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In conventional processes, such as evaporation, higher levels of concentration can be reached compared with freeze concentration or membrane techniques. However, the advantage of the freeze concentration technique is based on the quality of the product obtained due to the low temperatures used in the process, which makes it a very suitable technology for the processing of fruit juices. There are two basic methods for concentrating solutions by freezing: suspension and film freeze concentration. Suspension freeze concentration systems (FCS) already have operating equipment in the food industry, while film FCSs, also called layer crystallization, is still at an experimental stage. This review summarizes the most important studies relating to the suspension and film freeze concentration in fruit juices and sugar solutions, illustrating the different possibilities that freeze concentration has in the fruit juices industry; it also presents trends and suggests improvements for the future development of this technology. It is noted that most recent publications refer to the film FCS. The technology used to design, build and maintain layer crystallization equipment is simple and it can be available to any operator in the food industry, layer systems will be used in the future if their results can be improved in terms of ice purity and degree of fluid concentration.

The flow in a completely filled cylinder driven by a rotating endwall has multiple time-dependent stable states when the endwall rotation exceeds a critical value. These states have been observed experimentally and computed numerically elsewhere. In this article, the linear stability of the basic state, which is a non-trivial axisymmetric flow, is analysed at parameter values where the unsteady solutions exist. We show that the basic state undergoes a succession of Hopf bifurcations and the corresponding eigenvalues and eigenvectors of these excited modes describe most of the characteristics of the observed time-dependent states. IntroductionThe flow in a cylinder with a rotating endwall has continued to attract much attention since Vogel (1968) first observed the vortex breakdown of the central core vortex that forms. Recent experiments (Stevens, Lopez & Cantwell 1999) have observed a multiplicity of unsteady states that coexist over a range of the governing parameters. To date, it is not understood well where these oscillatory states originate from, how they are interrelated, nor how they are related to the steady, axisymmetric basic state.The flow in a completely filled cylinder of radius R and height H is driven by the constant rotation of one endwall at angular speed Ω. A schematic of the flow configuration is shown in figure 1. The flow is governed by just two non-dimensional parameters, the aspect ratio Λ = H/R, and the Reynolds number Re = ΩR 2 /ν, where ν is the kinematic viscosity of the incompressible fluid. Since there are just two parameters, only codimension-one or -two bifurcations can be observed. The system has one type of symmetry, invariance to rotations about the cylinder axis, generating the symmetry group SO(2). For low Re, there is a unique branch of solutions that is steady and retains all the symmetries of the system. The only local codimensionone bifurcations that this branch can undergo are saddle-node or Hopf ones. The saddle-node of the basic state has not been observed in this system. With the Hopf bifurcation, the SO(2) can either be preserved or not; both situations have been observed as Re is increased in different ranges of Λ. When SO(2) is preserved, the oscillatory state that results remains axisymmetric, and if SO(2) is broken the result is a rotating wave (Knobloch 1994) where the axisymmetric component of the flow remains steady and a particular azimuthal mode becomes finite and precesses.Experiments (Escudier 1984;Stevens et al. 1999) have shown that for aspect ratios Λ ∼ 2.5, the basic state loses stability to an axisymmetric time-periodic state, and

A numerical study of several time integration methods for solving the threedimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.

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