Shift Strategy for Non-overdamped Quadratic Eigen-problems

ABSTRACT In this paper we study properties of non-overdamped quadratic eigenproblems. For the non-overdamped Eigen-value problems we cannot apply variational characterization in full. One of the subintervals of the interval in which we can apply variational characterization for Eigen-values of a negative type is known. In this paper we expand this subinterval by giving better right boundry of the variational characterization interval. This is achieved by getting bigger lower boundary for δ +. New strategy is seen in fact that we join suitably selected hyperbolic quadratic pencil to non-overdamped quadratic pencil. From the variational characterization of the hyperbolic eigenproblem we get better lower boundary for δ +

On the analysis of the contact angle for impacting droplets using a polynomial fitting approach

ractical considerations on the measurement of the dynamic contact angle and the spreading diameter of impacting droplets are discussed in this paper. The contact angle of a liquid is commonly obtained either by a polynomial or a linear fitting to the droplet profile around the triple phase point. Previous works have focused on quasi-static or sessile droplets, or in cases where inertia does not play a major role on the contact angle dynamics. Here, we study the effect of droplet shape, the order of the fitting polynomial, and the fitting domain, on the measurement of the contact angle on various stages following droplet impact where the contact line is moving. Our results, presented in terms of the optical resolution and the droplet size, show that a quadratic fitting provides the most consistent results for a range of various droplet shapes. As expected, our results show that contact angle values are less sensitive to the fitting conditions for the cases where the droplet can be approximated to a spherical cap. Our experimental conditions include impact events with liquid droplets of different sizes and viscosities on various substrates. In addition, validating past works, our results show that the maximum spreading diameter can be parameterised by the Weber number and the rapidly advancing contact angle

Analysis of impact of droplets on horizontal surfaces

This paper presents the results of an experimental investigation of droplets impacting on horizontal surfaces. The effects of the impact parameters on the droplet impingement are studied. The results are presented for different droplet Weber numbers, ranging from 50 to 1080 and for three liquids: water, isopropanol and glycerin. Four kinds of surfaces were used with characteristic wettability (given in terms of the contact angle): smooth glass, PVC, wax and rough glass. We studied in some detail the kinematics of the moving contact line during the spreading process. Particularly we are interested in the effects of the wettability of the wall by the liquid. The surface wettability has been observed to have a strong influence on the spreading of droplet in the later stages of the process. The results are presented in the form of charts describing the spreading diameter and apex height of droplets in terms of time