Mass conservation for

The humidity and contaminant transport calculation is based on the previously calculated airflows, applying again the principle of mass conservation for the species under consideration. For each time step, the concentrations are calculated on the basis of the airflows, the source and sink strengths in the zones, and the concentration values at the previous time step. In contrast to the airflow calculation, which is a steady-state calculation at each time step, the contaminant transport calculation is dynamic. Therefore, the accuracy of the concentration results depends on the selected time-step interval. 

Via Eq. (136) the kinematic condition Eq. (131) is fulfilled automatically. Furthermore, a conservative discretization of the transport equation such as achieved with the FVM method guarantees local mass conservation for the two phases separately. With a description based on the volume fraction fimction, the two fluids can be regarded as a single fluid with spatially varying density and viscosity, according to... 

Mass conservation for component i implies that at a certain point in space, the time dependence of c, is related to the divergence of the flux of i. It is easily understood that a finite positive divergence in the flux will lead to depletion, i.e. to a lowering of the concentration. This can be expressed as ... 

We next have to consider the continuity equation, which students first encounter seriously in introductory chemistry and physics as the principle of mass conservation. For any fluid we require that the total mass flow into some element of volume minus the flow out is equal to the accumulation of mass, and we either write these as integral balances (stoichiometry) or as differential balances on a differential element of volume. 

Mass conservation for a trace element in dynamic melting requires... 

For a closed system the laws of mass conservation for various atoms must be met... 

The transport Equations (1) are supplemented by mass conservation equations. Mass conservation for each conservative ion species is expressed by,... 

Let d be the volumetric molar concentration of Mi in Q and C12 the surface molar concentration of M12 on TG. Assuming that both types of ions have the same diffusion coefficient D > 0 and since crystalline is immobile, mass conservation for M% gives... 

A two-step procedure was used for numerical computation of the mixing performance [47]. First, the velocity and pressure fields were derived by solving the Navier-Stokes equations and the equation of mass conservation for an incompressible fluid. In a second step, trajectories of mass less particles were computed by streamline integration of the velocity field. 

Differential equations governing the kinetics of chemical reaction systems may be thought of as arising from statements of mass conservation. For example, consider the well mixed system illustrated in Figure 3.1, containing reactants A and B in a dilute system of constant volume, V. 

In the first description of mass conservation for our system, we consider on arbitrarily chosen volume element (here called a control volume) of fixed position and shape as illustrated in Fig. 2-2. Thus, at each point on its surface, there is a mass flux of fluid pu n through the surface. With n chosen as the outer unit normal to the surface, this mass flux will be negative at points where fluid enters the volume element and positive where it exits. 

Figure 2-3. An arbitrarily chosen material control volume shown at some initial moment 1=0 and at a later time t, after which it has translated and distorted in shape because each point on its surface moves with the local fluid velocity u. Equation (2-6) represents a statement of mass conservation for this material volume.

Thus, as expected, the design, operation, and performance of the EKR system are not easy. Mathematical models are necessary in order to gain a better understanding of the processes that occurs in the EKR and to allow predictions for the field-scale remediation. Generally, it is a good policy to keep the mathematical model as simple as possible while adequately describing the behavior of the main parameters of the system (principle of parsimony). Thus, models with relatively simple transport equations and few equilibrium equations are able to predict the evolution of parameters such as the rate of recovery of the toxic ion, the maximum recovery, the rate of acid addition, and the energy requirements. The equation of mass conservation for a pore water solute species (e.g. an ion) in an EKR system can be expressed as follows ... 

Fig. 7 Examples showing the temporal evolution of contact angle in the course of dewetting, as derived from mass conservation for the system described in Fig. 6 (for the film thicknesses indicated)...

At p = 0, we obtain dmo/dt = 0, which leads to the obvious condition of total mass conservation for a dissolved substance. From the equation for the first moment one obtains dmi/tfe 0 at r —> 00. It means that at r 00, the center of mass of dissolved substance moves with the average flow velocity U. The second moment at r 00 tends to... 

There is a concentration gradient present in the fluid flowing over the length of the reactor at a rate F [m /h]. This requires dealing with the mass conservation for S using differential volume elements, as in Fig. 3.38 and Equ. 3.95 (with no recycling). 

The equation for mass conservation for an incompressible nematic can still be used in the form of divv = 0. 

Equation of Mass Conservation for water flow in the aquifer and tube well ... 

The prepreg fibre bed is typically assumed to be an elastic porous medium with incompressible and inextensible fibres and fully saturated with the resin. The resin is assumed to flow in the pores between the fibres, and the fibre mass in the laminate remains constant during cure. The governing equations of the system must describe the behaviour of the composite constituents the fibre bed and the resin. Firstly, the equilibrium of forces on the representative element is considered. Secondly, the mass conservation for the representative element must be satisfied. For a porous medium saturated with a single phase fluid, the total stress tensor a,) is separated into two parts as (tensile stresses are considered positive) ... 

We here introduce a process of diffusion and reaction in the solid phase similar to that in the fluid phase. By drawing an analogy to the analysis of the fluid phase, we have the following equation of mass conservation for the ath component ... 

To compare the SFM with the conventional TFM, we combine the mass and momentum equations in the SFM for the four structural subelements, yielding the mass conservation for the gas phase. 

The d3mamics of the liquid-vapor interface is determined by mass conservation. For incompressible and nonvolatile fluids the velocity v fiiv of the interface in the normal direction is given by the corresponding component of the flow velocity ... 

Furthermore, mass conservation for fluid flow obeys the continuity equation ... 

Due to the continuum and laminar nature of liquids in microchannels [21], mass conservation for fluid flows obeys the continuity equation ... 

Mass conservation for the mixture of liquid plus vapor is... 

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