Paste density critical values

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

The momentum, which is a certain amount of mass moving at a certain velocity (v), takes into account the fluid s density (p) and the diameter of the tube (Df). The momentum of the fluid can be increased by increasing the velocity or the diameter of the tube or both. The resistance to flow is expressed as the absolute or dynamic viscosity of the fluid (rj), which is in units of grams per centimeter-second, or centipoise (cP). The transition from laminar to turbulent-flow occurs as Re increases past a critical value between 2000 and 3000 in a straight tube having a smooth internal surface. 

Fig. 7.5.3. Variation of the Landau free energy density with the order parameter at temperatures above, at, and below the critical temperature and for changes in direction of the magnetic fields. The heavy dots indicate the value of i) for which the Landau free enei density is minimized. The central row represents a discontinuous first order transition as the temperature is dropped past the its critical value. After Goldenfeld loc. cit.

Paste density determines the density of the active masses after formation. There is a lower eritieal value for the paste density, below which the structure of the formed aetive mass disintegrates, and an upper critical value above which the pore system in the formed aetive mass is not capable to transport ions to all parts of the active mass. 

The duration and quality of cure of the fresh mix determine the hydration progress and the volume of hydration products, which may eventually fill up the capillary pores and reduce their permeability. For reduced w c and prolonged cure the pore size distribution diagrams are shifted towards smaller sizes, with decreasing total volume. The saturation of capillary pores plays an important role in the composite durability if the material is exposed to freeze-thaw cycles. Damage is more probable when the critical value of the saturation is attained and the increasing volume of ice cannot be accommodated without additional stresses. The hardened paste density is also important to ensure resistance against all other external attacks. 

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