# Advances in Colloid and Interface Science (v.98, #3)

Critical Eotvos numbers for buoyancy-induced oil drop detachment based on shape analysis by Jaideep Chatterjee

*(265-283)*. Critical values of the Eotvos number, which is half the Bond number, above which buoyancy induced drop detachment occurs, are estimated based on force balance equations available in the literature [Colloids Surf. A: Physicochem. Eng. Aspects 178 (2001) 249]. Since there are two significantly different expressions of the capillary retention force responsible for holding oil drops on a solid substrate in an aqueous phase, the critical dimensionless number is estimated with these two distinct equations. The differential equation defining the drop shape, with the constraints of the drop volume and the ‘pinned’ or ‘receding’ contact line, is numerically solved. The equilibrium drop shapes predicted are shown to match the experimentally observed variations in drop shape. From the numerical solution, it is observed that for interfacial tension (IFT) values lower than a certain limit for a given drop size, no numerically estimated drop shape can fulfil the drop volume constraint. Similarly, for the dimensionless number above a critical value, no shape can meet all the constraints. These critical Eotvos numbers are estimated, based on the above numerical approach, for initial contact angles measured in oil varying from 20° to 90°. It is found that the critical Eotvos numbers estimated from the numerical shape analysis are between the critical values estimated from the two force-balance equations. Near 90°, the critical values estimated from the drop shape analysis matches the values from one of the force balance estimates, but merges with the critical values of the dimensionless number, estimated from the other force balance model near 10°. From this analysis, it appears that a combination of the two equations for the capillary retention force is required, with one dominating when the contact angles are high, while the other applies for low values of the contact angle.

**Keywords:**Critical Eotvos number; Critical Bond number; Buoyancy-induced removal; Necking; Roll-up; Drop shape; Oil removal; Oil recovery; Young–Laplace equation;

Chirality, twist and structures of micellar lyotropic cholesteric liquid crystals in comparison to the properties of chiralic thermotropic phases by Hans-Dieter Dörfler

*(285-340)*. Phase chirality in disk-like lyotropic cholesteric phases (Ch

_{D}) was investigated, which was induced by addition of center and axial chiral dopants to achiral lyotropic nematic host phases (N_{D}). In a lyotropic nematic matrix of the disk-like N_{D}phase in the ternary system hexadecyldimethylethyl ammonium bromide (C_{16}Me_{2}EABr)/water/*n*-decanol, a disk-like lyotropic cholesteric phase Ch_{D}was induced by addition of the axial optically active compound R(−)-1,1′-binaphthalene-2,2′-diyl-hydrogen-phosphate (BDP). The helical twisting power (*HTP*) of the BDP is generally lower than the*HTP*value of inducing substances with center chirality as cholesterol, prednisolone and taurocholic acid. At constant composition of the N_{D}phase, the helix lengths were determined in dependence on the BDP and steroid concentration by means of evaluation of the ‘spaghetti-like’ texture using polarizing microscopy. The reciprocal helix lengths are changing linearly with rising BDP concentration. The properties of the Ch_{D}phase (textures, helix lengths, structural parameters of the micelles) induced by the chiral compounds and changed by the composition of host phases can give information to the mechanism of chirality transfer from the molecular level to that of the micellar aggregates and finally, to the liquid crystalline superstructure. Furthermore, the matrix influence of the N_{D}phase on the helix formation was examined at constant BDP and steroid concentration. The structure in the Ch_{D}phase was described in terms of micelle parameters. Finally, the inducing properties of a center chiral optically active compound such as cholesterol, prednisolone and taurocholic acid were compared with those of the axial chiral compound BDP. Last but not least, the situation of the theoretical and structural background for helix formation in liquid crystals, e.g. the explanation of chiralic transfer between micelles is analyzed and discussed. Two main conditions are necessary to build up the helix in the Ch_{D}phase: the formation of H-bridges; and the existence of a specific chiralic interaction energy between neighboring micelles in the cholesteric superstructure.**Keywords:**Disk-like lyotropic cholesteric phase; X-Ray diffraction and scattering; Mechanism of helix formation; Center and axial chirality; Structural parameters;

Analysis of different approaches for evaluation of surface energy of microbial cells by contact angle goniometry by P.K Sharma; K Hanumantha Rao

*(341-463)*. Microbial adhesion on solid substrate is important in various fields of science. Mineral–microbe interactions alter the surface chemistry of the minerals and the adhesion of the bacterial cells to mineral surface is a prerequisite in several biobeneficiation processes. Apart from the surface charge and hydrophobic or hydrophilic character of the bacterial cells, the surface energy is a very important parameter influencing their adhesion on solid surfaces. There were many thermodynamic approaches in the literature to evaluate the cells surface energy. Although contact angle measurements with different liquids with known surface tension forms the basis in the calculation of the value of surface energy of solids, the results are different depending on the approach followed. In the present study, the surface energy of 140 bacterial and seven yeast cell surfaces has been studied following Fowkes, Equation of state, Geometric mean and Lifshitz–van der Waals acid–base (LW–AB) approaches. Two independent issues were addressed separately in our analysis. At first, the surface energy and the different components of the surface energy for microbial cells surface are examined. Secondly, the different approaches are evaluated for their internal consistency, similarities and dissimilarities. The Lifshitz–van der Waals component of surface energy for most of the microbial cells is realised to be approximately 40 mJ/m

^{2}±10%. Equation of state and Geometric mean approaches do not possess any internal consistency and yield different results. The internal consistency of the LW–AB approach could be checked only by varying the apolar liquid and it evaluates coherent surface energy parameters by doing so. The electron-donor surface energy component remains exactly the same with the change of apolar liquid. This parameter could differentiate between the Gram-positive and Gram-negative bacterial cells. Gram-negative bacterial cells having higher electron-donor parameter had lower nitrogen, oxygen and phosphorous content on their cell surfaces. Among the four approaches, LW–AB was found to give the most consistent results. This approach provides more detailed information about the microbial cell surface and the electron–donor parameter differentiates different type of cell surfaces.**Keywords:**Microbial surface energy; Contact angle; Fowkes; Equation of state; LW–AB;

Fundamentals of Interface and Colloid Science, Vol. III, Liquid–Fluid Interfaces by Tharwat Tadros

*(465-466)*.