Influence of attractive van der Waals interactions on the optimal excitations in thermocapillary-driven spreading

Recent investigations of microfluidic flows have focused on manipulating the motion of very thin liquid films by modulating the surface tension through an applied streamwise temperature gradient. The extent to which the choice of contact line model affects the flow and stability of such thermocapillary-driven films is not completely understood. Regardless of the contact line model used, the linearized disturbance operator corresponding to the evolution of the film height is non-normal, and a generalized non-modal stability analysis is required. Surprisingly, early predictions of frontal instability that stemmed from conventional modal analysis of thermocapillary flow on a flat, infinite precursor film showed excellent agreement with experiment. Within the more rigorous framework provided by a generalized stability analysis, this work investigates the transient dynamics and amplification of optimal disturbances subject to a finite precursor film generated by attractive van der Waals forces. Convergence of the disturbance growth rates and perturbed shapes to the asymptotic solutions obtained by conventional linear stability analysis occurs early in the spreading process. In addition, the level of transient disturbance amplification is minimal. The equations governing thermocapillary-driven spreading exhibit a small degree of non-normality, which explains the source of agreement between modal theory and experiment. The more rigorous generalized stability analysis presented here, however, affords critical insight into the types of disturbances leading to maximum unstable growth and the exact influence of the contact line model used

Influence of boundary slip on the optimal excitations in thermocapillary driven spreading

Thin liquid films driven to spread on homogeneous surfaces by thermocapillarity can undergo frontal breakup and parallel rivulet formation with well-defined wavelength. Previous modal analyses have relieved the well-known divergence in stress that occurs at a moving contact line by matching the front region to a precursor film. Because the linearized disturbance operator is non-normal, a generalized, nonmodal analysis is required to probe film stability at all times. The effect of the contact line model on nonmodal stability has not been previously investigated. This work examines the influence of boundary slip on thermocapillary driven spreading using a transient stability analysis, which recovers the conventional modal results in the long-time limit. In combination with earlier work on thermocapillary driven spreading, this study verifies that the dynamics and stability of this system are rather insensitive to the choice of contact line model and that the leading eigenvalue is physically determinant, thereby assuring results that agree with the eigenspectrum. Modal results for the flat precursor film model are reproduced with appropriate choice of slip coefficient and contact line slope

On a generalized approach to the linear stability of spatially nonuniform thin film flows

The presence of a deformable free surface in thin films driven to spread by body or shear forces gives rise to base states that are spatially nonuniform. This nonuniformity produces linearized disturbance operators that are non-normal and an eigenvalue spectrum that does not necessarily predict stability behavior. The falling film provides a simple example for demonstrating a more generalized, rigorous nonmodal approach to linear stability for free surface flows. Calculations of the pseudospectra and maximum disturbance amplification in this system, however, reveal weak effects of non-normality and transient growth such that the modal growth rate is rapidly recovered. Subdominant modes contribute little energy to the leading eigenvector because the oscillatory behavior is rapidly damped by surface tension. Generalization of these results to numerous other lubrication flows involving surface tension suggests similarly weak non-normality and transient growth

Generalized linear stability of noninertial coating flows over topographical features

The transient evolution of perturbations to steady lubrication flow over a topographically patterned surface is investigated via a nonmodal linear stability analysis of the non-normal disturbance operator. In contrast to the capillary ridges that form near moving contact lines, the stationary capillary ridges near trenches or elevations have only stable eigenvalues. Minimal transient amplification of perturbations occurs, regardless of the magnitude or steepness of the topographical features. The absence of transient amplification and the stability of the ridge are explained on physical grounds. By comparison to unstable ridge formation on smooth, flat, and homogeneous surfaces, the lack of closed, recirculating streamlines beneath the capillary ridge is linked to the linear stability

WHAT ROLE DOES SPECIALIZATION PLAY IN FARM SIZE IN THE U.S. HOG INDUSTRY?

Replaced with revised version of paper 02/09/04.Farm Management,

Milk Marketing Order Winners and Losers

Determining the impacts on consumers of government policies affecting the demand for food products requires a theoretically consistent micro-level demand model. We estimate a system of demands for weekly city-level dairy product purchases by nonlinear three stage least squares to account for joint determination between quantities and prices. We analyze the distributional effects of federal milk marketing orders, and find results that vary substantially across demographic groups. Families with young children suffer, while wealthier childless couples benefit. We also find that households with lower incomes bear a greater regulatory burden due to marketing orders than those with higher income levels.Milk, marketing orders, dairy industry regulation

A Unified Approach to High-Gain Adaptive Controllers

It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales