Simultaneous spreading and evaporation: Recent developments

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1–2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.     

Logical Kronecker delta deconstruction of the absolute value function and the treatment of absolute deviations

A logical Kronecker delta reformulation of the absolute value function and the related discrete problem of the optimal absolute deviation are studied as the basic step towards applications of first order norms in theoretical chemistry. Absolute value function derivatives appear in the present context related to unit step function, Dirac delta function and its derivatives. The absolute value of the difference of two Minkowski normalized Gaussian functions is analyzed as an example. The proposed logical Kronecker delta deconstruction manner to express the absolute value function is also applied to the absolute deviation from the median of a set of numerical values, which looks to be just the optimal first order norm.     

Multifunctional microgel magnetic/optical traps for SERS ultradetection

We report on the fabrication of a SERS substrate comprising magnetic and silver particles encapsulated within a poly(N-isopropylacrylamide) (pNIPAM) thermoresponsive microgel. This colloidal substrate has the ability to adsorb analytes from solution while it is expanded (low temperature) and reversibly generate hot spots upon collapse (high temperature or drying). Additionally, the magnetic functionality permits concentration of the composite particles into small spatial regions, which can be exploited to decrease the amount of material per analysis while improving its SERS detection limit. Proof of concept for the sequestration of uncommon molecular systems is demonstrated through the first SERS analysis of pentachlorophenol (PCP), a chlorinated ubiquitous environmental pollutant.     

NMR methods for unravelling the spectra of complex mixtures

The main methods for the simplification of the NMR of complex mixtures by selective attenuation/suppression of the signals of certain components are presented. The application of relaxation, diffusion and PSR filters and other techniques to biological samples, pharmaceuticals, foods, living organisms and natural products are illustrated with examples.     

Translocation versus cyclisation in radicals derived from N-3-alkenyl trichloroacetamides

Under radical reaction conditions, two different and competitive reaction pathways were observed for N-(α-methylbenzyl)trichloroacetamides with a N-3-cyclohexenyl substituent: 1,4-hydrogen translocation and radical addition to a double bond. However, for radicals with an acyclic alkenyl side chain, the direct cyclisation process was exclusively observed. The dichotomy between translocation and direct radical cyclisation in these substrates has been theoretically studied using density functional theory (DFT) methods at the B3LYP/6-31G** computational level.     

Distributive Lattices with a Generalized Implication: Topological Duality

In this paper we introduce the notion of generalized implication for lattices, as a binary function ⇒ that maps every pair of elements of a lattice to an ideal. We prove that a bounded lattice A is distributive if and only if there exists a generalized implication ⇒ defined in A satisfying certain conditions, and we study the class of bounded distributive lattices A endowed with a generalized implication as a common abstraction of the notions of annihilator (Mandelker, Duke Math J 37:377–386, 1970), Quasi-modal algebras (Celani, Math Bohem 126:721–736, 2001), and weakly Heyting algebras (Celani and Jansana, Math Log Q 51:219–246, 2005). We introduce the suitable notions of morphisms in order to obtain a category, as well as the corresponding notion of congruence. We develop a Priestley style topological duality for the bounded distributive lattices with a generalized implication. This duality generalizes the duality given in Celani and Jansana (Math Log Q 51:219–246, 2005) for weakly Heyting algebras and the duality given in Celani (Math Bohem 126:721–736, 2001) for Quasi-modal algebras.     

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.     

Theoretical Development of a Novel Equation for Dynamic Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

In oil recovery from fractured reservoirs, dynamic spontaneous imbibition (DSI) plays an important role. Conventional equations used for characterizing dynamic spontaneous imbibition neglect the effects of the driving forces acting across the wetting and non-wetting phases which are flowing in opposite directions. Such effects, defined as interfacial coupling effects (ICE), are known to cause a decrease in the calculated flow rate in drainage processes. Moreover, none of the numerical models have considered a variable inlet saturation (S*) for DSI. A new theoretical model has been developed using generalized transport equations to describe dynamic spontaneous imbibition for immiscible two-phase flow processes. The inclusion of interfacial coupling effects provides a more accurate way to describe dynamic spontaneous imbibition. Furthermore, the addition of variable inlet saturation allows one to establish whether the inlet-face saturation (S*) increases from the initial saturation to 1−Sro, or whether it can remain constant and equal to one minus the residual saturation to the non-wetting phase (1−Sro).     

Ueber eine allgemeinere Theorie der Adsorption von Lösungen

Ohne Zusammenfassung