## 1. Introduction

[2] The geometry of pores controls intrapore fluid flow behavior that manifests as continuum-scale flow characteristics and hydraulic parameters. Therefore, a fundamental understanding of continuum-scale phenomenon is underpinned by a thorough understanding of pore-level fluid dynamics. Fluid dynamics at the pore scale has largely been studied using the classical capillary tube model, more recently by lattice Boltzmann methods [*Chukwudozie et al*., 2012; *Maier et al*., 1998, 1999; *Pan et al*., 2004; *Rothman*, 1988; *Yoon et al*., 2012], and pore-network models [*Balhoff and Wheeler*, 2009; *Blunt et al*., 2002; *Bryant and Blunt*, 1992; *Joekar-Niasar et al*., 2010].

[3] Capillary tube models assume a packing of spherical grains such that the flow pathways or fluid conduits can be represented by cylindrical tubes or capillaries. To consider or correct for the differences in grain shapes, *Kozeny* [1927], *Blake* [1922], and *Carman* [1938] introduced shape factors that represent capillary tubes with cross sections such as a circle, a square, or a triangle. Similarly, in pore-network models, the effect of grain shapes are represented by cross-sectional shapes such as a star, a square, and a triangle [*Blunt et al*., 2002; *Joekar-Niasar et al*., 2010; *Man and Jing*, 1999; *Valvatne et al*., 2005]. However, both capillary tube models and pore-network models still assume no variation, such as a realistic diverging-converging pore geometry in the direction of flow. Therefore, the complete effects of pore geometries in modifying the flow field are not well understood.

[4] Grains comprising geologic porous media can be very angular to round in shape, which results in flow channels having a diverse range of diverging-converging pore to pore-throat geometries. Few studies have investigated the fluid flow fields in idealized diverging-converging pores, but with simplistic pore geometries; for example, pore walls with sinusoidal curves [*Bolster et al*., 2009; *Bouquain et al*., 2012; *Dykaar and Kitanidis*, 1996; *Kitanidis and Dykaar*, 1997; *Malevich et al*., 2006; *Pozrikidis*, 1987; *Sisavath et al*., 2001], ellipses [*McClure et al*., 2010], a box shape [*Cao and Kitanidis*, 1998; *Ma and Ruth*, 1993, 1994; *Meleshko*, 1996; *Panfilov and Fourar*, 2006], tortuous pores [*Cardenas*, 2008; *Cardenas et al*., 2007; *Chaudhary et al*., 2011; *Fourar et al*., 2004], or periodic porous media [*Brenner and Adler*, 1982]. Moreover, most of the above-mentioned studies use Stokes flow or viscous flow, and only few inspect the flow fields in detail at increasing inertial flow regimes [*Chaudhary et al*., 2011; *Fourar et al*., 2004; *Leneweit and Auerbach*, 1999; *Ma and Ruth*, 1993; *Meleshko*, 1996; *Panfilov and Fourar*, 2006]. All the studies mentioned here notice eddies either during viscous flows or during inertial flow regimes, but none quantify the effect of growth in eddies and their feedback with different diverging-converging pore geometries in modification of the fluid flow field spanning from viscous to inertial flow regimes.

[5] Studying the effects of different diverging-converging pore geometries and eddies therein modifying fluid flow behavior bears important implications for addressing many critical issues including, for example, in natural settings, the flow and fate of nutrients and contaminants as mediated by microbes and biofilms [*Bennett et al*., 2000; *Guglielmini et al*., 2011], and in engineering applications, the pump and treat of aquifer contaminants, enhanced oil recovery operations, and geological storage of CO_{2} [*Balhoff and Wheeler*, 2009]. In this paper, we specifically addressed the following questions: How does the geometry of diverging-converging pores control eddy behavior including its interaction with the bulk flow and effective hydraulic conductivity during viscous flows? How does the feedback between pore geometries and growth behavior of eddies determine Forchheimer flow characteristics?

[6] To address these related questions, we designed 10 diverging-converging pores and compared fluid flow characteristics and hydraulic properties from these pores with that of a pipe, which represents a capillary tube model and is the building-block for a pore-network model. We used a dimensionless hydraulic shape factor *β* to characterize and compare the different pore geometries. Microscale-steady laminar flow fields are obtained through computational fluid dynamics simulations, which represent flows from viscous to inertial regimes. Sensitivity analyses explore the role of different pore geometries (*β*) and related eddies on hydraulic conductivity, failure of Darcy's law, and characteristics of Forchheimer flows. Our analysis is focused on using fluid physics to examine the velocity and vorticity distributions inside pores and the force balance along pore boundaries.