Line tension

The presence of the transition zone between a drop or a bubble and thin liquid interlayers can be described in terms of line tension, x, a concept first introduced by Gibbs (see for example [22]). In the case of surface tension, the transition zone between the liquid and vapor is replaced by a plane of tension with excess surface energy, y. By analogy, the transition zone between a drop or a bubble and the thin liquid interlayer may be replaced by a three-phase contact line with an excess linear energy, x. In contrast to surface tension defined always as positive, the value of the line tension may be positive and negative. When positive, it contracts the wetting perimeter, whereas the perimeter expands if the line tension is negative [33-36]. [Pg.130]

If we now introduce a new real equilibrium contact angle that takes into account the line tension as 0 and use the previous definition of the contact angle, which is referred to now as 6 according to Equation 2.47, then Equation 2.190 can be rewritten as [Pg.131]

Note that the derivative in the preceding equation is usually neglected without any justification. Neglecting the derivative of the line tension in Equation 2.191 results in [Pg.131]

If the line tension is negative, then the influence of line tension results in a bigger contact angle as compared with predictions according to Equation 2.192. In the general case. Equation 2.191 can be rewritten as [Pg.131]

For water and aqueous electrolyte solutions, the line tension values are in the range of lO -Kh dyn [23] and below. Thus, the terms on the right-hand side of Equation 2.193 become noticeable at Tq 10 cm. [Pg.132]

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle [Pg.112]

Donahue and Bartell verified Eq. IV-16 for several organic alcohol-water systems. [Pg.113]

For very large lenses, a limiting thickness is reached. Langmuir [59] gave the equation [Pg.113]

The expressions for the energies above were given per unit length of dislocation. When not normalized for a unit length, this energy is proportional to the length of the dislocation [Pg.220]

As a consequence, a dislocation will tend to decrease its length to a minimum to decrease its energy. A curved dislocation line has a tension, T, which acts along its line and may be expressed as a change in energy with the length [Pg.220]

The units of line tension in Eq. (3.45) are in energy-per-unit length. [Pg.220]

ro was replaced by 5b, assumed to represent the core of the dislocation. The line tension, T, is acting tangentially to shorten the dislocation line and, thus, to reduce the dislocation energy. The curving of the dislocation line segment, due to its normal force, rbl, as a result of the applied shear stress, is shown in Fig. 3.45. For force equilibrium in the y direction, since it is balanced by the line tension, it is possible to write [Pg.220]

The coefficient 2 arises from the fact that the fine tension acts at points A and B of the dislocation line segment. For small angles, sin (0/2) — 0/2. Substituting for T from Eq. (3.46), t can be expressed as [Pg.221]

Very small sessile drops have a shape that depends on the line tension along the circular contact line if large enough it induces a dewetting transition detaching the drop from the surface [84]. [Pg.30]

The free energy of a monolayer domain in the coexistence region of a phase transition can be described as a balance between the dipolar electrostatic energy and the line tension between the two phases. Following the development of McConnell [168], a monolayer having n circular noninteracting domains of radius R has a free energy... [Pg.136]

Several groups have studied the structure of chiral phases illustrated in Fig. IV-15 [167,168]. These shapes can be understood in terms of an anisotropic line tension arising from the molecular symmetry. The addition of small amounts of cholesterol reduces X and produces thinner domains. Several studies have sought an understanding of the influence of cholesterol on lipid domain shapes [168,196]. [Pg.139]

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. [Pg.359]

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... [Pg.363]

Suppose that the line tension for a given three-phase line is 1 x 10 dyn. Calculate ff for drops of radius 0.1, 0.01, and 0.001 cm if the value for a large drop is 56. Assume water at 20°C. [Pg.381]

D. Platikanov and M. Nedyalkov, Contact Angles and Line Tension at Microscopic Three Phase Contacts, in Microscopic Aspects of Adhesion and Lubrication, J. M. Georges, ed., Elsevier, Amsterdam, 1982. [Pg.386]

Remarkable chiral patterns, such as those in Figs. IV-15 and XV-8, are found in mixtures of cholesterol and 5-dipalmitoyl PC (DPPC) on compression to the plateau region (as in Fig. XV-6). As discussed in Section IV-4F, this behavior has been modeled in terms of an anisotropic line tension arising from molecular symmetry [46-49]. [Pg.545]

When a dislocation segment of length L is pinned at the ends under the influence of an applied shear stress t, a balance between the line tension and the applied stress produces a radius of curvature R given by [37]... [Pg.232]

W. Koeh, S. Dietrieh, M. Napiorkowski. Moiphology and line tension of liquid films adsorbed on ehemieally struetured substrates. Phys Rev E 57 3300-3317, 1995. [Pg.75]

We now regard the step as a flexible linear object with a line tension 7. Its deformation h x) at a position. x costs an energy... [Pg.872]

Linien-spanntmg, /. (Elec.) line tension, line voltage, -spektnun, n. line spectrum, -vcr-sohiebung, /. displacement of lines, -zahl, /. number of lines, -zug, m. line, trace (in a graph). [Pg.279]

Excellent agreement between experiment and onr calculations is obtained when considering the low temperature deformation in the hard orientation. Not only are the Peierls stresses almost exactly as large as the experimental critical resolved shear stresses at low temperatures, but the limiting role of the screw character can also be explained. Furthermore the transition from (111) to (110) slip at higher temperatures can be understood when combining the present results with a simple line tension model. [Pg.354]

Toi calculate the design factor for multipart string-ups,. Figures 4-fiS and 4-69 can be tisbd to determine the value of W. W is the-fast line tension and equals the fast line factor - times the hook-load weight indicator. readinjg.- As an example, see. below , ..,. ... [Pg.585]

FAST LINE TENSION = FAST LINE FACTOR X LOAD... [Pg.586]

Each process parameter directly affects both the machinery dynamics and the vibration profiles. For example, the line tension, strip width, and hardness of the incoming strip radically affect the vibration profile generated by a continuous process line in a steel mill. With few exceptions, process variations such as these must be considered in the vibration analysis. [Pg.714]

The line can only behave in this way by being flexible. It has an energy per unit length (line tension). This energy per unit length has two parts ... [Pg.89]

Fig. 2 Top Freely jointed chain (FJC) model, where N bonds of length a are connected to form a flexihle chain with a certain end-to-end distance R. Bottom in the simplified model, appropriate for more advanced theoretical calculations, a continuous line is governed hy some bending rigidity or line tension. This continuous model can be used when the relevant length scales are much larger than the monomer size...

LB. Ivanov, A.S. Dimitrov, A.D. Nikolov, N.D. Denkov, and P.A. Kralchevsky Contact Angle Film and Line Tension of Foam Films. II. Film and Line Tension Measurements. J. Colloid Interface Sci. 151, 446 (1992). [Pg.103]

Figure 4 The free energy of pore formation in a DPPC bilayer. The dashed line is a quadratic function, while the dotted line is a fit to a model of pore expansion with a line tension of 40 pN, and is close to linear (Adapted from ref. 78 courtesy of O. Edholm).

Tolpekina, T.V., den Otter, W.K., Briels, W.J. Simulations of stable pores in membranes system size dependence and line tension. J. Chem. Phys. 2004, 121, 8014-20. [Pg.20]

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