I am interested in the theoretical and numerical analysis of interface dynamics in nonequilibrium growth processes. A remarkable example of such a process is the dissolution of porous or fractured rock, such as the limestone dissolution by carbon dioxideenriched water which leads to the formation of spectacular cave and karst features.
The evolving topography of the pore space depends strongly on the fluid flow and mineral dissolution rates. Remarkably, there exists a wide parameter range in which the positive feedback between fluid transport and mineral dissolution leads to the spontaneous formation of pronounced channels, frequently referred to as "wormholes". As dissolution proceeds the growing channels interact, competing for the available flow, and eventually the growth of the shorter ones cease. This leads to selfsimilar patterns of growth, with the flow becoming concentrated in fewer active channels. The understanding of dissolution dynamics is not only basic for a proper description of cave formation processes, but also important in a number of geochemical applications, such as CO2 sequestration and stimulation of petroleum reservoirs.
In recent years, together with Tony Ladd from University of Florida, we have constructed a detailed, threedimensional numerical model of a dissolving fractured rock, capable of simulating relatively large fractures. Additionaly, a number of simpler models were constructed, aimed to capture the fundamental physics of the channelchannel interaction process. In particular, since the pressure field in the rock matrix obeys the Laplace equation, the competition between the channels may be described in terms of a Laplacian growth model and solved using conformal mapping techniques.

 F. Osselin, P. Kondratiuk, A Budek, O. Cybulski, P. Garstecki, P. Szymczak Microfluidic observation of the onset of reactive infiltration instability in an analog fracture, Geophys. Res. Lett., 43, 69076915, 2016 [pdf]
 K. Petrus, P. Szymczak, Influence of layering on the formation and
growth of solution pipes, Front. Phys., 3, 92, 2016 [pdf]
 Y. Cohen, O. Devauchelle, H. F. Seybold, R. S. Yi, P. Szymczak, D. Rothman, Path selection in the growth of rivers, Proc. Natl. Acad. Sci. USA, 112 , 1413214137, 2015 [pdf] [press coverage]
 V. K. Upadhyay, P. Szymczak, A. J. C. Ladd, Initial conditions or emergence; what determines dissolution patterns in rough fractures?, J. Geophys. Res. Solid Earth, 120, 61026121, 2015 [pdf] [movie1] [movie2] [movie3] [movie4] [movie5]
 A. Budek, P. Garstecki, A. Samborski, and P. Szymczak, Thinfinger growth and droplet pinchoff in miscible and immiscible displacements in a periodic network of microfluidic channels, Phys. Fluids., 27, 112109, 2015 [pdf]
 P. Kondratiuk, P. Szymczak, Steadily translating parabolic dissolution fingers, SIAM J. Appl. Math., 75, 21932213, 2015 [pdf]
 P. Kondratiuk, H. Tredak, A.J.C. Ladd, P. Szymczak, Synchronization of dissolution and precipitation
fronts during infiltrationdriven replacement in porous rocks, Geophys. Res. Lett. 44, 22442252, 2015 [pdf]
 M. Pecelerowicz, A. Budek, P. Szymczak, Effective description of the interaction between anisotropic viscous fingers, EPL, 108, 14001, 2014 (Editor's choice) [pdf]
 M. Pecelerowicz, A. Budek, P. Szymczak, Competition between anisotropic
viscous fingers, Eur. Phys. J. Special Topics, 223, 18951906, 2014 [pdf]
 P. Szymczak, A. J. C. Ladd, Reactiveinfiltration instabilities in rocks. Part II: Dissolution of a porous matrix., J. Fluid Mech., 738, 591630, 2014 [pdf]
 P. Szymczak, A. J. C. Ladd, Interacting length scales in the reactiveinfiltration instability, Geophys. Res. Lett., 40, 30363041, 2013 [pdf] [supplementary]
 A. Budek, P. Szymczak, Network models of dissolution of porous media, Phys. Rev. E, 86, 056318, 2012 [pdf]
 P. Szymczak, A. J. C. Ladd, Reactiveinfiltration instabilities in rocks. Fracture dissolution., J. Fluid Mech., 702, 239264, 2012 [pdf]
 P. Szymczak, A. J. C. Ladd, Instabilities in the dissolution of a porous matrix, Geophys. Res. Lett., 38, L07403, 2011 [pdf]
 P. Szymczak, A. J. C. Ladd, The initial stages of cave formation: Beyond the onedimensional paradigm, Earth Planet. Sci. Lett., 301, 424432, 2011 [pdf] [movie] Press Coverage: [Science Editor's Choice] [Science News] [Wired]
 P. Szymczak, A. J. C. Ladd, Wormhole formation in dissolving fractures, J. Geophys. Res., 114, B06203, 2009 [pdf]
 P. Szymczak, A. J. C. Ladd, Comment on: "From pore scale to wellbore scale: Impact of geometry on wormhole growth in carbonate acidization" by C. E. Cohen et al., Chem. Eng. Sci., 64, 3029, 2009 [pdf]
 T. Gubiec, P. Szymczak, Fingered growth in channel geometry: A Loewner equation approach , Phys. Rev. E, 77, 041602, 2008 [pdf]
 P. Szymczak, A. J. C. Ladd, A network model of channel competition in fracture dissolution, Geophys. Res. Lett., 33, L05401, 2006 [pdf]
 P. Szymczak, A. J. C. Ladd, Microscopic simulations of fracture dissolution, Geophys. Res. Lett., 31, L23606, 2004 [pdf]
 P. Szymczak, A. J. C. Ladd, Stochastic boundary conditions to the convectiondiffusion equation including chemical reactions at solid surfaces, Phys. Rev. E, 69, 036704, 2004 [pdf]
 P. Szymczak, A. J. C. Ladd, Boundary conditions for stochastic solutions of the convectiondiffusion equation, Phys. Rev. E, 68, 036704, 2003 [pdf]
