perturbations is studied. Constant-volume and constant-pressure stability regions are constructed in slenderness versus cylindrical volume diagrams for fixed contact angles. Bifurcations along the stability-region boundaries are characterized by the structure of axisymmetric bridge branches and families of equilibria. A wave-number definition is presented based on the pieces-of-sphere states at branch terminal points to classify equilibrium branches and identify branch connections. Compared with liquid bridges pinned at two equal disks, the free contact line breaks the equatorial and reflective symmetries, affecting the lower boundary of the constant-volume stability region where axisymmetric perturbations are critical. Stability is lost at transcritical bifurcations and turning points along this boundary. Our results furnish the maximum-slenderness stability limit for drop deposition on real surfaces when the contact angle approaches the receding contact angle.

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To evaluate solvent performance, mass transfer calculation of gas−liquid phases and good prediction of catalyst activity and polymer product yield, precise experimental solubility data are required in slurry-phase ethene polymerization. The solubility of ethene in n-hexane and n-heptane as commercial solvent of ethene slurry-phase polymerization was measured at pressures from 0.18 to 1.6 MPa and temperatures ranging from 303 to 348 K. A static apparatus is used to measure the experimental data. The experimental data are modeled using Peng−Robinson cubic equation of state (PR CEOS) with vdW mixing rule with two adjustable parameters. The modeling results show the PR CEOS is capable to represent the experimental data well.

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We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of simply connected and doubly connected menisci. Using variational and spectral methods, stability is related to the slope of equilibrium branches in the liquid content versus pressure diagram for the constrained and unconstrained problems. The second-variation spectra are separately determined for the membrane and meniscus, showing that the membrane out-of-plane spectrum and the in-plane spectrum at large elatocapillary numbers are both positive, so that only meniscus perturbations can cause instability. At small elastocapillary numbers, the in-plane spectrum has a negative eigenvalue, inducing wrinkling instabilities in thin membranes. In contrast, the smallest eigenvalue of the meniscus spectrum always changes sign at a pressure turning point where stability exchange occurs in the unconstrained problem. We also examine configurations in which the meniscus and membrane are individually stable, while the elastocapillary system as a whole is not; this emphasizes the connection between stability and the coupling of elastic and capillary forces.

To estimate the amount of dissolved propene gas in various industrial solvents especially in the early time of polymerization in slurry-phase propene polymerization and consequently achieve real polymer productivity, the precise experimental solubility data are needed. The solubility of propene in methylbenzene and heptane was measured at pressures from (0.13 to 1.27) MPa and temperatures ranging from (313 to 359) K. A static apparatus is used to measure the experimental data. The experimental data are modeled using the Peng−Robinson cubic equation of state (PR CEOS) with the van der Waals (vdW) mixing rule with two adjustable parameters. The modeling results show that the PR CEOS is capable to represent the experimental data well.