Experiment based development of a non-isothermal pore network model with secondary capillary invasion

Abstract

Drying of capillary porous media is a process of gradual receding of the liquid phase inside the porous medium and simultaneous invasion of the void space with gas. The phase patterns that evolve during the drying process depend on the capillary number, Bond number as well as the temperature profile along the porous medium. If the drying process is slow and capillarity controlled, invasion of the pore space by the gas phase can be assumed as quasi-steady. The evolving distributions of gas and liquid phase resemble invasion percolation patterns, with penetrating gas branches and numerous disconnected liquid clusters. Understandably, the discrete pore-level events that can lead to such ramified phase distributions cannot be captured by macroscopic continuum models that average the volume elements of the porous medium. Instead, due to the conformity of drying and invasion percolation patterns, pore network models (PNMs) are applied to model capillarity driven drying of porous media. PNMs are discrete mathematical models that originate from hydrology and the oil-recovery related research. In this, the void space of the porous medium is represented by a network of interconnected pores and pore throats. Liquid and gas phase mass transfer equations are expressed in each pore throat and the boundary conditions are given by the state of neighboring pores. Consequently, the number of mass balances to be solved is consistent with the number of pores inside the pore network (PN), usually restricting the computable size of PNs. Current studies cover a wide range of drying processes from drying of inorganic matrices to drying of biological materials, from drying regular 2-dimensional PNs to drying of irregular particle packings, from removal of non-viscous liquid to salt solutions and particle suspensions, i.a.; further application of PN modelling aims at the estimation of parameters to be used in continuous drying models. Common strength of all PNMs is the discrete character which allows study of temporally and spatially discretized pore-level phenomena, such as the simultaneous evaporation and condensation, local structure of liquid films or crystallization. This is useful for the investigation of the relation between pore level events and macroscopic drying behavior. In this thesis, PN simulations of drying are compared with experimentally obtained data from drying of a representative 2D microfluidic network in SiO2 under varying thermal conditions with the aim to identify governing physical pore scale effects. Gravity and viscous effects are disregarded in this thesis. Instead drying with slight local temperature variation and drying with imposed thermal gradients are studied. Based on this investigation, a powerful non-isothermal PNM is developed. This model incorporates i) the phenomena associated with the temperature dependency of pore scale invasion, namely thermally affected capillary invasion and vapor flow as well as ii) the secondary effects induced by wetting liquid films of different morphology. This study clearly evidences that the macroscopic drying behavior is fundamentally dictated by the temperature gradient imposed on the PN and moreover by the secondary capillary invasion as well. In agreement with literature, invasion patterns as in invasion percolation with progressive evaporation of single clusters are observed in drying with negligible local temperature variation; gradients with temperature decreasing from the surface (negative temperature gradient) can stabilize the drying front, evolving between the invading gas phase and the receding liquid phase, whereas temperature increasing from the surface (positive temperature gradient) leads to destabilization of the liquid phase with early breakthrough of a gas branch and initiation of a second invasion front migrating in opposite direction to the evaporation front receding from the open surface of the PN. Special attention is paid on the distinct drying regimes found in the situation of a positive gradient because they are associated with different pore scale invasion processes. More precisely, temperature dependency of surface tension dictates the order of invasion as long as the liquid phase is connected in a main liquid cluster (usually found during the first period of drying). In contrast to this, detailed study of the vapor transfer mechanisms emphasizes that vapor diffusion through the partially saturated region can control the pore level distributions of liquid and gas phase during the period of drying when the liquid phase is disconnected into small clusters. This is also related to the cluster growth induced by partial condensation of vapor. It is shown and discussed in detail in this thesis that this effect not only depends on direction and height of the temperature gradient for a given pore size distribution but that moreover the overall evaporation rate influences the cluster growth mechanism. This indicates that liquid migration during drying of porous media might be controlled by the interplay of thermal gradients and drying rate. In summary, the study of thermally affected drying of the 2-dimensional PN reveals complex pore scale mechanisms, usually also expected in drying of real porous media. This leads to the development of a strong mathematical pore scale model based on experimental findings. It is demonstrated how this model might be applied to understand and develop modern drying processes based on the simulation of thermally affected pore scale mass transfer.